DSP System Toolbox User`s Guide

DSP System Toolbox User`s Guide
‫معرفی چند منبع در زمینه آموزش برنامه نویسی ‪ MATLAB‬یا متلب‬
‫کتاب های به زبان انگلیسی‬
‫عنوان‪Matlab, Third Edition: A Practical Introduction to :‬‬
‫‪Programming and Problem Solving‬‬
‫ترجمه عنوان‪ :‬متلب‪ :‬مقدمه ای عملی بر برنامه نويسی و حل مساله‪ ،‬چاپ سوم‬
‫مولفین‪Stormy Attaway :‬‬
‫سال چاپ‪2013 :‬‬
‫انتشارات‪Butterworth-Heinemann :‬‬
‫کتاب های به زبان فارسی‬
‫عنوان‪ :‬اصول و مبانی متلب برای علوم مهندسی‬
‫مولفین‪ :‬برايان هان‪ ،‬دانیل تی‪ ،‬والنتین‬
‫مترجمین‪ :‬رامین موالنا پور‪ ،‬سارا موالناپور‪ ،‬نینا اسدی پور‬
‫انتشارات‪ :‬سها دانش‬
‫لینک دسترسی‪ :‬لینک‬
‫لینک دسترسی‪ :‬لینک‬
‫عنوان‪MATLAB For Dummies :‬‬
‫ترجمه عنوان‪ :‬تلب به زبان ساده‬
‫مولفین‪Jim Sizemore, John Paul Mueller :‬‬
‫سال چاپ‪2014 :‬‬
‫انتشارات‪For Dummies :‬‬
‫عنوان‪ :‬کاربرد ‪ MATLAB‬در علوم مهندسی‬
‫مولفین‪ :‬حیدرعلی شايانفر‪ ،‬حسین شايقی‬
‫انتشارات‪ :‬ياوريان‬
‫لینک دسترسی‪ :‬لینک‬
‫لینک دسترسی‪ :‬لینک‬
‫عنوان‪Essential MATLAB for Engineers and Scientists :‬‬
‫عنوان‪ :‬برنامه نويسی ‪ MATLAB‬برای مهندسان‬
‫ترجمه عنوان‪ :‬آنچه بايد مهندسین و دانشمندان از متلب بدانند‬
‫مولفین‪ :‬محمود کشاورز مهر‪ ،‬بهزاد عبدی‬
‫مولفین‪Brian Hahn, Daniel Valentine:‬‬
‫سال چاپ‪2013 :‬‬
‫انتشارات‪Academic Press :‬‬
‫انتشارات‪ :‬نوپردازان‬
‫لینک دسترسی‪ :‬لینک‬
‫لینک دسترسی‪ :‬لینک‬
‫عنوان‪MATLAB: An Introduction with Applications :‬‬
‫عنوان‪ :‬آموزش کاربردی مباحث پیشرفته با ‪MATLAB‬‬
‫ترجمه عنوان‪ :‬مقدمه ای بر متلب و کاربردهای آن‬
‫مولفین‪ :‬نیما جمشیدی‪ ،‬علی ابويی مهريزی‪ ،‬رسول مواليی‬
‫مولف‪Amos Gilat :‬‬
‫انتشارات‪ :‬عابد‬
‫سال چاپ‪2014 :‬‬
‫انتشارات‪Wiley :‬‬
‫لینک دسترسی‪ :‬لینک‬
‫لینک دسترسی‪ :‬لینک‬
‫عنوان‪MATLAB For Beginners: A Gentle Approach:‬‬
‫عنوان‪ :‬کاملترين مرجع آموزشی و کاربردی ‪MATLAB‬‬
‫ترجمه عنوان‪ :‬متلب برای افراد مبتدی با يک رويکرد تدريجی‬
‫مولفین‪ :‬علی اکبر علمداری‪ ،‬نسرين علمداری‬
‫مولف‪Peter I. Kattan:‬‬
‫انتشارات‪ :‬نگارنده دانش‬
‫سال چاپ‪2008 :‬‬
‫انتشارات‪CreateSpace Independent Publishing Platform :‬‬
‫لینک دسترسی‪ :‬لینک‬
‫لینک دسترسی‪ :‬لینک‬
‫عنوان‪MATLAB for Engineers :‬‬
‫عنوان‪ :‬برنامه نويسی ‪ MATLAB‬برای مهندسین‬
‫ترجمه عنوان‪ :‬متلب برای مهندسین‬
‫مولف‪ :‬استفن چاپمن‬
‫مولف‪Holly Moore :‬‬
‫سال چاپ‪2011 :‬‬
‫انتشارات‪Prentice Hall :‬‬
‫لینک دسترسی‪ :‬لینک‬
‫عنوان‪Mastering MATLAB :‬‬
‫ترجمه عنوان‪ :‬تسلط بر متلب‬
‫مولفین‪Duane C. Hanselman, Bruce L. Littlefield :‬‬
‫سال چاپ‪2011 :‬‬
‫انتشارات‪Prentice Hall :‬‬
‫لینک دسترسی‪ :‬لینک‬
‫مترجم‪ :‬سعدان زکائی‬
‫انتشارات‪ :‬دانشگاه صنعتی خواجه نصیرالدين طوسی‬
‫لینک دسترسی‪ :‬لینک‬
‫عنوان‪ :‬آموزش گام به گام محاسبات عددی با متلب‬
‫مولف‪ :‬کلیو مولر‬
‫مترجم‪ :‬رسول نصیری‬
‫انتشارات‪ :‬نشر گستر‬
‫لینک دسترسی‪ :‬لینک‬
‫منابع آموزشی آنالین‬
‫عنوان‪ :‬مجموعه فرادرسهای برنامهنويسی متلب‬
‫مدرس‪ :‬دکتر سید مصطفی کالمی هريس‬
‫مدت زمان‪ ۹ :‬ساعت و ‪ ۳‬دقیقه‬
‫زبان‪ :‬فارسی‬
‫ارائه دهنده‪ :‬فرادرس‬
‫لینک دسترسی‪ :‬لینک‬
‫عنوان‪ :‬مجموعه فرادرسهای متلب برای علوم و مهندسی‬
‫مدرس‪ :‬دکتر سید مصطفی کالمی هريس‬
‫مدت زمان‪ 14 :‬ساعت و ‪ 2۲‬دقیقه‬
‫زبان‪ :‬فارسی‬
‫ارائه دهنده‪ :‬فرادرس‬
‫لینک دسترسی‪ :‬لینک‬
‫عنوان‪ :‬مجموعه فرادرسهای برنامه نويسی متلب پیشرفته‬
‫مدرس‪ :‬دکتر سید مصطفی کالمی هريس‬
‫مدت زمان‪ ۲ :‬ساعت و ‪ 12‬دقیقه‬
‫زبان‪ :‬فارسی‬
‫ارائه دهنده‪ :‬فرادرس‬
‫لینک دسترسی‪ :‬لینک‬
‫عنوان‪Introduction to Programming with MATLAB :‬‬
‫ترجمه عنوان‪ :‬آشنايی با برنامهنويسی متلب‬
‫مدرسین‪Akos Ledeczi, Michael Fitzpatrick, Robert Tairas :‬‬
‫زبان‪ :‬انگلیسی‬
‫ارائه دهنده‪Vanderbilt University :‬‬
‫لینک دسترسی‪ :‬لینک‬
‫عنوان‪Introduction to MATLAB :‬‬
‫ترجمه عنوان‪ :‬مقدمهای بر متلب‬
‫مدرس‪Danilo Šćepanović :‬‬
‫زبان‪ :‬انگلیسی‬
‫ارائه دهنده‪MIT OCW :‬‬
‫لینک دسترسی‪ :‬لینک‬
‫عنوان‪Up and Running with MATLAB :‬‬
‫ترجمه عنوان‪ :‬شروع سريع کار با متلب‬
‫مدرس‪Patrick Royal :‬‬
‫زبان‪ :‬انگلیسی‬
‫ارائه دهنده‪lynda.com :‬‬
‫لینک دسترسی‪ :‬لینک‬
‫عنوان‪Modelling and Simulation using MATLAB :‬‬
‫ترجمه عنوان‪ :‬مدلسازی و شبیهسازی با استفاده از متلب‬
‫مدرسین‪ Prof. Dr.-Ing. Georg Fries :‬و دیگران‬
‫زبان‪ :‬انگلیسی‬
‫ارائه دهنده‪iversity.org :‬‬
‫لینک دسترسی‪ :‬لینک‬
DSP System Toolbox™
User's Guide
R2014b
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How to Contact MathWorks
Latest news:
www.mathworks.com
Sales and services:
www.mathworks.com/sales_and_services
User community:
www.mathworks.com/matlabcentral
Technical support:
www.mathworks.com/support/contact_us
Phone:
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The MathWorks, Inc.
3 Apple Hill Drive
Natick, MA 01760-2098
DSP System Toolbox™ User's Guide
© COPYRIGHT 2011–2014 by The MathWorks, Inc.
The software described in this document is furnished under a license agreement. The software may be used
or copied only under the terms of the license agreement. No part of this manual may be photocopied or
reproduced in any form without prior written consent from The MathWorks, Inc.
FEDERAL ACQUISITION: This provision applies to all acquisitions of the Program and Documentation
by, for, or through the federal government of the United States. By accepting delivery of the Program
or Documentation, the government hereby agrees that this software or documentation qualifies as
commercial computer software or commercial computer software documentation as such terms are used
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government agrees to return the Program and Documentation, unused, to The MathWorks, Inc.
Trademarks
MATLAB and Simulink are registered trademarks of The MathWorks, Inc. See
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Patents
MathWorks products are protected by one or more U.S. patents. Please see
www.mathworks.com/patents for more information.
Revision History
April 2011
September 2011
March 2012
September 2012
March 2013
September 2013
March 2014
October 2014
First printing
Online only
Online only
Online only
Online only
Online only
Online only
Online only
Revised for Version 8.0 (R2011a)
Revised for Version 8.1 (R2011b)
Revised for Version 8.2 (R2012a)
Revised for Version 8.3 (R2012b)
Revised for Version 8.4 (R2013a)
Revised for Version 8.5 (R2013b)
Revised for Version 8.6 (R2014a)
Revised for Version 8.7 (R2014b)
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Contents
DSP Tutorials
1
Introduction to Streaming Signal Processing in MATLAB . .
1-2
Filter Frames of a Noisy Sine Wave Signal in MATLAB . . .
1-10
Filter Frames of a Noisy Sine Wave Signal in Simulink . . .
Source . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Lowpass Filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Spectrum Analyzer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1-12
1-13
1-15
1-15
Lowpass Filter Design in MATLAB . . . . . . . . . . . . . . . . . . . .
1-18
Lowpass IIR Filter Design in Simulink . . . . . . . . . . . . . . . .
Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Butterworth Filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Chebyshev Type I Filter . . . . . . . . . . . . . . . . . . . . . . . . . . .
Chebyshev Type II Filter . . . . . . . . . . . . . . . . . . . . . . . . . .
Elliptic Filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Minimum-Order Designs . . . . . . . . . . . . . . . . . . . . . . . . . . .
1-27
1-27
1-28
1-30
1-32
1-34
1-36
Create Moving Average System object . . . . . . . . . . . . . . . . .
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Create the Class Definition . . . . . . . . . . . . . . . . . . . . . . . . .
Moving Average Filter Properties . . . . . . . . . . . . . . . . . . . .
Moving Average Filter Constructor . . . . . . . . . . . . . . . . . . .
Moving Average Filter Setup . . . . . . . . . . . . . . . . . . . . . . .
Moving Average Filter Step . . . . . . . . . . . . . . . . . . . . . . . .
Moving Average Filter Reset . . . . . . . . . . . . . . . . . . . . . . . .
Input Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Object Saving and Loading . . . . . . . . . . . . . . . . . . . . . . . . .
System object Usage in MATLAB . . . . . . . . . . . . . . . . . . . .
Simulink Customization Methods . . . . . . . . . . . . . . . . . . . .
System object Usage in Simulink . . . . . . . . . . . . . . . . . . . .
1-40
1-40
1-41
1-41
1-42
1-43
1-43
1-44
1-44
1-44
1-45
1-46
1-46
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iii
iv
Contents
Tunable Lowpass Filtering of Audio Input in Simulink . . .
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1-48
1-49
1-50
Desktop Real-time Audio Acceleration with MATLAB
Coder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Notch Filtering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
C Code Generation Speedup . . . . . . . . . . . . . . . . . . . . . . . .
1-53
1-53
1-53
1-54
Fixed-Point Filter Design in MATLAB . . . . . . . . . . . . . . . . .
1-56
Sample Rate Conversion of Audio Signal in MATLAB and
Simulink . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Design and Analysis of Sample Rate Converter . . . . . . . . . .
Using the Sample Rate Converter in MATLAB . . . . . . . . . .
Using the Sample Rate Converter in Simulink . . . . . . . . . .
Specifying Tolerance to Reduce Filter Order . . . . . . . . . . . .
1-65
1-65
1-65
1-67
1-69
1-72
Visualizing Multiple Signals Using Logic Analyzer . . . . . . .
Model Programmable FIR Filter . . . . . . . . . . . . . . . . . . . . .
Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Use the Logic Analyzer . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Modify the Display . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1-74
1-74
1-75
1-76
1-78
Signal Visualization and Measurements in MATLAB . . . . .
1-88
Filter Frames of a Noisy Sine Wave Signal using Testbench
Generator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1-103
Create Composite System object . . . . . . . . . . . . . . . . . . . . .
Create MultiNotchFilter . . . . . . . . . . . . . . . . . . . . . . . . . .
Contain System Objects as Private Properties . . . . . . . . . .
Work with Dependent Properties . . . . . . . . . . . . . . . . . . .
Use the Multi-Notch Filter - Initialization . . . . . . . . . . . . .
Use the Multi-Notch Filter - Streaming . . . . . . . . . . . . . . .
1-110
1-110
1-110
1-111
1-112
1-112
Measure Audio Latency in MATLAB and Simulink . . . . . .
1-115
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2
Input, Output, and Display
Discrete-Time Signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Time and Frequency Terminology . . . . . . . . . . . . . . . . . . . . .
Recommended Settings for Discrete-Time Simulations . . . . .
Other Settings for Discrete-Time Simulations . . . . . . . . . . . .
2-2
2-2
2-3
2-6
Continuous-Time Signals . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Continuous-Time Source Blocks . . . . . . . . . . . . . . . . . . . . .
Continuous-Time Nonsource Blocks . . . . . . . . . . . . . . . . . .
2-11
2-11
2-11
Create Sample-Based Signals . . . . . . . . . . . . . . . . . . . . . . . . .
Create Signals Using Constant Block . . . . . . . . . . . . . . . . .
Create Signals Using Signal from Workspace Block . . . . . .
2-12
2-12
2-14
Sample-Based Row Vector Processing Changes . . . . . . . . .
2-17
Create Frame-Based Signals . . . . . . . . . . . . . . . . . . . . . . . . .
Create Signals Using Sine Wave Block . . . . . . . . . . . . . . . .
Create Signals Using Signal from Workspace Block . . . . . .
2-19
2-19
2-22
Create Multichannel Sample-Based Signals . . . . . . . . . . . . .
Multichannel Sample-Based Signals . . . . . . . . . . . . . . . . . .
Create Multichannel Signals by Combining Single-Channel
Signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Create Multichannel Signals by Combining Multichannel
Signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-26
2-26
Create Multichannel Frame-Based Signals . . . . . . . . . . . . .
Multichannel Frame-Based Signals . . . . . . . . . . . . . . . . . . .
Create Multichannel Signals Using Concatenate Block . . . .
2-32
2-32
2-32
Deconstruct Multichannel Sample-Based Signals . . . . . . . .
Split Multichannel Signals into Individual Signals . . . . . . .
Split Multichannel Signals into Several Multichannel
Signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2-36
2-36
Deconstruct Multichannel Frame-Based Signals . . . . . . . . .
Split Multichannel Signals into Individual Signals . . . . . . .
Reorder Channels in Multichannel Frame-Based Signals . .
2-43
2-43
2-47
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2-26
2-29
2-39
v
3
vi
Contents
Import and Export Sample-Based Signals . . . . . . . . . . . . . .
Import Sample-Based Vector Signals . . . . . . . . . . . . . . . . .
Import Sample-Based Matrix Signals . . . . . . . . . . . . . . . . .
Export Sample-Based Signals . . . . . . . . . . . . . . . . . . . . . . .
2-52
2-52
2-55
2-59
Import and Export Frame-Based Signals . . . . . . . . . . . . . . .
Import Frame-Based Signals . . . . . . . . . . . . . . . . . . . . . . . .
Export Frame-Based Signals . . . . . . . . . . . . . . . . . . . . . . . .
2-64
2-64
2-67
Musical Instrument Digital Interface . . . . . . . . . . . . . . . . . .
About MIDI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
MIDI Control Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Using MIDI Control Surfaces with MATLAB and Simulink .
2-72
2-72
2-72
2-73
Display Time-Domain Data . . . . . . . . . . . . . . . . . . . . . . . . . . .
Configure the Time Scope Properties . . . . . . . . . . . . . . . . .
Use the Simulation Controls . . . . . . . . . . . . . . . . . . . . . . . .
Modify the Time Scope Display . . . . . . . . . . . . . . . . . . . . . .
Inspect Your Data (Scaling the Axes and Zooming) . . . . . . .
Manage Multiple Time Scopes . . . . . . . . . . . . . . . . . . . . . . .
2-77
2-78
2-83
2-84
2-86
2-89
Display Frequency-Domain Data in Spectrum Analyzer . .
2-93
Visualize Central Limit Theorem in Array Plot . . . . . . . . .
Display a Uniform Distribution . . . . . . . . . . . . . . . . . . . . .
Display the Sum of Many Uniform Distributions . . . . . . . .
Inspect Your Data by Zooming . . . . . . . . . . . . . . . . . . . . .
2-100
2-100
2-101
2-103
Data and Signal Management
Sample- and Frame-Based Concepts . . . . . . . . . . . . . . . . . . . .
Sample- and Frame-Based Signals . . . . . . . . . . . . . . . . . . . .
Model Sample- and Frame-Based Signals in MATLAB and
Simulink . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
What Is Sample-Based Processing? . . . . . . . . . . . . . . . . . . . .
What Is Frame-Based Processing? . . . . . . . . . . . . . . . . . . . .
3-2
3-2
Inspect Sample and Frame Rates in Simulink . . . . . . . . . . . .
Sample Rate and Frame Rate Concepts . . . . . . . . . . . . . . . .
3-8
3-8
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3-3
3-4
3-4
Inspect
Inspect
Inspect
Inspect
4
Sample-Based Signals Using Probe Block . . . . . . . . .
Frame-Based Signals Using Probe Block . . . . . . . . .
Sample-Based Signals Using Color Coding . . . . . . .
Frame-Based Signals Using Color Coding . . . . . . . .
3-9
3-11
3-13
3-15
Convert Sample and Frame Rates in Simulink . . . . . . . . . .
Rate Conversion Blocks . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Rate Conversion by Frame-Rate Adjustment . . . . . . . . . . . .
Rate Conversion by Frame-Size Adjustment . . . . . . . . . . . .
Avoid Unintended Rate Conversion . . . . . . . . . . . . . . . . . . .
Frame Rebuffering Blocks . . . . . . . . . . . . . . . . . . . . . . . . . .
Buffer Signals by Preserving the Sample Period . . . . . . . . .
Buffer Signals by Altering the Sample Period . . . . . . . . . . .
3-19
3-19
3-20
3-24
3-28
3-34
3-36
3-39
Buffering and Frame-Based Processing . . . . . . . . . . . . . . . .
Frame Status . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Buffer Sample-Based Signals into Frame-Based Signals . . .
Buffer Sample-Based Signals into Frame-Based Signals with
Overlap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Buffer Frame-Based Signals into Other Frame-Based
Signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Buffer Delay and Initial Conditions . . . . . . . . . . . . . . . . . .
Unbuffer Frame-Based Signals into Sample-Based Signals .
3-43
3-43
3-43
Delay and Latency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Computational Delay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Algorithmic Delay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Zero Algorithmic Delay . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Basic Algorithmic Delay . . . . . . . . . . . . . . . . . . . . . . . . . . .
Excess Algorithmic Delay (Tasking Latency) . . . . . . . . . . . .
Predict Tasking Latency . . . . . . . . . . . . . . . . . . . . . . . . . . .
3-59
3-59
3-60
3-61
3-64
3-67
3-69
3-46
3-51
3-54
3-54
Filter Analysis, Design, and Implementation
Design a Filter in Fdesign — Process Overview . . . . . . . . . .
Process Flow Diagram and Filter Design Methodology . . . . .
4-2
4-2
Design a Filter in the Filterbuilder GUI . . . . . . . . . . . . . . . .
The Graphical Interface to Fdesign . . . . . . . . . . . . . . . . . . .
4-10
4-10
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vii
viii
Contents
Use FDATool with DSP System Toolbox Software . . . . . . . .
Design Advanced Filters in FDATool . . . . . . . . . . . . . . . . .
Access the Quantization Features of FDATool . . . . . . . . . . .
Quantize Filters in FDATool . . . . . . . . . . . . . . . . . . . . . . . .
Analyze Filters with a Noise-Based Method . . . . . . . . . . . .
Scale Second-Order Section Filters . . . . . . . . . . . . . . . . . . .
Reorder the Sections of Second-Order Section Filters . . . . .
View SOS Filter Sections . . . . . . . . . . . . . . . . . . . . . . . . . .
Import and Export Quantized Filters . . . . . . . . . . . . . . . . .
Generate MATLAB Code . . . . . . . . . . . . . . . . . . . . . . . . . . .
Import XILINX Coefficient (.COE) Files . . . . . . . . . . . . . . .
Transform Filters Using FDATool . . . . . . . . . . . . . . . . . . . .
Design Multirate Filters in FDATool . . . . . . . . . . . . . . . . . .
Realize Filters as Simulink Subsystem Blocks . . . . . . . . . . .
4-14
4-14
4-18
4-20
4-28
4-33
4-37
4-42
4-47
4-52
4-53
4-53
4-62
4-74
Digital Frequency Transformations . . . . . . . . . . . . . . . . . . .
Details and Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . .
Frequency Transformations for Real Filters . . . . . . . . . . . .
Frequency Transformations for Complex Filters . . . . . . . . .
4-77
4-77
4-85
4-99
Digital Filter Design Block . . . . . . . . . . . . . . . . . . . . . . . . . .
Overview of the Digital Filter Design Block . . . . . . . . . . . .
Select a Filter Design Block . . . . . . . . . . . . . . . . . . . . . . .
Create a Lowpass Filter in Simulink . . . . . . . . . . . . . . . . .
Create a Highpass Filter in Simulink . . . . . . . . . . . . . . . .
Filter High-Frequency Noise in Simulink . . . . . . . . . . . . .
4-111
4-111
4-112
4-113
4-114
4-116
Filter Realization Wizard . . . . . . . . . . . . . . . . . . . . . . . . . . .
Overview of the Filter Realization Wizard . . . . . . . . . . . . .
Design and Implement a Fixed-Point Filter in Simulink . .
Set the Filter Structure and Number of Filter Sections . . .
Optimize the Filter Structure . . . . . . . . . . . . . . . . . . . . . .
4-121
4-121
4-121
4-130
4-131
Digital Filter Implementations . . . . . . . . . . . . . . . . . . . . . .
Using Digital Filter Blocks . . . . . . . . . . . . . . . . . . . . . . . .
Implement a Lowpass Filter in Simulink . . . . . . . . . . . . .
Implement a Highpass Filter in Simulink . . . . . . . . . . . . .
Filter High-Frequency Noise in Simulink . . . . . . . . . . . . .
Specify Static Filters . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Specify Time-Varying Filters . . . . . . . . . . . . . . . . . . . . . . .
Specify the SOS Matrix (Biquadratic Filter Coefficients) . .
4-133
4-133
4-133
4-134
4-135
4-140
4-140
4-141
Analog Filter Design Block . . . . . . . . . . . . . . . . . . . . . . . . . .
4-143
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Removing High-Frequency Noise from an ECG Signal . . .
4-145
Adaptive Filters
5
Overview of Adaptive Filters and Applications . . . . . . . . . . .
Introduction to Adaptive Filtering . . . . . . . . . . . . . . . . . . . . .
Adaptive Filtering Methodology . . . . . . . . . . . . . . . . . . . . . .
Choosing an Adaptive Filter . . . . . . . . . . . . . . . . . . . . . . . . .
System Identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Inverse System Identification . . . . . . . . . . . . . . . . . . . . . . . .
Noise or Interference Cancellation . . . . . . . . . . . . . . . . . . . .
Prediction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5-2
5-2
5-2
5-4
5-5
5-6
5-7
5-7
Adaptive Filters in DSP System Toolbox Software . . . . . . . .
Overview of Adaptive Filtering in DSP System Toolbox
Software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Using Adaptive Filter Objects . . . . . . . . . . . . . . . . . . . . . . .
5-9
5-9
5-9
5-12
LMS Adaptive Filters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
LMS Methods for adaptfilt Objects . . . . . . . . . . . . . . . . . . .
System Identification Using adaptfilt.lms . . . . . . . . . . . . . .
System Identification Using adaptfilt.nlms . . . . . . . . . . . . .
Noise Cancellation Using adaptfilt.sd . . . . . . . . . . . . . . . . .
Noise Cancellation Using adaptfilt.se . . . . . . . . . . . . . . . . .
Noise Cancellation Using adaptfilt.ss . . . . . . . . . . . . . . . . .
5-13
5-13
5-15
5-18
5-20
5-23
5-27
RLS Adaptive Filters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Compare RLS and LMS Adaptive Filter Algorithms . . . . . .
Inverse System Identification Using adaptfilt.rls . . . . . . . . .
5-32
5-32
5-33
Signal Enhancement Using LMS and Normalized LMS . . .
Create the Signals for Adaptation . . . . . . . . . . . . . . . . . . . .
Construct Two Adaptive Filters . . . . . . . . . . . . . . . . . . . . . .
Choose the Step Size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Set the Adapting Filter Step Size . . . . . . . . . . . . . . . . . . . .
Filter with the Adaptive Filters . . . . . . . . . . . . . . . . . . . . .
Compute the Optimal Solution . . . . . . . . . . . . . . . . . . . . . .
Plot the Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5-37
5-37
5-38
5-38
5-39
5-40
5-40
5-40
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ix
6
x
Contents
Compare the Final Coefficients . . . . . . . . . . . . . . . . . . . . . .
Reset the Filter Before Filtering . . . . . . . . . . . . . . . . . . . . .
Investigate Convergence Through Learning Curves . . . . . . .
Compute the Learning Curves . . . . . . . . . . . . . . . . . . . . . .
Compute the Theoretical Learning Curves . . . . . . . . . . . . .
5-42
5-43
5-43
5-44
5-45
Adaptive Filters in Simulink . . . . . . . . . . . . . . . . . . . . . . . . .
Create an Acoustic Environment in Simulink . . . . . . . . . . .
LMS Filter Configuration for Adaptive Noise Cancellation .
Modify Adaptive Filter Parameters During Model
Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Adaptive Filtering Examples . . . . . . . . . . . . . . . . . . . . . . . .
5-46
5-46
5-48
Selected Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5-60
5-54
5-59
Multirate and Multistage Filters
Multirate Filters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Why Are Multirate Filters Needed? . . . . . . . . . . . . . . . . . . .
Overview of Multirate Filters . . . . . . . . . . . . . . . . . . . . . . . .
6-2
6-2
6-2
Multistage Filters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Why Are Multistage Filters Needed? . . . . . . . . . . . . . . . . . . .
Optimal Multistage Filters in DSP System Toolbox . . . . . . . .
6-6
6-6
6-6
Example Case for Multirate/Multistage Filters . . . . . . . . . . .
Example Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Single-Rate/Single-Stage Equiripple Design . . . . . . . . . . . . .
Reduce Computational Cost Using Mulitrate/Multistage
Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Compare the Responses . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Further Performance Comparison . . . . . . . . . . . . . . . . . . . . .
6-7
6-7
6-7
6-8
6-8
6-9
Filter Banks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Dyadic Analysis Filter Banks . . . . . . . . . . . . . . . . . . . . . . .
Dyadic Synthesis Filter Banks . . . . . . . . . . . . . . . . . . . . . .
6-11
6-11
6-15
Multirate Filtering in Simulink . . . . . . . . . . . . . . . . . . . . . . .
6-19
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7
Transforms, Estimation, and Spectral Analysis
Transform Time-Domain Data into Frequency Domain . . . .
7-2
Transform Frequency-Domain Data into Time Domain . . . .
7-7
Linear and Bit-Reversed Output Order . . . . . . . . . . . . . . . .
FFT and IFFT Blocks Data Order . . . . . . . . . . . . . . . . . . . .
Find the Bit-Reversed Order of Your Frequency Indices . . .
7-12
7-12
7-12
Calculate Channel Latencies Required for Wavelet
Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Analyze Your Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Calculate the Group Delay of Your Filters . . . . . . . . . . . . .
Reconstruct the Filter Bank System . . . . . . . . . . . . . . . . . .
Equalize the Delay on Each Filter Path . . . . . . . . . . . . . . .
Update and Run the Model . . . . . . . . . . . . . . . . . . . . . . . . .
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7-14
7-14
7-16
7-18
7-18
7-21
7-22
Spectral Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7-23
Power Spectrum Estimates . . . . . . . . . . . . . . . . . . . . . . . . . .
Create the Block Diagram . . . . . . . . . . . . . . . . . . . . . . . . . .
Set the Model Parameters . . . . . . . . . . . . . . . . . . . . . . . . . .
View the Power Spectrum Estimates . . . . . . . . . . . . . . . . . .
7-24
7-24
7-25
7-32
Spectrograms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Modify the Block Diagram . . . . . . . . . . . . . . . . . . . . . . . . .
Set the Model Parameters . . . . . . . . . . . . . . . . . . . . . . . . . .
View the Spectrogram of the Speech Signal . . . . . . . . . . . . .
7-35
7-35
7-37
7-41
Mathematics
8
Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Statistics Blocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Basic Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Running Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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8-2
8-2
8-2
8-3
xi
Linear Algebra and Least Squares . . . . . . . . . . . . . . . . . . . . .
Linear Algebra Blocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Linear System Solvers . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Matrix Factorizations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Matrix Inverses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Fixed-Point Design
9
xii
Contents
8-5
8-5
8-5
8-7
8-8
Fixed-Point Signal Processing . . . . . . . . . . . . . . . . . . . . . . . . .
Fixed-Point Features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Benefits of Fixed-Point Hardware . . . . . . . . . . . . . . . . . . . . .
Benefits of Fixed-Point Design with System Toolboxes
Software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9-2
9-2
9-2
Fixed-Point Concepts and Terminology . . . . . . . . . . . . . . . . .
Fixed-Point Data Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Scaling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Precision and Range . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9-4
9-4
9-5
9-6
Arithmetic Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Modulo Arithmetic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Two's Complement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Addition and Subtraction . . . . . . . . . . . . . . . . . . . . . . . . . .
Multiplication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Casts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9-9
9-9
9-10
9-11
9-12
9-14
Fixed-Point Support for MATLAB System Objects . . . . . . .
Get Information About Fixed-Point System Objects . . . . . . .
Display Fixed-Point Properties for System Objects . . . . . . .
Set System Object Fixed-Point Properties . . . . . . . . . . . . . .
Full Precision for Fixed-Point System Objects . . . . . . . . . . .
9-19
9-19
9-22
9-23
9-24
Specify Fixed-Point Attributes for Blocks . . . . . . . . . . . . . .
Fixed-Point Block Parameters . . . . . . . . . . . . . . . . . . . . . . .
Specify System-Level Settings . . . . . . . . . . . . . . . . . . . . . . .
Inherit via Internal Rule . . . . . . . . . . . . . . . . . . . . . . . . . . .
Specify Data Types for Fixed-Point Blocks . . . . . . . . . . . . .
9-25
9-25
9-28
9-29
9-39
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9-3
Quantizers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Scalar Quantizers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Vector Quantizers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9-47
9-47
9-54
Fixed-Point Filter Design . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Overview of Fixed-Point Filters . . . . . . . . . . . . . . . . . . . . . .
Data Types for Filter Functions . . . . . . . . . . . . . . . . . . . . .
Floating-Point to Fixed-Point Filter Conversion . . . . . . . . .
Create an FIR Filter Using Integer Coefficients . . . . . . . . .
Fixed-Point Filtering in Simulink . . . . . . . . . . . . . . . . . . . .
9-61
9-61
9-61
9-62
9-71
9-87
C Code Generation
10
11
Understanding C Code Generation . . . . . . . . . . . . . . . . . . . .
C Code Generation with the Simulink Coder Product . . . . .
Highly Optimized Generated ANSI C Code . . . . . . . . . . . . .
10-2
10-2
10-3
Functions and System Objects Supported for C Code
Generation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10-4
C Code Generation from MATLAB . . . . . . . . . . . . . . . . . . .
10-12
C Code Generation from Simulink . . . . . . . . . . . . . . . . . . .
Open and Run the Model . . . . . . . . . . . . . . . . . . . . . . . . .
Generate Code from the Model . . . . . . . . . . . . . . . . . . . . .
Build and Run the Generated Code . . . . . . . . . . . . . . . . . .
10-13
10-13
10-15
10-15
How to Run a Generated Executable Outside MATLAB . .
10-18
DSP System Toolbox Supported Hardware . . . . . . . . . . . .
10-19
Define New System Objects
Summary List of Methods for Defining New System
Objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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11-3
xiii
xiv
Contents
Define Basic System Objects . . . . . . . . . . . . . . . . . . . . . . . . .
11-5
Change Number of Step Inputs or Outputs . . . . . . . . . . . . .
11-7
Specify System Block Input and Output Names . . . . . . . .
11-11
Validate Property and Input Values . . . . . . . . . . . . . . . . . .
11-13
Initialize Properties and Setup One-Time Calculations . .
11-16
Set Property Values at Construction Time . . . . . . . . . . . . .
11-19
Reset Algorithm State . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11-21
Define Property Attributes . . . . . . . . . . . . . . . . . . . . . . . . . .
11-23
Hide Inactive Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11-27
Limit Property Values to Finite String Set . . . . . . . . . . . .
11-29
Process Tuned Properties . . . . . . . . . . . . . . . . . . . . . . . . . . .
11-32
Release System Object Resources . . . . . . . . . . . . . . . . . . . .
11-34
Define Composite System Objects . . . . . . . . . . . . . . . . . . . .
11-36
Define Finite Source Objects . . . . . . . . . . . . . . . . . . . . . . . .
11-39
Save System Object . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11-41
Load System Object . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11-44
Clone System Object . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11-47
Define System Object Information . . . . . . . . . . . . . . . . . . .
11-48
Define System Block Icon . . . . . . . . . . . . . . . . . . . . . . . . . . .
11-50
Add Header to System Block Dialog . . . . . . . . . . . . . . . . . .
11-52
Add Property Groups to System Object and Block Dialog
11-54
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12
Set Output Size . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11-58
Set Output Data Type . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11-60
Set Output Complexity . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11-62
Specify Whether Output Is Fixed- or Variable-Size . . . . . .
11-64
Specify Discrete State Output Specification . . . . . . . . . . .
11-66
Use Update and Output for Nondirect Feedthrough . . . . .
11-68
Enable For Each Subsystem Support . . . . . . . . . . . . . . . . .
11-71
Methods Timing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Setup Method Call Sequence . . . . . . . . . . . . . . . . . . . . . . .
Step Method Call Sequence . . . . . . . . . . . . . . . . . . . . . . . .
Reset Method Call Sequence . . . . . . . . . . . . . . . . . . . . . . .
Release Method Call Sequence . . . . . . . . . . . . . . . . . . . . .
11-73
11-73
11-73
11-74
11-75
System Object Input Arguments and ~ in Code Examples
11-76
What Are Mixin Classes? . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11-77
Best Practices for Defining System Objects . . . . . . . . . . . .
11-78
HDL Code Generation
What is HDL Code Generation? . . . . . . . . . . . . . . . . . . . . . . .
12-2
Blocks With HDL Support . . . . . . . . . . . . . . . . . . . . . . . . . . .
Filtering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Math Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Signal Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Signal Management . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Sinks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Transforms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
12-3
12-3
12-3
12-3
12-3
12-4
12-4
12-4
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xv
System Objects With HDL Support . . . . . . . . . . . . . . . . . . . .
13
14
15
Links to Category Pages
Signal Management Library . . . . . . . . . . . . . . . . . . . . . . . . . .
13-2
Sinks Library . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
13-3
Math Functions Library . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
13-4
Filtering Library . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
13-5
Designing Lowpass FIR Filters
Lowpass FIR Filter Design . . . . . . . . . . . . . . . . . . . . . . . . . . .
14-2
Controlling Design Specifications in Lowpass FIR Design .
14-7
Designing Filters with Non-Equiripple Stopband . . . . . . .
14-13
Minimizing Lowpass FIR Filter Length . . . . . . . . . . . . . . .
14-18
FDATool: A Filter Design and Analysis GUI
Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
FDATool . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Filter Design Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Using the Filter Design and Analysis Tool . . . . . . . . . . . . .
Analyzing Filter Responses . . . . . . . . . . . . . . . . . . . . . . . . .
Filter Design and Analysis Tool Panels . . . . . . . . . . . . . . . .
Getting Help . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
xvi
Contents
12-5
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15-2
15-2
15-2
15-3
15-4
15-4
15-5
16
Using FDATool . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Choosing a Response Type . . . . . . . . . . . . . . . . . . . . . . . . .
Choosing a Filter Design Method . . . . . . . . . . . . . . . . . . . .
Setting the Filter Design Specifications . . . . . . . . . . . . . . . .
Computing the Filter Coefficients . . . . . . . . . . . . . . . . . . .
Analyzing the Filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Editing the Filter Using the Pole/Zero Editor . . . . . . . . . .
Converting the Filter Structure . . . . . . . . . . . . . . . . . . . . .
Exporting a Filter Design . . . . . . . . . . . . . . . . . . . . . . . . .
Generating a C Header File . . . . . . . . . . . . . . . . . . . . . . .
Generating MATLAB Code . . . . . . . . . . . . . . . . . . . . . . . .
Managing Filters in the Current Session . . . . . . . . . . . . . .
Saving and Opening Filter Design Sessions . . . . . . . . . . . .
15-6
15-6
15-7
15-8
15-12
15-12
15-17
15-21
15-23
15-28
15-29
15-30
15-32
Importing a Filter Design . . . . . . . . . . . . . . . . . . . . . . . . . . .
Import Filter Panel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Filter Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
15-33
15-33
15-34
Designing a Filter in the Filterbuilder GUI
Filterbuilder Design Process . . . . . . . . . . . . . . . . . . . . . . . . .
Introduction to Filterbuilder . . . . . . . . . . . . . . . . . . . . . . . .
Design a Filter Using Filterbuilder . . . . . . . . . . . . . . . . . . .
Select a Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Select a Specification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Select an Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Customize the Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . .
Analyze the Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Realize or Apply the Filter to Input Data . . . . . . . . . . . . . .
Designing a FIR Filter Using filterbuilder . . . . . . . . . . . . .
FIR Filter Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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16-2
16-2
16-2
16-2
16-5
16-5
16-7
16-9
16-9
16-11
16-11
xvii
Bibliography
A
xviii
Contents
Advanced Filters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
A-2
Adaptive Filters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
A-3
Multirate Filters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
A-4
Frequency Transformations . . . . . . . . . . . . . . . . . . . . . . . . . .
A-5
Fixed-Point Filters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
A-6
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1
DSP Tutorials
• “Introduction to Streaming Signal Processing in MATLAB” on page 1-2
• “Filter Frames of a Noisy Sine Wave Signal in MATLAB” on page 1-10
• “Filter Frames of a Noisy Sine Wave Signal in Simulink” on page 1-12
• “Lowpass Filter Design in MATLAB” on page 1-18
• “Lowpass IIR Filter Design in Simulink” on page 1-27
• “Create Moving Average System object” on page 1-40
• “Tunable Lowpass Filtering of Audio Input in Simulink” on page 1-48
• “Desktop Real-time Audio Acceleration with MATLAB Coder” on page 1-53
• “Fixed-Point Filter Design in MATLAB” on page 1-56
• “Sample Rate Conversion of Audio Signal in MATLAB and Simulink” on page 1-65
• “Visualizing Multiple Signals Using Logic Analyzer” on page 1-74
• “Signal Visualization and Measurements in MATLAB” on page 1-88
• “Filter Frames of a Noisy Sine Wave Signal using Testbench Generator” on page
1-103
• “Create Composite System object” on page 1-110
• “Measure Audio Latency in MATLAB and Simulink” on page 1-115
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1
DSP Tutorials
Introduction to Streaming Signal Processing in MATLAB
This example shows how to do basic signal processing on an audio signal streamed
frame by frame from a file. The same framework applies to streaming live audio from a
microphone or audio line input.
Introduction
This example shows how to use components in the DSP System Toolbox called System
objects, which are optimized for streaming signal processing. The signals are read in and
processed frame by frame (or block by block). You control the frame size.
In this example, frames of 1024 samples are read from an audio file every time a while
loop executes. The audio in the file is sampled at 44.1 kHz and contains two channels
(stereo). Each frame of data is approximately 23.2 milliseconds.
The example filters the audio signal using a notch filter. Because filtering is done on each
frame, the state of the filter must be maintained from one frame to the next to ensure
smooth processing.
Initialization
Streaming components must be initialized before use. Initialize the audio file reader and
audio player to listen to the filtered audio.
FrameSize = 1024;
AR = dsp.AudioFileReader('Filename','guitar10min.ogg',...
'SamplesPerFrame',FrameSize);
Fs = AR.SampleRate;
AP = dsp.AudioPlayer('SampleRate',Fs,...
'OutputNumUnderrunSamples',true);
Notch Filter
This example uses a simple second order IIR notch filter with a biquad (second-order
sections) structure to filter the audio signal. The filter has a notch at 200 Hz and a Qfactor of 35. The higher the Q-factor, the narrower the 3 dB bandwidth of the notch. You
can change these values and listen to the resulting audio for different filter specifications
if desired. The notch filter retains state each time it is executed making it well-suited for
streaming data.
1-2
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Introduction to Streaming Signal Processing in MATLAB
Wo = 200/(Fs/2);
Q = 35;
BW = Wo/Q;
[b,a] = iirnotch(Wo,BW);
NotchFilter = dsp.BiquadFilter('SOSMatrix',[b,a]);
Streaming
Next, stream in and process your signal. Construct a while loop to run for 20 seconds.
A counter keeps track of how many frames are processed during the 20-second period.
Because each frame is 23.2 ms of audio, at least 861 frames must be processed in the 20second period for the system to operate in real time or faster.
tic
Tstop = 20;
count = 0;
while toc < Tstop
audioIn = step(AR);
audioOut = step(NotchFilter,audioIn);
plot(audioOut)
drawnow
count = count + 1;
end
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1-3
1
DSP Tutorials
On a reasonably fast computer, the value of count exceeds 861 frames meaning the
processing can be done in real time or faster.
Streaming Without DSP Components
Instead of using System objects, you can use the audioread and filter functions.
However, audioread is not well-suited for streaming, because the file name and position
must be provided at each call. As a result, the performance of audioread is considerably
slower than the performance of the System object file reader in a streaming application.
filter provides adequate performance, but state must be passed in and out of filter
for use in a streaming application. This can result in inefficient and complicated code if
there are many components with state that must be handled manually.
z = [];
1-4
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Introduction to Streaming Signal Processing in MATLAB
tic
count = 0;
while toc < Tstop
audioIn = audioread('guitar10min.ogg',count*FrameSize+[1 FrameSize]);
[audioOut,z] = filter(b,a,audioIn,z);
plot(audioOut)
drawnow
count = count + 1;
end
The plot update gives a visual indication of how much slower the code is with audioread
and filter is compared to the System object implementation. In particular, count
is considerably less than 861 frames, and therefore processing real-time audio in this
fashion is not feasible.
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1-5
1
DSP Tutorials
Listening to The Filtered Signal
On computers capable of processing the data in real time or better, you have to add only
a single line of code to listen to the filtered signal as it is being processed. A new variable,
dropped, keeps count of any dropped samples due to buffer underrun.
tic
dropped = 0;
count = 0;
while toc < Tstop
audioIn = step(AR);
audioOut = step(NotchFilter,audioIn);
plot(audioOut)
drawnow
count = count + 1;
dropped = dropped + step(AP,audioOut);
end
1-6
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Introduction to Streaming Signal Processing in MATLAB
On most machines, there are no dropped samples.
Better Way of Plotting
Rather than using plot and drawnow to monitor the audio signal, use a System object
time scope. The time scope provides better performance along with many other features,
for example, measurements and panning. If you want to plot the spectrum of the signal
in real time, you can use a spectrum analyzer (dsp.SpectrumAnalyzer).
TS = dsp.TimeScope('YLimits',[-1,1],'SampleRate',Fs,...
'TimeSpan',FrameSize/Fs);
step(TS,audioOut);
tic
count = 0;
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1-7
1
DSP Tutorials
while toc < Tstop % Run for 20 seconds
audioIn = step(AR);
audioOut = step(NotchFilter,audioIn);
step(TS,audioOut);
count = count + 1;
dropped = dropped + step(AP,audioOut);
end
However, for maximum performance, avoid plotting the signal in time or frequency.
1-8
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Introduction to Streaming Signal Processing in MATLAB
Streaming Live Audio
To stream audio from a microphone or line input, use the audio recorder,
dsp.AudioRecorder. If you want to write the processed audio to disk, use the audio
file writer, dsp.AudioFileWriter. The audio file writer supports a number of the most
common audio formats such as WAV, OGG, FLAC, and M4A.
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1-9
1
DSP Tutorials
Filter Frames of a Noisy Sine Wave Signal in MATLAB
This example shows how to lowpass filter a noisy signal and visualize the original and
filtered signals using a spectrum analyzer. There is a Simulink version of this example:
Filter Frames of a Noisy Signal in Simulink
Source
The input signal is the sum of two sine waves with frequencies of 1 kHz and 10 kHz. The
sampling frequency is 44.1 kHz.
Sine1 = dsp.SineWave('Frequency',1e3,'SampleRate',44.1e3);
Sine2 = dsp.SineWave('Frequency',10e3,'SampleRate',44.1e3);
Lowpass Filter
The lowpass FIR filter uses a constrained equiripple filter design (firceqrip). The filter's
cutoff frequency is 5 kHz and the linear ripples in the passband and stopband are equal
to 0.05 and 0.001.
FIRLowPass = dsp.FIRFilter('Numerator', ...
firceqrip(30,5e3*2/44.1e3,[0.05 1e-3]));
Spectrum Analyzer
Set up the spectrum analyzer to compare the power spectra of the original and filtered
signals. The spectrum units are dBm.
SpecAna = dsp.SpectrumAnalyzer('PlotAsTwoSidedSpectrum',false, ...
'SampleRate',Sine1.SampleRate, ...
'ReducePlotRate',false, ...
'ShowLegend',true, ...
'YLimits',[-145,45]);
Frame-Based Processing
This example uses frame-based processing. In frame-based processing, the data is
processed one frame at a time. Each frame of data contains sequential samples from
an independent channel. Frame-based processing is advantageous for many signal
processing applications because you can process multiple samples at once. By buffering
your data into frames and processing multi-sample frames of data, you often improve the
computational time of your signal processing algorithms. In this example, the number
of samples per frame is 1024. The FIR filter uses frame-based processing if the input is
frame based.
1-10
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Filter Frames of a Noisy Sine Wave Signal in MATLAB
Sine1.SamplesPerFrame = 1024;
Sine2.SamplesPerFrame = 1024;
Simulation Results
Add zero-mean white Gaussian noise with a standard deviation of 0.1 to the sum of sine
waves and filter the result with the FIR filter. While running the simulation, you see in
the spectrum analyzer that frequencies above 4 kHz in the source signal are attenuated.
The resulting signal maintains the peak at 1 kHz because it falls in the passband of the
lowpass filter.
tic
while toc<5
x = step(Sine1)+step(Sine2)+0.1.*randn(Sine1.SamplesPerFrame,1);
y = step(FIRLowPass,x);
step(SpecAna,[x,y]);
end
release(SpecAna)
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1-11
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DSP Tutorials
Filter Frames of a Noisy Sine Wave Signal in Simulink
This example shows how to lowpass filter a noisy signal in Simulink® and visualize the
power spectra of the original and filtered signals with a spectrum analyzer. There is
also a MATLAB® version of this example: “Filter Frames of a Noisy Sine Wave Signal in
MATLAB” on page 1-10.
The example is based on the following model:
model = 'ex_filtering_frames';
open_system(model);
In this section...
“Source” on page 1-13
1-12
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Filter Frames of a Noisy Sine Wave Signal in Simulink
In this section...
“Lowpass Filter” on page 1-15
“Spectrum Analyzer” on page 1-15
Source
Three source blocks comprise the input signal. The input signal consists of the sum of two
sine waves and white Gaussian noise with mean 0 and variance 0.01. The frequencies of
the sine waves are 1 kHz and 10 kHz. The sampling frequency is 44.1 kHz. The following
figure shows the block parameters for the 1 kHz sine wave. Open the other source blocks
to see their parameters.
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‫‪DSP Tutorials‬‬
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‫‪1‬‬
‫‪1-14‬‬
Filter Frames of a Noisy Sine Wave Signal in Simulink
Lowpass Filter
The lowpass filter is modeled using a Discrete FIR Filter block. The example uses a
constrained equiripple FIR filter design, firceqrip. The filter's cutoff frequency is 5
kHz, and the linear ripples in the passband and stopband are equal to 0.05 and 1e-3.
Spectrum Analyzer
The power spectra of the original and filtered signals are compared using a spectrum
analyzer (Spectrum Analyzer). The spectrum units are in dBm.
This example uses frame-based processing. In frame-based processing, blocks process
data one frame at a time. Each frame of data contains sequential samples from an
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1-15
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DSP Tutorials
independent channel. Frame-based processing is advantageous for many signal
processing applications because you can process multiple samples at once. By buffering
your data into frames and processing multi-sample frames of data, you often improve the
computational time of your signal processing algorithms. In this example, the number of
samples per frame is 1024. Specify frame-based processing on the FIR filter by setting
the Input Processing parameter to 'Columns as channels (frame based)'.
To run the simulation, click the Run button in the model. To stop the simulation, click
the Stop button in the Spectrum Analyzer. Alternatively, you can execute the following
code to run the simulation for 200 frames of data.
set_param(model,'StopTime','1024/44100 * 200')
sim(model);
1-16
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Filter Frames of a Noisy Sine Wave Signal in Simulink
In the spectrum analyzer you see that frequencies above 4 kHz in the source signal are
attenuated. The resulting signal maintains the peak at 1 kHz because it falls in the
passband of the lowpass filter.
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1-17
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DSP Tutorials
Lowpass Filter Design in MATLAB
This example shows how to design lowpass filters. The example highlights some of the
most commonly used command-line tools in the DSP System Toolbox. Alternatively, you
can use the Filter Builder app to implement all the designs presented here. For more
design options, see Designing Low Pass FIR Filters.
Introduction
When designing a lowpass filter, the first choice you make is whether to design an FIR
or IIR filter. You generally choose FIR filters when a linear phase reponse is important.
FIR filters also tend to be preferred for fixed-point implementations because they
are typically more robust to quantization effects. FIR filters are also used in many
high-speed implementations such as FPGAs or ASICs because they are suitable for
pipelining. IIR filters (in particular biquad filters) are used in applications (such as
audio signal processing) where phase linearity is not a concern. IIR filters are generally
computationally more efficient in the sense that they can meet the design specifications
with fewer coefficients than FIR filters. IIR filters also tend to have a shorter transient
response and a smaller group delay. However, the use of minimum-phase and multirate
designs can result in FIR filters comparable to IIR filters in terms of group delay and
computational efficiency.
FIR Lowpass Designs - Specifying the Filter Order
There are many practical situations in which you must specify the filter order. One
such case is if you are targeting hardware which has constrained the filter order to a
specific number. Another common scenario is when you have computed the available
computational budget (MIPS) for your implementation and this affords you a limited
filter order. FIR design functions in the Signal Processing Toolbox (including fir1,
firpm, and firls) are all capable of designing lowpass filters with a specified order.
In the DSP System Toolbox, the preferred function for lowpass FIR filter design with a
specified order is firceqrip. This function designs optimal equiripple lowpass/highpass
FIR filters with specified passband/stopband ripple values and with a specified passbandedge frequency. The stopband-edge frequency is determined as a result of the design.
Design a lowpass FIR filter for data sampled at 48 kHz. The passband-edge frequency is
8 kHz. The passband ripple is 0.01 dB and the stopband attenuation is 80 dB. Constrain
the filter order to 120.
N
Fs
1-18
= 120;
= 48e3;
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Lowpass Filter Design in MATLAB
Fp = 8e3;
Ap = 0.01;
Ast = 80;
Obtain the maximum deviation for the passband and stopband ripples in linear units.
Rp = (10^(Ap/20) - 1)/(10^(Ap/20) + 1);
Rst = 10^(-Ast/20);
Design the filter using firceqrip and view the magnitude frequency response.
NUM = firceqrip(N,Fp/(Fs/2),[Rp Rst],'passedge');
fvtool(NUM,'Fs',Fs)
The resulting stopband-edge frequency is about 9.64 kHz.
Minimum-Order Designs
Another design function for optimal equiripple filters is firgr. firgr can design a
filter that meets passband/stopband ripple constraints as well as a specified transition
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DSP Tutorials
width with the smallest possible filter order. For example, if the stopband-edge frequency
is specified as 10 kHz, the resulting filter has an order of 100 rather than the 120thorder filter designed with firceqrip. The smaller filter order results from the larger
transition band.
Specify the stopband-edge frequency of 10 kHz. Obtain a minimum-order FIR filter with
a passband ripple of 0.01 dB and 80 dB of stopband attenuation.
Fst
= 10e3;
NumMin = firgr('minorder',[0 Fp/(Fs/2) Fst/(Fs/2) 1], [1 1 0 0],[Rp,Rst]);
Plot the magnitude frequency responses for the minimum-order FIR filter obtained with
firgr and the 120th-order filter designed with firceqrip. The minimum-order design
results in a filter with order 100. The transition region of the 120th-order filter is, as
expected, narrower than that of the filter with order 100.
fvtool(NUM,1,NumMin,1,'Fs',Fs);
legend('N = 120','N = 100');
1-20
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Lowpass Filter Design in MATLAB
Filtering Data
To apply the filter to data, you can use the filter command or you can use
dsp.FIRFilter. dsp.FIRFilter has the advantage of managing state when executed
in a loop. dsp.FIRFilter also has fixed-point capabilities.
Filter 10 seconds of white noise with zero mean and unit standard deviation in frames
of 256 samples with the 120th-order FIR lowpass filter. View the result on a spectrum
analyzer.
LP_FIR = dsp.FIRFilter('Numerator',NUM);
SA
= dsp.SpectrumAnalyzer('SampleRate',Fs,'SpectralAverages',5);
tic
while toc < 10
x = randn(256,1);
y = step(LP_FIR,x);
step(SA,y);
end
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DSP Tutorials
Using FDESIGN
fdesign is an alternative to firceqrip and firgr that provides several additional
capabilities. The fdesign filter design process consists of two steps. In the first step, you
provide your design specifications. In the second step, you design the filter based on your
specifications. With fdesign, you can enter magnitude specifications directly in decibels
and frequency specifications directly in Hz.
Design a lowpass FIR filter for data sampled at 48 kHz. The passband-edge frequency is
8 kHz. The passband ripple is 0.01 dB and the stopband attenuation is 80 dB. Constrain
the filter order to 120. Create a dsp.FIRFilter based on your specifications.
LP_Specs = fdesign.lowpass('N,Fp,Ap,Ast',N,Fp,Ap,Ast,Fs);
LP_FIR
= design(LP_Specs,'equiripple','SystemObject',true);
The coefficients in LP_FIR.Numerator are identical to the coefficients in NUM. Because
LP_FIR is a dsp.FIRFilter object, you can use LP_FIR to filter data directly, as shown
in the preceding example. You can also analyze the filter using FVTool or measure the
response using measure.
fvtool(LP_FIR,'Fs',Fs);
measure(LP_FIR)
ans =
Sample Rate
Passband Edge
3-dB Point
6-dB Point
Stopband Edge
Passband Ripple
Stopband Atten.
Transition Width
1-22
:
:
:
:
:
:
:
:
48 kHz
8 kHz
8.5843 kHz
8.7553 kHz
9.64 kHz
0.01 dB
79.9981 dB
1.64 kHz
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Lowpass Filter Design in MATLAB
Minimum-Order Designs with FDESIGN
You can use fdesign to design minimum-order filters and use measure to verify that
the design meets the prescribed specifications. The order of the filter is again 100.
LP_Specs_minOrd = fdesign.lowpass('Fp,Fst,Ap,Ast',Fp,Fst,Ap,Ast,Fs);
LP_FIR_minOrd
= design(LP_Specs_minOrd,'equiripple','SystemObject',true);
measure(LP_FIR_minOrd)
Order = length(LP_FIR_minOrd.Numerator)-1
ans =
Sample Rate
Passband Edge
3-dB Point
6-dB Point
Stopband Edge
Passband Ripple
:
:
:
:
:
:
48 kHz
8 kHz
8.7134 kHz
8.9219 kHz
10 kHz
0.0099327 dB
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1-23
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DSP Tutorials
Stopband Atten. : 80.0363 dB
Transition Width : 2 kHz
Order =
100
Designing IIR Filters
Elliptic filters are the IIR counterpart to optimal equiripple FIR filters. Accordingly, you
can use the same specifications to design elliptic filters. The filter order you obtain for an
IIR filter is much smaller than the order of the corresponding FIR filter.
Design an elliptic filter with the same sampling frequency, cutoff frequency, passbandripple constraint, and stopband attenuation as the 120th-order FIR filter. Reduce the
filter order for the elliptic filter to 10.
LP_Specs.FilterOrder = 10;
LP_IIR = design(LP_Specs,'ellip','SystemObject',true);
Compare the FIR and IIR designs. Compute the cost of the two implementations.
hfvt = fvtool(LP_FIR,LP_IIR,'Fs',Fs);
legend(hfvt,'FIR Equiripple, N = 120', 'IIR Elliptic, N = 10');
cost_FIR = cost(LP_FIR)
cost_IIR = cost(LP_IIR)
cost_FIR =
Number of Multipliers
Number of Adders
Number of States
Multiplications per Input Sample
Additions per Input Sample
:
:
:
:
:
121
120
120
121
120
:
:
:
:
:
20
20
10
20
20
cost_IIR =
Number of Multipliers
Number of Adders
Number of States
Multiplications per Input Sample
Additions per Input Sample
1-24
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Lowpass Filter Design in MATLAB
The FIR and IIR filters have similar magnitude responses. The cost of the IIR filter is
about 1/6 the cost of the FIR filter.
Running the IIR Filters
The IIR filter is designed as a biquad filter and implemented using dsp.BiquadFilter.
To apply the filter to data, use the same commands as in the FIR case.
Filter 10 seconds of white Gaussian noise with zero mean and unit standard deviation
in frames of 256 samples with the 10th-order IIR lowpass filter. View the result on a
spectrum analyzer.
SA = dsp.SpectrumAnalyzer('SampleRate',Fs,'SpectralAverages',5);
tic
while toc < 10
x = randn(256,1);
y = step(LP_IIR,x);
step(SA,y);
end
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‫‪DSP Tutorials‬‬
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‫‪1‬‬
‫‪1-26‬‬
Lowpass IIR Filter Design in Simulink
Lowpass IIR Filter Design in Simulink
In this section...
“Model” on page 1-27
“Butterworth Filter” on page 1-28
“Chebyshev Type I Filter” on page 1-30
“Chebyshev Type II Filter” on page 1-32
“Elliptic Filter” on page 1-34
“Minimum-Order Designs” on page 1-36
This example shows how to design classic lowpass IIR filters in Simulink. The initial
focus is on the situation in which the critical design parameter is the cutoff frequency
where the filter's power decays to half (-3 dB) the nominal passband value.
The example shows how to replace a Butterworth design with either a Chebyshev or
elliptic filter of the same order and obtain a steeper roll-off at the expense of some ripple
in the passband and/or stopband of the filter. The example also explores minimum-order
designs.
Model
This example is based on the Simulink model ex_iir_design. The model includes one
lowpass filter for each of the four designs: Butterworth, Chebyshev type 1, Chebyshev
type 2, and elliptic. You can use the link under Select Filter to switch between designs
at any point during the simulation.
A stereo audio signal sampled at 44.1 kHz is passed through the filter. The audio input is
corrupted by N(0,10-5) Gaussian noise passed through a highpass filter. The original and
filtered signals are displayed in a spectrum analyzer. You can listen to either the original
or filtered signal by toggling the Manual Switch at the input of the To Audio Device
block.
The filters in this example all use direct-form II second-order sections (SOS).
model = 'ex_iir_design';
open_system(model);
set_param(model,'StopTime','1024/44100 * 100')
sim(model);
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1-27
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DSP Tutorials
Butterworth Filter
The first filter block is an 8-th order Butterworth lowpass filter with a cutoff frequency
of 5 kHz. This filter is maximally flat (no ripple in the passband or in the stopband).
Double click on the block to open the block dialog. You can visualize the filter's frequency
response by clicking the View Filter Response button on the block's dialog.
1-28
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Lowpass IIR Filter Design in Simulink
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1-29
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DSP Tutorials
Chebyshev Type I Filter
A Chebyshev type I design allows you to control the passband. There are still no ripples
in the stopband. Larger ripples enable a steeper roll-off. In this model, the peak-to-peak
ripple is specified to be 0.5 dB.
1-30
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Lowpass IIR Filter Design in Simulink
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1-31
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DSP Tutorials
Zooming in on the passband, you can see that the ripples are contained in the range [-0.5,
0] dB.
Chebyshev Type II Filter
A Chebyshev type II design allows you to control the stopband attenuation. There are no
ripples in the passband. A smaller stopband attenuation enables a steeper roll-off. In this
example, the stopband attenuation is 80 dB.
1-32
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Lowpass IIR Filter Design in Simulink
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1-33
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DSP Tutorials
Elliptic Filter
An elliptic filter can provide steeper roll-off compared to previous designs by allowing
ripples in both the stopband and passband. To illustrate this, use the same passband and
stopband characteristics specified in the Chebyshev designs.
1-34
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Lowpass IIR Filter Design in Simulink
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1-35
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DSP Tutorials
Minimum-Order Designs
In cases where you specify the passband and stopband in terms of frequencies and the
amount of tolerable ripple, you can use a minimum-order design. As an example, the
Order mode of the Butterworth filter is set to Minimum. The normalized passband and
stopband frequencies are set to 0.1*22050 Hz and 0.3*22050 Hz. The passband ripple
is 1 dB and the stopband attenuation is 60 dB. A 7-th order filter is necessary to meet the
specifications with a Butterworth design. By following the same approach on the other
filter blocks, you can verify that a 5-th order filter is required for Chebyshev type I and
type II designs. A 4-th order filter is sufficient for the elliptic design.
1-36
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Lowpass IIR Filter Design in Simulink
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The following figure shows the magnitude response for the 7-th order Butterworth
design.
The pole-zero plot for the 7-th order Butterworth design shows the expected clustering of
7 poles around an angle of zero radians on the unit circle and the corresponding 7 zeros
at angle of π radians.
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Lowpass IIR Filter Design in Simulink
Close the model to finish the tutorial.
close_system(model,0);
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Create Moving Average System object
In this section...
“Introduction” on page 1-40
“Create the Class Definition ” on page 1-41
“Moving Average Filter Properties” on page 1-41
“Moving Average Filter Constructor” on page 1-42
“Moving Average Filter Setup” on page 1-43
“Moving Average Filter Step” on page 1-43
“Moving Average Filter Reset” on page 1-44
“Input Validation” on page 1-44
“Object Saving and Loading” on page 1-44
“System object Usage in MATLAB” on page 1-45
“Simulink Customization Methods” on page 1-46
“System object Usage in Simulink” on page 1-46
Introduction
This example shows how to create a System object™ that implements a moving average
filter. The example shows how to use the System object in MATLAB and Simulink
through the MATLAB System block. MovingAverageFilter is a simple moving
average System object filter, which computes the unweighted mean of the previous
WindowLength input samples, where WindowLength is the length of the moving
average window.
The System object accepts single-precision and double-precision 2-D input matrices.
Each column of the input matrix is treated as an independent (1-D) channel. The first
dimension of the input defines the length of the channel (or the input frame size).
MovingAverageFilter independently computes the moving average of each input
channel over time.
“System object Usage in MATLAB” on page 1-45 and “System object Usage in
Simulink” on page 1-46 show how to use your System object with data.
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Create Moving Average System object
Create the Class Definition
In the MATLAB Home tab select New -> System Object -> Simulink Extension to
open a System object template. This template includes customizations of the System
object for use in the MATLAB System block. You can edit the template file, using it as
guideline, to create your own System object.
Replace all occurrences of Untitled in the file with MovingAverageFilter and save
the file as MovingAverageFilter.m in a folder where you have write permission. You
need to add this folder to the MATLAB path to use the System object. For convenience,
the entire System object is provided in the file dspdemo.MovingAverageFilter.m. To
view this file enter
edit dspdemo.MovingAverageFilter
at the MATLAB command prompt. The prefix dspdemo on
dspdemo.MovingAverageFilter is a package name. Packages are special folders
that can contain class folders, function and class definition files, and other packages.
Package folders always begin with the + character such as +dspdemo. Packages define
the scope of the contents of the package folder (that is, a namespace in which names
must be unique). This means function and class names need to be unique only within
the package. Using a package provides a means to organize classes and functions and
to select names for these components that other packages can reuse. You do not have
to use packages when creating your System object. For more information on packages
in MATLAB, see “Packages Create Namespaces”. The remainder of this example shows
you how to create the MovingAverageFilter object from the System object template
without using a package. However, you can also review and use the completed version,
dspdemo.MovingAverageFilter.
Moving Average Filter Properties
The MovingAverageFilter object has one public property that controls the length of
the moving average. Because the algorithm depends on this value being constant once
data processing begins, the property is defined as nontunable. Additionally, the property
only accepts real, positive integers. To ensure correct input, add the PositiveInteger
attribute to the property. The default value of this property is 5.
properties (PositiveInteger, Nontunable)
% WindowLength Moving average filter length
%
Specify the length of the moving average filter as a
%
scalar positive integer value. The default value of this
%
property is 5.
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WindowLength = 5
end
The state of the moving average filter is defined with the DiscreteState attribute. Get
the value of the state by calling the getDiscreteState method.
properties (DiscreteState)
State;
end
A moving average filter is an FIR Filter with numerator coefficients equal to
ones(WindowLength,1)/WindowLength. Because the coefficients do not change
during the streaming operation, the coefficients are defined in a property for optimization
purposes. Additionally, to ensure the coefficients are not accessible to users of the System
object, use the private attribute.
properties (Access = private, Nontunable)
pCoefficients;
end
Finally, the System object operates on a possibly multichannel input and therefore
requires a property for the number of channels. This property is not accessible to users
and therefore you use the private attribute. The value of this property is determined
from the number of columns in the input.
properties (Access = private)
% pNumChannels Property used to cache the number of input channels
% (columns). Varying the number of channels during the streaming
% operation is not allowed (since it modifes the number of required
% states). The default of -1 means that the streaming operation has
% not started yet (i.e. the number ofo channels is still unknown).
pNumChannels = -1;
end
Moving Average Filter Constructor
The System object constructor is a method that has the same name as the class
(MovingAverageFilter in this example). Within that method, use the setProperties
method to allow standard name-value pair handling at construction, filt =
MovingAverageFilter('WindowLength',10).
methods
% Constructor
function obj = MovingAverageFilter(varargin)
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Create Moving Average System object
% Support name-value pair arguments when constructing the
% object.
setProperties(obj,nargin,varargin{:});
end
end
Moving Average Filter Setup
The setupImpl method sets up the object and implements one-time initialization tasks.
The filter coefficients are computed based on the specified window length. The filter's
states are initialized to zero. Note that there are WindowLength-1 states per input
channel. If you would like to initialize the states to a custom value, you can create a
public InitialConditions property and use the property value to set the object state
(obj.State) in setupImpl. Finally, the number of channels is determined from the
number of columns in the input.
function setupImpl(obj,x)
numChannels = size(x,2);
obj.State = zeros(obj.WindowLength-1,numChannels,'like',x);
% Cache the number of channels
obj.pNumChannels = numChannels;
obj.pCoefficients = ones(1,obj.WindowLength)/obj.WindowLength;
end
Note: You must set Access = protected for this method.
Moving Average Filter Step
The object's algorithm is defined in the stepImpl method. The algorithm in stepImpl
is executed when the user of the System object calls step at the command line. In this
example, stepImpl calculates the output and updates the object's state values using the
filter function.
function Y = stepImpl(obj,X)
% Compute output and update state
[Y,obj.State] = filter(obj.pCoefficients,1,X,obj.State);
end
Note: You must set Access = protected for this method.
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Moving Average Filter Reset
The state reset equations are defined in the resetImpl method. In this example, the
states are reset to zero. If you want to reset the states to a custom value, you can create
a public InitialConditions property and use the property value to reset state in
resetImpl.
function resetImpl(obj)
obj.State(:) = 0;
end
Note: You must set methods(Access = protected) for this method.
Input Validation
validateInputsImpl validates inputs to the step method at initialization and at each
subsequent call to step where the input attributes (such as dimensions, data type or
complexity) change. In this example, validattributes ensures that the input is a 2-D
matrix with floating-point data.
function validateInputsImpl(obj, u)
validateattributes(u,{'double','single'}, {'2d',...
'nonsparse'},'','input');
% The number of input channels is not allowed to change. If
% pNumChannels = -1. This means that the streaming operation
% has not started yet (i.e. setupImpl has not been invoked
% yet). Do not perform the check in that case.
coder.internal.errorIf(obj.pNumChannels~=-1 && obj.pNumChannels ~= size(u,2
end
Note: You must set methods(Access = protected) for this method.
Object Saving and Loading
saveObjectImpl defines what property and state values are saved in a MAT-file when
you call save on that object. If you do not define a saveObjectImpl method for your
System object class, only public properties and properties with the DiscreteState
attribute are saved. Save the state of an object only if the object is locked. When you load
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Create Moving Average System object
the saved object, the object loads in that locked state. In this System object, the filter
coefficients are saved if the object is locked.
function s = saveObjectImpl(obj)
s = [email protected](obj);
if isLocked(obj)
s.pCoefficients = obj.pCoefficients;
s.pNumChannels = obj.pNumChannels;
end
end
loadObjectImpl defines what System object property and state values are loaded when
you load a MAT-file. loadObjectImpl should correspond to your saveObjectImpl to
ensure that all saved properties and data are loaded.
function loadObjectImpl(obj,s,wasLocked)
if wasLocked
obj.pCoefficients = s.pCoefficients;
obj.pNumChannels = s.pNumChannels;
end
[email protected](obj,s,wasLocked);
end
Note: You must set Access = protected for this method.
System object Usage in MATLAB
This example uses the System object to remove noise from a noisy pulse
sequence. The length of the moving average filter is 30 samples. If you are using
the predefined dspdemo.MovingAverageFilter, substitute that name for
MovingAverageFilter in the class constructor, for example movingAverageFilter =
dspdemo.MovingAverageFilter('WindowLength',30);.
movingAverageFilter = MovingAverageFilter('WindowLength',30);
scope = dsp.TimeScope('SampleRate',1e3,...
'TimeSpan',256 * .01,...
'ShowGrid',true,...
'NumInputPorts',2,...
'LayoutDimensions',[2 1]);
for i=1:100
input = (1-2*randi([0 1],1)) * ones(256,1) + 0.5 * randn(256,1);
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output = step(movingAverageFilter,input);
step(scope,input,output)
end
Simulink Customization Methods
You need to define a few more methods to be able to use the System object in a Simulink
MATLAB System block. These methods are not required if you use the System object
only in MATLAB. getOutputSizeImpl returns the sizes of each output port. For
System objects with one input and one output and where you want the input and
output sizes to be the same, you do not need to implement this method. In the case of
MovingAverageFilter, there is one input and output and the size of each is the same.
Therefore, remove this method from the class definition of MovingAverageFilter.
getDiscreteStateSpecificationImpl returns the size, data type, and complexity of
a property. This property must be a discrete-state property. You must define this method
if your System object has discrete-state properties and is used in the MATLAB System
block. In this example, the method is used to define the State property.
function [sz,dt,cp] = getDiscreteStateSpecificationImpl(obj,~)
inputSize = propagatedInputSize(obj,1);
sz = [obj.WindowLength-1 inputSize(2)];
dt = propagatedInputDataType(obj,1);
cp = propagatedInputComplexity(obj,1);
end
Note: You must set Access = protected for this method.
System object Usage in Simulink
To use your System object in a Simulink model, drag a MATLAB System block from the
User-Defined Functions library in Simulink to your model.
Open the block dialog box and set the System object name to MovingAverageFilter.
The model ex_movingaverage_filter illustrates the use of the System object in
Simulink to filter a noisy pulse sequence.
model = 'ex_movingaverage_filter';
open_system(model);
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Create Moving Average System object
Run the model by clicking the Run button in the model or entering:
sim(model)
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Tunable Lowpass Filtering of Audio Input in Simulink
In this section...
“Introduction” on page 1-49
“Simulation” on page 1-50
This example shows how to lowpass filter a streaming audio signal by dynamically
setting the passband frequency. A slider is used to set this parameter while the
simulation is running. The power spectrum of the input and filtered audio are compared
using a spectrum analyzer.
This example is based on the following Simulink model.
model = 'ex_tunable_audio_lowpass';
open_system(model);
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Tunable Lowpass Filtering of Audio Input in Simulink
Introduction
The input signal in this example is audio sampled at 22.5 kHz. The audio is read in from
a file 256 samples at a time. The audio is passed through a lowpass variable bandwidth
IIR filter and the result is played through the system's default audio output device. You
can use the switch in the model to compare the filtered and unfiltered audio. The filter
is implemented in dsp.VariableBandwidthIIRFilter and used in Simulink in a
MATLAB System block.
Having a variable bandwidth filter allows you to change the filter parameters while
the simulation is running. In this example, the passband frequency of the lowpass
filter is tunable. The algorithm in dsp.VariableBandwidthIIRFilter works by
using frequency transformations to recompute the filter coefficients when the passband
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frequency is changed. This removes the need to redesign the whole filter. This also
explains why the filter order, passband ripple, and stopband attenuation are not tunable
in real time.
Simulation
Simulating the model, you can hear the filtered audio and compare the power spectrum
of the filtered audio to the original unfiltered version.
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Tunable Lowpass Filtering of Audio Input in Simulink
You can also change the passband frequency of the filter while the simulation is running.
In order to do this, either double-click the Variable Bandwidth IIR Filter block or click on
the blue Tune passband frequency link. In the dialog that opens, change the value of
the Filter passband frequency. The effect of this change is immediately applied and
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you can observe the effects in the spectrum analyzer as well as hear the change in the
audio output.
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Desktop Real-time Audio Acceleration with MATLAB Coder
Desktop Real-time Audio Acceleration with MATLAB Coder
In this section...
“Introduction” on page 1-53
“Notch Filtering” on page 1-53
“C Code Generation Speedup” on page 1-54
This example shows how to accelerate a real-time audio application using C code
generation with MATLAB Coder™. You must have the MATLAB Coder software
installed to run this example.
Introduction
Replacing parts of your MATLAB code with an automatically generated MATLAB
executable (MEX-function) can speedup simulation. Using MATLAB Coder, you can
generate readable and portable C code and compile it into a MEX-function that replaces
the equivalent section of your MATLAB algorithm.
This example showcases code generation using an audio notch filtering application.
Notch Filtering
A notch filter is used to eliminate a specific frequency from a signal. Typical filter design
parameters for notch filters are the notch center frequency and the 3 dB bandwidth. The
center frequency is the frequency at which the filter has a linear gain of zero. The 3 dB
bandwidth measures the frequency width of the notch of the filter computed at the halfpower or 3 dB attenuation point.
The helper function used in this example is helperAudioToneRemoval. The
function reads an audio signal corrupted by a 250 Hz sinusoidal tone from a file.
helperAudioToneRemoval uses a notch filter to remove the interfering tone and writes
the filtered signal to a file.
You can visualize the corrupted audio signal using a spectrum analyzer.
scope = dsp.SpectrumAnalyzer('SampleRate',44.1e3,...
'RBWSource','Property','RBW',5,...
'PlotAsTwoSidedSpectrum',false,...
'SpectralAverages',10,...
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'FrequencySpan','Start and stop frequencies',...
'StartFrequency',20,...
'StopFrequency',1000,...
'Title','Audio signal corrupted by 250 Hz tone');
reader = dsp.AudioFileReader('guitar_plus_tone.ogg');
while ~isDone(reader)
audio = step(reader);
step(scope,audio(:,1));
end
C Code Generation Speedup
Measure the time it takes to read the audio file, filter out the interfering tone, and write
the filtered output using MATLAB code. Because helperAudioToneRemoval writes
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Desktop Real-time Audio Acceleration with MATLAB Coder
an audio file output, you must have write permission in the current directory. To ensure
write access, change directory to your system’s temporary folder.
mydir = pwd; addpath(mydir); cd(tempdir);
tic;
helperAudioToneRemoval;
t1 = toc;
fprintf('MATLAB Simulation Time: %d\n',t1);
Next, generate a MEX-function from helperAudioToneRemoval using the MATLAB
Coder function, codegen.
codegen helperAudioToneRemoval
Measure the time it takes to execute the MEX-function and calculate the speedup gain
with a compiled function.
tic;
helperAudioToneRemoval_mex
t2 = toc;
fprintf('Code Generation Simulation Time: %d\n',t2);
fprintf('Speedup factor: %6.2f\n',t1/t2);
cd(mydir);
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Fixed-Point Filter Design in MATLAB
This example shows how to design filters for use with fixed-point input. The example
analyzes the effect of coefficient quantization on filter design. You must have the FixedPoint Designer software™ to run this example.
Introduction
Fixed-point filters are commonly used in digital signal processors where data storage
and power consumption are key limiting factors. With the constraints you specify, DSP
System Toolbox software allows you to design efficient fixed-point filters. The filter for
this example is a lowpass equiripple FIR filter. Design the filter first for floating-point
input to obtain a baseline. You can use this baseline for comparison with the fixed-point
filter.
FIR Filter Design
The lowpass FIR filter has the following specifications:
• Sample rate: 2000 Hz
• Center frequency: 450 Hz
• Transition width: 100 Hz
• Equiripple design
• Maximum 1 dB of ripple in the passband
• Minimum 80 dB of attenuation in the stopband
samplingFrequency = 2000;
centerFrequency = 450;
transitionWidth = 100;
passbandRipple = 1;
stopbandAttenuation = 80;
designSpec = fdesign.lowpass('Fp,Fst,Ap,Ast',...
centerFrequency-transitionWidth/2, ...
centerFrequency+transitionWidth/2, ...
passbandRipple,stopbandAttenuation, ...
samplingFrequency);
LPF = design(designSpec,'equiripple','SystemObject',true)
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Fixed-Point Filter Design in MATLAB
LPF =
System: dsp.FIRFilter
Properties:
Structure:
NumeratorSource:
Numerator:
InitialConditions:
FrameBasedProcessing:
'Direct form'
'Property'
[1x52 double]
0
true
View the baseline frequency response. The dotted red lines show the design specifications
used to create the filter.
fvtool(LPF)
Full-Precision Fixed-Point Operation
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The fixed-point properties of the filter are contained in the Fixed-point properties
section in the display of the object. By default, the filter uses full-precision arithmetic
to deal with fixed-point inputs. With full-precision arithmetic, the filter uses as many
bits for the product, accumulator, and output as needed to prevent any overflow
or rounding. If you do not want to use full-precision arithmetic, you can set the
FullPrecisionOverride property to false and then set the product, accumulator,
and output data types independently.
rng default
inputWordLength = 16;
fixedPointInput = fi(randn(100,1),true,inputWordLength);
floatingPointInput = double(fixedPointInput);
floatingPointOutput = step(LPF,floatingPointInput);
release(LPF)
fullPrecisionOutput = step(LPF,fixedPointInput);
norm(floatingPointOutput-double(fullPrecisionOutput),'inf')
ans =
6.8994e-05
The result of full-precision fixed-point filtering comes very close to floating point, but
the results are not exact. The reason for this is coefficient quantization. In the fixedpoint filter, the CoefficientsDataType property has the same word length (16) for
the coefficients and the input. The frequency response of the filter in full-precision mode
shows this more clearly. The measure function shows that the minimum stopband
attenuation of this filter with quantized coefficients is 76.6913 dB, less than the 80 dB
specified for the floating-point filter.
LPF.CoefficientsDataType
fvtool(LPF)
measure(LPF)
ans =
Same word length as input
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Fixed-Point Filter Design in MATLAB
ans =
Sample Rate
Passband Edge
3-dB Point
6-dB Point
Stopband Edge
Passband Ripple
Stopband Atten.
Transition Width
:
:
:
:
:
:
:
:
2 kHz
400 Hz
416.2891 Hz
428.1081 Hz
500 Hz
0.96325 dB
76.6913 dB
100 Hz
The filter was last used with fixed-point input and is still in a locked state. For that
reason, fvtool displays the fixed-point frequency response. The dash-dot response is
that of the reference floating-point filter, and the solid plot is the response of the filter
that was used with fixed-point input. The desired frequency response cannot be matched
because the coefficient word length has been restricted to 16 bits. This accounts for the
difference between the floating-point and fixed-point designs. Increasing the number of
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bits allowed for the coefficient word length makes the quantization error smaller and
enables you to match the design requirement for 80 dB of stopband attenuation. Use a
coefficient word length of 24 bits to achieve an attenuation of 80.1275 dB.
LPF24bitCoeff = design(designSpec,'equiripple','SystemObject',true);
LPF24bitCoeff.CoefficientsDataType = 'Custom';
coeffNumerictype = numerictype(fi(LPF24bitCoeff.Numerator,true,24));
LPF24bitCoeff.CustomCoefficientsDataType = numerictype(true, ...
coeffNumerictype.WordLength,coeffNumerictype.FractionLength);
fullPrecisionOutput32bitCoeff = step(LPF24bitCoeff,fixedPointInput);
norm(floatingPointOutput-double(fullPrecisionOutput32bitCoeff),'inf')
fvtool(LPF24bitCoeff)
measure(LPF24bitCoeff)
ans =
4.1077e-07
ans =
Sample Rate
Passband Edge
3-dB Point
6-dB Point
Stopband Edge
Passband Ripple
Stopband Atten.
Transition Width
1-60
:
:
:
:
:
:
:
:
2 kHz
400 Hz
416.2901 Hz
428.1091 Hz
500 Hz
0.96329 dB
80.1275 dB
100 Hz
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Fixed-Point Filter Design in MATLAB
Design Parameters and Coefficient Quantization
In many fixed-point design applications, the coefficient word length is not flexible.
For example, supposed you are restricted to work with 14 bits. In such cases, the
requested minimum stopband attenuation of 80 dB cannot be reached. A filter with 14bit coefficient quantization can achieve a minimum attenuation of only 67.2987 dB.
LPF14bitCoeff = design(designSpec,'equiripple','SystemObject',true);
coeffNumerictype = numerictype(fi(LPF14bitCoeff.Numerator,true,14));
LPF14bitCoeff.CoefficientsDataType = 'Custom';
LPF14bitCoeff.CustomCoefficientsDataType = numerictype(true, ...
coeffNumerictype.WordLength,coeffNumerictype.FractionLength);
measure(LPF14bitCoeff,'Arithmetic','fixed')
ans =
Sample Rate
Passband Edge
: 2 kHz
: 400 Hz
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3-dB Point
6-dB Point
Stopband Edge
Passband Ripple
Stopband Atten.
Transition Width
:
:
:
:
:
:
416.2939 Hz
428.1081 Hz
500 Hz
0.96405 dB
67.2987 dB
100 Hz
For FIR filters in general, each bit of coefficient word length provides approximately 5 dB
of stopband attenuation. Accordingly, if your filter's coefficients are always quantized to
14 bits, you can expect the minimum stopband attenuation to be only around 70 dB. In
such cases, it is more practical to design the filter with stopband attenuation less than 70
dB. Relaxing this requirement results in a design of lower order.
designSpec.Astop = 60;
LPF60dBStopband = design(designSpec,'equiripple','SystemObject',true);
LPF60dBStopband.CoefficientsDataType = 'Custom';
coeffNumerictype = numerictype(fi(LPF60dBStopband.Numerator,true,14));
LPF60dBStopband.CustomCoefficientsDataType = numerictype(true, ...
coeffNumerictype.WordLength,coeffNumerictype.FractionLength);
measure(LPF60dBStopband,'Arithmetic','fixed')
order(LPF14bitCoeff)
order(LPF60dBStopband)
ans =
Sample Rate
Passband Edge
3-dB Point
6-dB Point
Stopband Edge
Passband Ripple
Stopband Atten.
Transition Width
:
:
:
:
:
:
:
:
2 kHz
400 Hz
419.3391 Hz
432.9718 Hz
500 Hz
0.92801 dB
59.1829 dB
100 Hz
ans =
51
ans =
1-62
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Fixed-Point Filter Design in MATLAB
42
The filter order decreases from 51 to 42, implying that fewer taps are required to
implement the new FIR filter. If you still want a high minimum stopband attenuation
without compromising on the number of bits for coefficients, you must relax the other
filter design constraint: the transition width. Increasing the transition width might
enable you to get higher attenuation with the same coefficient word length. However, it is
almost impossible to achieve more than 5 dB per bit of coefficient word length, even after
relaxing the transition width.
designSpec.Astop = 80;
transitionWidth = 200;
designSpec.Fpass = centerFrequency-transitionWidth/2;
designSpec.Fstop = centerFrequency+transitionWidth/2;
LPF300TransitionWidth = design(designSpec,'equiripple', ...
'SystemObject',true);
LPF300TransitionWidth.CoefficientsDataType = 'Custom';
coeffNumerictype = numerictype(fi(LPF300TransitionWidth.Numerator, ...
true, 14));
LPF300TransitionWidth.CustomCoefficientsDataType = numerictype(true, ...
coeffNumerictype.WordLength,coeffNumerictype.FractionLength);
measure(LPF300TransitionWidth,'Arithmetic','fixed')
ans =
Sample Rate
Passband Edge
3-dB Point
6-dB Point
Stopband Edge
Passband Ripple
Stopband Atten.
Transition Width
:
:
:
:
:
:
:
:
2 kHz
350 Hz
385.4095 Hz
408.6465 Hz
550 Hz
0.74045 dB
74.439 dB
200 Hz
As you can see, increasing the transition width to 200 Hz allows 74.439 dB of stopband
attenuation with 14-bit coefficients, compared to the 67.2987 dB attained when the
transition width was set to 100 Hz. An added benefit of increasing the transition width is
that the filter order also decreases, in this case from 51 to 27.
order(LPF300TransitionWidth)
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‫‪DSP Tutorials‬‬
‫‪1‬‬
‫= ‪ans‬‬
‫‪27‬‬
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‫‪1-64‬‬
Sample Rate Conversion of Audio Signal in MATLAB and Simulink
Sample Rate Conversion of Audio Signal in MATLAB and Simulink
In this section...
“Introduction” on page 1-65
“Design and Analysis of Sample Rate Converter ” on page 1-65
“Using the Sample Rate Converter in MATLAB” on page 1-67
“Using the Sample Rate Converter in Simulink” on page 1-69
“Specifying Tolerance to Reduce Filter Order” on page 1-72
Introduction
This example shows how to use a multistage/multirate approach to sample rate
conversion between different audio rates. The example features both MATLAB and
Simulink implementations.
Digital audio recordings use many different sample rates. Examples include: 8 kHz,
11.025 kHz, 16 kHz, 22.05 kHz, 24 kHz, 44.1 kHz, 48 kHz, and 96 kHz. The lower
rates are used for speech or low fidelity audio, while the higher rates are primarily
used for high fidelity audio. Data is commonly resampled for use with different media
or equipment. When lower fidelity is acceptable, resampling can reduce data storage
requirements.
This example uses simple-to-design polyphase filters to convert a speech signal sampled
at 44.1 kHz (CD quality) to a signal sampled at 8 kHz (telephone systems).
Design and Analysis of Sample Rate Converter
You are required to specify three parameters:
• Audio input sampling frequency
• Audio output sampling frequency
• Two-sided bandwidth of interest, for example [-3600, 3600] or 7200 Hz.
inFs = 44100;
outFs = 8000;
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bw = 7200;
SRC = dsp.SampleRateConverter('Bandwidth',bw,'InputSampleRate',inFs,...
'OutputSampleRate',outFs);
Obtain information on the filters and visualize the filter responses.
info(SRC)
visualizeFilterStages(SRC)
ans =
Overall Interpolation Factor
: 80
Overall Decimation Factor
: 441
Number of Filters
: 2
Multiplications per Input Sample: 23.619048
Number of Coefficients
: 7350
Filters:
Filter 1:
dsp.FIRDecimator
- Decimation Factor
: 3
Filter 2:
dsp.FIRRateConverter - Interpolation Factor: 80
- Decimation Factor
: 147
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Sample Rate Conversion of Audio Signal in MATLAB and Simulink
The sample rate converter is a cascade of two stages: a FIR decimator followed by a
FIR fractional rate converter. The sample rate converter preserves the band of interest
between 0 and 3600 Hz, and suppresses the spectral replicas outside that band.
Using the Sample Rate Converter in MATLAB
To execute the following example, change to a directory where you have write permission.
Read in an audio file sampled at 44100 Hz in frames of 441 samples at a time. Use a
sample-rate converter to lowpass filter the input and convert the sample rate to 8000 Hz.
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View the short-time Fourier transform (spectrogram) of the sample-rate converter output
in a spectrum analyzer and write the output to a FLAC file in the current directory.
afr = dsp.AudioFileReader('dft_speech44100.wav','SamplesPerFrame',441);
afw = dsp.AudioFileWriter('dft_speech8000.flac','SampleRate',outFs,...
'FileFormat','FLAC','DataType','int16');
specana = dsp.SpectrumAnalyzer('SpectrumType','Spectrogram',...
'SampleRate',outFs,...
'PlotAsTwoSidedSpectrum',false,...
'FrequencyResolutionMethod', 'WindowLength',...
'WindowLength',441, ...
'FFTLengthSource','Property',...
'FFTLength',512,...
'OverlapPercent',25);
while ~isDone(afr)
audio = step(afr);
audioconvert = step(SRC, audio);
step(specana,audioconvert);
step(afw, audioconvert);
end
release(afr);
release(afw);
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Sample Rate Conversion of Audio Signal in MATLAB and Simulink
Using the Sample Rate Converter in Simulink
You can use the sample rate converter in Simulink with a MATLAB System block. The
model ex_audio_src, which is a Simulink version of “Using the Sample Rate Converter
in MATLAB”, is provided for convenience. The model writes an audio file output so make
sure you run the example from a folder where you have write permission.
open_system('ex_audio_src');
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DSP Tutorials
To run the model, click the Run button on the model toolbar or enter the following
command.
sim('ex_audio_src')
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Sample Rate Conversion of Audio Signal in MATLAB and Simulink
The model reads in a speech signal sampled at 44.1 kHz. The sample rate is converted to
8 kHz and the short-time Fourier transform (spectrogram) of the output is displayed in
a spectrum analyzer. A FLAC file (dft_speech8000.flac) is written containing the output
sampled at 8 kHz. You can verify the sample rate of the output file after you run the
model with the following code.
audioinfo('dft_speech8000.flac')
ans =
Filename: 'tmp/\dft_speech8000.flac'
CompressionMethod: 'FLAC'
NumChannels: 1
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SampleRate: 8000
TotalSamples: 41280
Duration: 5.1600
Title: []
Comment: []
Artist: []
BitsPerSample: 16
Specifying Tolerance to Reduce Filter Order
If you do not have an exact requirement for the output sample rate, you can allow for a
certain tolerance by setting the ‘OutputRateTolerance’ property to a non-zero value.
Setting a non-zero tolerance for the output rate can often result in a filter design with
fewer coefficients. Compare the filter design with and without a specified output rate
tolerance.
tol = 0.01;
SRCwithTolerance = dsp.SampleRateConverter('Bandwidth', bw, ...
'InputSampleRate', inFs, ...
'OutputSampleRate', outFs, ...
'OutputRateTolerance', tol);
info(SRC)
info(SRCwithTolerance)
ans =
Overall Interpolation Factor
: 80
Overall Decimation Factor
: 441
Number of Filters
: 2
Multiplications per Input Sample: 23.619048
Number of Coefficients
: 7350
Filters:
Filter 1:
dsp.FIRDecimator
- Decimation Factor
: 3
Filter 2:
dsp.FIRRateConverter - Interpolation Factor: 80
- Decimation Factor
: 147
ans =
Output Sample Rate Tolerance
Adjusted Output Sample Rate
1-72
: 1.000000 %
: 8018.181818
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Sample Rate Conversion of Audio Signal in MATLAB and Simulink
Overall Interpolation Factor
: 2
Overall Decimation Factor
: 11
Number of Filters
: 1
Multiplications per Input Sample: 45.363636
Number of Coefficients
: 499
Filters:
Filter 1:
dsp.FIRRateConverter - Interpolation Factor: 2
- Decimation Factor
: 11
With a 0.01 tolerance, the number of coefficients of the sample rate converter reduces
from 7350 to 499. One of the stages in the cascade is eliminated and the interpolation
and decimation factors are reduced. Using this tolerance, the output sample rate is
8018.18 Hz, which may be an acceptable approximation in most cases to the desired rate
of 8000 Hz.
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Visualizing Multiple Signals Using Logic Analyzer
This example shows how to visualize multiple signals of a programmable FIR filter using
a logic analyzer. For more information on the model used in this example and how to
configure the model to generate HDL code, see “Generate HDL Code for Programmable
FIR Filter”.
Model Programmable FIR Filter
Open the example model.
modelname = 'dspprogfirhdl';
open_system(modelname);
Consider two FIR filters, one with a lowpass response and the other with a highpass
response. The coefficients can be specified using the InitFcn* callback function. To
specify the callback, select File > Model Properties > Model Properties. In the dialog
box, in the Callbacks tab, select InitFcn*.
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Visualizing Multiple Signals Using Logic Analyzer
The Programmable FIR via Registers block loads the lowpass coefficients from the Host
Behavioral Model block and processes the input chirp samples first. The block then loads
the highpass coefficients and processes the same chirp samples again.
Open the Programmable FIR via Registers block.
systemname = [modelname '/Programmable FIR via Registers'];
open_system(systemname);
Simulation
Run the example model.
sim(modelname)
Open the scope.
open_system([modelname '/Scope']);
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Compare the DUT (Design under Test) output with the reference output.
Use the Logic Analyzer
The logic analyzer enables you to view multiple signals in one window. It also makes it
easy to detect signal transitions.
The signals of interest (input coefficient, write address, write enable, write
done, filter in, filter out, reference out, and error) have been logged to a
Simulink.SimulationData.Dataset named dspprogfirhdl_logsout in the
MATLAB workspace.
The helper function dspprogfirhdlReorderDataset creates a waveform for every
input provided in the dspprogfirhdl_logsout data set. Tto make the default order of
display more meaningful, the data set is reordered to make the coefficient signals appear
first and the data signals next. The error values are converted to logical values.
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Visualizing Multiple Signals Using Logic Analyzer
logsout_r = dspprogfirhdlReorderDataset(dspprogfirhdl_logsout);
Display the data in the logic analyzer. Use the helper function
analyzeLogicFromSimulink, which launches a logic analyzer, adds in a waveform for
every input, labels the waveform, and displays the data. analyzeLogicFromSimulink
returns a handle to the logic analyzer that you can use to modify the display.
analyzer = analyzeLogicFromSimulink(logsout_r);
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Modify the Display
In the logic analyzer, you can modify the height of all the displayed channels, the spacing
between the channels, and the time span of the display.
analyzer.DisplayChannelSpacing = 2;
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Visualizing Multiple Signals Using Logic Analyzer
analyzer.DisplayChannelHeight
analyzer.TimeSpan = 12;
= 2;
You can also control the display on a per-waveform or per-divider basis. To
modify an individual waveform or divider, use the tag associated with it. You
can obtain the tag associated with a waveform or divider as the return value
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1-79
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of addWave and addDivider, or you can get all the tags for the waveforms and dividers
using the getDisplayChannelTags method.
Get the tags for all the displayed waveforms.
displayTags = analyzer.getDisplayChannelTags;
View the write address (second waveform in the display) in decimal mode.
modifyDisplayChannel(analyzer, 'DisplayChannelTag', displayTags{2}, ...
'Radix', 'Signed decimal');
1-80
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Visualizing Multiple Signals Using Logic Analyzer
Another useful mode of visualization in the logic analyzer is the analog format. View the
Filter In, Filter Out, and Ref Out signals in analog format.
modifyDisplayChannel(analyzer, 'DisplayChannelTag', displayTags{5}, ...
'Format', 'Analog');
modifyDisplayChannel(analyzer, 'DisplayChannelTag', displayTags{6}, ...
'Format', 'Analog');
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modifyDisplayChannel(analyzer, 'DisplayChannelTag', displayTags{7}, ...
'Format', 'Analog');
analyzer.TimeSpan = 500;
You can also add dividers and waveforms. By default, a new waveform or divider is
added to the bottom of the display. If you want, you can pass in the display channel while
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Visualizing Multiple Signals Using Logic Analyzer
adding in the waveform or divider. You can also move the waveform or divider after it
has been added to the display.
Add dividers for the coefficient and data signals. The divider for the coefficient signals
is set to be shown in Display Channel 1. The divider for the data signals is added to the
bottom of the display.
addDivider(analyzer, 'DisplayChannel', 1, 'Name', 'Coeff');
divTagData = addDivider(analyzer, 'Name', 'Data');
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DSP Tutorials
Increase the size of the window so that all the waveforms and dividers are visible.
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Visualizing Multiple Signals Using Logic Analyzer
pos = analyzer.Position;
analyzer.Position = [pos(1) pos(2) pos(3) pos(4)+100];
Using the tag for a given waveform or divider, you can use moveDisplayChannel to
move it to the display channel of your choice.
Move the data signal divider to display channel 6.
moveDisplayChannel(analyzer, 'DisplayChannelTag', divTagData, 'DisplayChannel', 6);
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DSP Tutorials
You can also operate on individual channels by right-clicking the channel name.
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Visualizing Multiple Signals Using Logic Analyzer
See dsp.LogicAnalyzer for more details.
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DSP Tutorials
Signal Visualization and Measurements in MATLAB
This example shows how to visualize and measure signals in the time and frequency
domain in MATLAB using a time scope and spectrum analyzer. This example does not
demonstrate the full capabilities of the time scope or spectrum analyzer. To learn more
about the measurement capabilites of the time scope, see the Simulink example Time
Scope Measurements. To learn more about the use of measurements with the spectrum
analyzer, see the Simulink example Spectrum Analyzer Measurements.
Signal Visualization in Time and Frequency Domains
Create a sine wave with a frequency of 100 Hz sampled at 1000 Hz. Generate five
seconds of the 100-Hz sine wave with additive white Gaussian noise with mean 0 and
standard deviation 0.05. The signal is processed in one-second frames. Send the signal to
a time scope and spectrum analyzer for display and measurement.
SampPerFrame = 1000;
Fs = 1000;
SW = dsp.SineWave('Frequency', 100, ...
'SampleRate', Fs, 'SamplesPerFrame', SampPerFrame);
TS = dsp.TimeScope('SampleRate', Fs, 'TimeSpan', 0.1, ...
'YLimits', [-2, 2], 'ShowGrid', true);
SA = dsp.SpectrumAnalyzer('SampleRate', Fs);
tic;
while toc < 5
sigData = step(SW) + 0.05*randn(SampPerFrame,1);
step(TS, sigData);
step(SA, sigData);
end
release(TS);
release(SA);
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Signal Visualization and Measurements in MATLAB
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DSP Tutorials
Time-Domain Measurements
Using the time scope, you can make a number of signal measurements.
The following measurements are available:
• Cursor Measurements - puts screen cursors on all scope displays.
• Signal Statistics - displays maximum, minimum, peak-to-peak difference, mean,
median, RMS values of a selected signal, and the times at which the maximum and
minimum occur.
• Bilevel Measurements - displays information about a selected signal's transitions,
overshoots or undershoots, and cycles.
• Peak Finder - displays maxima and the times at which they occur.
You can enable and disable these measurements from the time scope toolbar or from the
Tools > Measurements menu.
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Signal Visualization and Measurements in MATLAB
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To illustrate the use of measurements in the time scope, simulate an ECG signal. Use
the ecg function to generate 2700 samples of the signal. Use a Savitzky-Golay filter to
smooth the signal and periodically extend the data to obtain approximately 11 periods.
x = 3.5*ecg(2700).';
y = repmat(sgolayfilt(x,0,21),[1 13]);
sigData = y(1:30000)';
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Signal Visualization and Measurements in MATLAB
Display the signal in the time scope and use the Peak Finder, Cursor and Signal
Statistics measurements. Assume a sample rate of 4 kHz.
TS_ECG = dsp.TimeScope('SampleRate', 4000, ...
'TimeSpanSource', 'Auto', 'ShowGrid', true);
step(TS_ECG, sigData);
TS_ECG.YLimits = [-4, 4];
release(TS_ECG);
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Peak Measurements
Enable Peak Measurements by clicking the corresponding toolbar icon or by clicking
the Tools > Measurements > Peak Finder menu item. Click Settings in the Peak
Finder panel to expand the Settings pane. Enter 10 for Max Num of Peaks and press
Enter. The time scope displays in the Peaks pane a list of 10 peak amplitude values and
the times at which they occur.
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Signal Visualization and Measurements in MATLAB
There is a constant time difference of 0.675 seconds between each heartbeat. Therefore,
the heart rate of the ECG signal is given by the following equation:
Cursor Measurements
Enable Cursor Measurements by clicking the corresponding toolbar icon or by
clicking the Tools > Measurements > Cursor Measurements menu item. The Cursor
Measurements panel opens and displays two cursors in the time scope. You can drag
the cursors and use them to measure the time between events in the waveform. In the
following figure, cursors are used to measure the time interval between peaks in the ECG
waveform. The
measurement in the Cursor Measurements panel demonstrates that
the time interval between the two peaks is 0.675 seconds corresponding to a heart rate of
1.482 Hz or 88.9 beats/min.
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Signal Statistics and Bilevel Measurements
You can also select Signal Statistics and Bilevel Measurements from the Tools >
Measurements menu. Signal Statistics can be used to determine the signal's minimum
and maximum values as well as other metrics like the peak-to-peak, mean, median, and
RMS values. Bilevel Measurements can be used to determine information about rising
and falling transitions, transition aberrations, overshoot and undershoot information,
pulse width, and duty cycle.
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Signal Visualization and Measurements in MATLAB
Frequency-Domain Measurements
This section explains how to make frequency domain measurements with the spectrum
analyzer.
The spectrum analyzer provides the following measurements:
• Cursor Measurements - places cursors on the spectrum display.
• Peak Finder - displays maxima and the frequencies at which they occur.
• Channel Measurements - displays occupied bandwidth and ACPR channel
measurements.
• Distortion Measurements - displays harmonic and intermodulation distortion
measurements.
• CCDF Measurements - displays complimentary cumulative distribution function
measurements.
You can enable and disable these measurements from the spectrum analyzer toolbar or
from the Tools > Measurements menu.
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Signal Visualization and Measurements in MATLAB
Distortion Measurements
To illustrate the use of measurements with the spectrum analyzer, create a 2.5 kHz
sine wave sampled at 48 kHz with additive white Gaussian noise. Evaluate a high-order
polynomial (9th degree) at each signal value to model non-linear distortion. Display the
signal in a spectrum analyzer.
Fs = 48e3;
SW = dsp.SineWave('Frequency', 2500, ...
'SampleRate', Fs, 'SamplesPerFrame', SampPerFrame);
SA_Distortion = dsp.SpectrumAnalyzer('SampleRate', Fs, ...
'PlotAsTwoSidedSpectrum', false);
y = [1e-6 1e-9 1e-5 1e-9 1e-6 5e-8 0.5e-3 1e-6 1 3e-3];
tic;
while toc < 5
x = step(SW) + 1e-8*randn(SampPerFrame,1);
sigData = polyval(y, x);
step(SA_Distortion, sigData);
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end
clear SA_Distortion;
Enable the harmonic distortion measurements by clicking the corresponding icon in
the toolbar or by clicking the Tools > Measurements > Distortion Measurements
menu item. In the Distortion Measurements, change the value for Num. Harmonics
to 9 and check the Label Harmonics checkbox. In the panel, you see the value of the
fundamental close to 2500 Hz and 8 harmonics as well as their SNR, SINAD, THD and
SFDR values, which are referenced with respect to the fundamental output power.
Peak Finder
You can track time-varying spectral components by using the Peak Finder measurement
dialog. You can show and optionally label up to 100 peaks. You can invoke the Peak
Finder dialog from the Tools > Measurements > Peak Finder menu item, or by
clicking the corresponding icon in the toolbar.
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Signal Visualization and Measurements in MATLAB
To illustrate the use of Peak Finder, create a signal consisting of the sum of three
sine waves with frequencies of 5, 15, and 25 kHz and amplitudes of 1, 0.1, and 0.01
respectively. The data is sampled at 100 kHz. Add
white Gaussian noise
to the sum of sine waves and display the one-sided power spectrum in the spectrum
analyzer.
Fs = 100e3;
SW1 = dsp.SineWave(1e0,
5e3, 0, 'SampleRate', Fs, 'SamplesPerFrame', SampPerFrame);
SW2 = dsp.SineWave(1e-1, 15e3, 0, 'SampleRate', Fs, 'SamplesPerFrame', SampPerFrame);
SW3 = dsp.SineWave(1e-2, 25e3, 0, 'SampleRate', Fs, 'SamplesPerFrame', SampPerFrame);
SA_Peak = dsp.SpectrumAnalyzer('SampleRate', Fs, 'PlotAsTwoSidedSpectrum', false);
tic;
while toc < 5
sigData = step(SW1) + step(SW2) + step(SW3) + 1e-4*randn(SampPerFrame,1);
step(SA_Peak, sigData);
end
clear SA_Peak;
Enable the Peak Finder to label the three sine wave frequencies. The frequency values
and powers in dBm are displayed in the Peak Finder panel. You can increase or
decrease the maximum number of peaks, specify a minimum peak distance, and change
other settings from the Settings pane in the Peak Finder Measurement panel.
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Filter Frames of a Noisy Sine Wave Signal using Testbench Generator
Filter Frames of a Noisy Sine Wave Signal using Testbench
Generator
This example shows how to use the DSP Testbench Generator app to generate DSP
algorithm testbenches. The DSP algorithm generated in this example is similar to the
algorithm in the Filter Frames of a Noisy Sine Wave Signal in MATLAB example. That
example filters a noisy sine wave signal using a FIR lowpass filter and displays the
power spectrum using a spectrum analyzer.
Testbench Generator Example App
The DSP Testbench Generator app helps you develop and test streaming signal
processing algorithms by enabling you to quickly generate testbenches. To launch
the Testbench Generator, enter testbenchGeneratorExampleApp at the MATLAB
command prompt. The command launches an interface through which you can:
1
Select a set of sources and sinks.
2
Enter the function name of your custom User Algorithm.
3
Customize the properties of each of the added sources and sinks.
Each source is treated as a separate input to your algorithm, but you can associate more
than one sink with the same output from your algorithm.
testbenchGeneratorExampleApp
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DSP Tutorials
Inputs - Sine Waves and White Noise
By default, the testbench generator selects a two-channel sine wave source and a white
Gaussian noise source. The two channels of the sine wave source have frequencies of 1
kHz and 10 kHz. The sampling frequency is 44.1 kHz. The white Gaussian noise input
has mean 0 and standard deviation 0.1. The data is processed in frames of 1024 samples.
To add more sources, use the list under Add a new source to the above list of inputs
to select one of the supported sources. Alternatively, you can add your custom System
object source by selecting Custom System object from the list and clicking Add. The
added source appears in the list of inputs.
After adding a source, you can select it and click Configure to change the selected
source's properties.
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Filter Frames of a Noisy Sine Wave Signal using Testbench Generator
User Algorithm - Lowpass Filter
The user algorithm in this example is a function hTestbenchLowpass. You can view the
code for this function by entering
edit hTestbenchLowpass
at the MATLAB command prompt. hTestbenchLowpass accepts two inputs, lowpass
filters the sum of those two inputs, and returns the filtered signal.
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DSP Tutorials
hTestbenchLowpass uses a constrained equiripple FIR filter design with a cutoff
frequency of 5 kHz. The ripples in the passband and stopband are equal to 0.05 and
0.001.
Filtering is performing using dsp.FIRFilter, which is optimized for streaming.
Output
The power spectrum of the output is displayed on a spectrum analyzer in dBm. You can
add more sinks to visualize or post-process the outputs. Similar to inputs, you can use
the list under Add a new sink to the above list of outputs to add a new sink, and
click Configure to modify the properties of the selected sink.
You can associate a single output from the user algorithm with one or more sinks. For
example, you can visualize the same output signal with both a time scope and spectrum
analyzer. To do this, add the required sinks and make sure you associate all of the sinks
to desired output from the user algorithm by changing the value under the Associate
selected sink with list.
Generate Code and Simulate
After you add and configure the sources and sinks and enter a function name in the User
Algorithm text box, the testbench generator is ready to generate testbench MATLAB
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Filter Frames of a Noisy Sine Wave Signal using Testbench Generator
code. To generate code, select Generate Code > Generate MATLAB Code. A new
untitled document opens in the MATLAB editor containing the generated testbench code.
You can edit the generated code to customize it before executing it. For the default
example, the generated code is included below. Executing this testbench code, you see
in the spectrum analyzer that the frequencies above 4 kHz in the source signal are
attenuated. The resulting signal maintains the peak at 1 kHz because 1 kHz falls in the
passband of the lowpass filter.
% DSP Testbench script
% Generated by DSP Testbench Generator Example App
% Initialization
maxIterations = 10000;
% Construct sources (for all inputs)
src1 = dsp.SineWave('Frequency',[1000 10000], ...
'SampleRate',44100, ...
'SamplesPerFrame',1024);
% Construct sinks (for all outputs)
sink1 = dsp.SpectrumAnalyzer('SampleRate',44100, ...
'PlotAsTwoSidedSpectrum',false, ...
'ShowLegend',true);
% Stream
clear hTestbenchLowpass;
for i = 1:maxIterations
% Sources
in1 = step(src1);
in2 = 0.1*randn(1024,2);
% User Algorithm
out1 = hTestbenchLowpass(in1,in2);
% Sinks
step(sink1,out1);
end
% Clean up
release(src1);
release(sink1);
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DSP Tutorials
More Customizations in Testbench Generator
The testbench generator offers additional top-level customizations, which you can
configure using the Testbench Generator Settings dialog box. To open this dialog box,
select Generate Code > Testbench Generator Settings ....
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Filter Frames of a Noisy Sine Wave Signal using Testbench Generator
You can also tune some of the parameters used in your algorithm during testbench
execution. To use the Parameter Tuning UI, check the Enable parameter tuning
check box under the User Algorithm and click Edit parameters table to add the
details of your tunable parameters before you generate testbench code. Also, make sure
that your user algorithm handles parameter tuning during execution. See the MATLAB
code for hTestbenchVariableBandwithFIR for an example of how to make your user
algorithm work with parameter tuning.
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Create Composite System object
This example shows how to create a System object composed of other System objects.
In this example, build a multi-notch filter using two dsp.NotchPeakFilter System
objects. Multi-notch filters are used in many applications. Examples include audio
phasers and applications that require the removal of multiple interfering tones.
Create MultiNotchFilter
“Create Moving Average System object” on page 1-40 explains in detail how to write a
System object using a template file. In this example, the entire System object is provided
for convenience in dspdemo.MultiNotchFilter. To view the MATLAB code, at the
command prompt enter:
edit dspdemo.MultiNotchFilter
dspdemo.MultiNotchFilter has five public properties. Public properties are
accessible to every user. The first property, SampleRate, is a nontunable property.
Nontunable properties cannot change when the filter is locked (after you use step
on the filter). The remaining properties, CenterFrequency1, CenterFrequency2,
QualityFactor1, and QualityFactor2 control settings in the two notch filters
contained in dspdemo.MultiNotchFilter. These four properties are tunable. You can
change the values of these properties while streaming data.
Contain System Objects as Private Properties
dspdemo.MultiNotchFilter uses dsp.NotchPeakFilter to design the two notch
filters. The notch filters are created in the class constructor.
methods
function obj = MultiNotchFilter(varargin)
% Construct two notch filters with default values
obj.NotchFilter1 = dsp.NotchPeakFilter(...
'Specification', 'Quality factor and center frequency',...
'CenterFrequency',400);
obj.NotchFilter2 = dsp.NotchPeakFilter(...
'Specification', 'Quality factor and center frequency',...
'CenterFrequency',800);
% Support name-value pair arguments
setProperties(obj,nargin,varargin{:});
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Create Composite System object
end
The ability to create more than one instance of a System object and having each instance
manage its own state is one of the biggest advantages of using System objects over
functions. The private properties NotchFilter1 and NotchFilter2 are used to store
the two notch filters.
properties (Access=private)
% This example class contains two notch filters (more can be added
% in the same way)
NotchFilter1
NotchFilter2
end
Work with Dependent Properties
The SampleRate property as well as the remaining four public properties are
implemented as dependent properties in this example. Whenever you assign a value to
one of the dependent properties, the value is set in the corresponding single-notch filter.
When you read one of the dependent properties, the value is read from the corresponding
single-notch filter. Find the following code block in dspdemo.MultiNotchFilter.
properties (Dependent)
%CenterFrequency1 Center frequency of first notch
%
Specify the first notch center frequency as a finite positive
%
numeric scalar in Hertz. The default is 400 Hz. This property
%
is tunable.
CenterFrequency1;
%QualityFactor1 Quality factor of first notch
%
Specify the quality factor (Q factor) for the first notch
%
filter. The default value is 5. This property is tunable.
QualityFactor1;
%CenterFrequency2 Center frequency of second notch
%
Specify the second notch center frequency as a finite positive
%
numeric scalar in Hertz. The default is 800 Hz. This property
%
is tunable.
CenterFrequency2;
%QualityFactor2 Quality factor of second notch
%
Specify the quality factor (Q factor) for the first notch
%
filter. The default value is 5. This property is tunable.
QualityFactor2;
end
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DSP Tutorials
Use the Multi-Notch Filter - Initialization
To use dspdemo.MultiNotchFilter, initialize the filter and any other required
components. In this example, initialize an audio file reader, a multi-notch filter, a
transfer function estimator, an array plotter, and an audio player.
FrameSize = 1024;
AFR = dsp.AudioFileReader('guitar10min.ogg','SamplesPerFrame',FrameSize);
Fs = AFR.SampleRate;
MNF = dspdemo.MultiNotchFilter('SampleRate',Fs);
TFE = dsp.TransferFunctionEstimator(...
'FrequencyRange','onesided','SpectralAverages',5);
AP = dsp.ArrayPlot('PlotType','Line','YLimits',[-85 15],...
'SampleIncrement',Fs/FrameSize);
P
= dsp.AudioPlayer;
Use the Multi-Notch Filter - Streaming
To illustrate the tunability of the two notch filter center frequencies, vary the center
frequencies sinusoidally in a loop. The starting center frequencies are 500 and 2000
Hz. The first center frequency oscillates over the range [100, 900] Hz with a frequency
of 0.2 Hz. The second center frequency oscillates over the range [1200, 2800] Hz with
a frequency of 0.5 Hz. Because CenterFrequency1 and CenterFrequency2 are
dependent properties, modifying their values in the loop changes the center frequencies
in the two notch filters contained in dspdemo.MultiNotchFilter. To visualize the
multi-notch filter, estimate and plot the transfer function continuously. The quality
factors remain constant. The simulation runs for 20 seconds.
MNF.QualityFactor1 = .5;
MNF.QualityFactor2 = 1;
f0 = 0.2;
f1 = 0.5;
k = 0;
tic,
while toc <20
x = step(AFR);
t = k*FrameSize/Fs;
k = k+1;
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Create Composite System object
MNF.CenterFrequency1 = 500 + 400*sin(2*pi*f0*t);
MNF.CenterFrequency2 = 2000 + 800*sin(2*pi*f1*t);
CF1(k) = MNF.CenterFrequency1;
CF2(k) = MNF.CenterFrequency2;
y = step(MNF,x);
H = step(TFE,x(:,1),y(:,1));
magdB = 20*log10(abs(H));
step(AP,magdB);
step(P,y);
end
Execute this code to show how the two notch center frequencies varied over the
simulation.
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DSP Tutorials
subplot(2,1,1)
plot(CF1);
title('Center Frequency 1');
ylabel('Notch CF (Hz)');
subplot(2,1,2)
plot(CF2);
title('Center Frequency 2');
ylabel('Notch CF (Hz)');
xlabel('Iteration')
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Measure Audio Latency in MATLAB and Simulink
Measure Audio Latency in MATLAB and Simulink
This example shows how to measure the latency introduced in audio signals when using
the audio player and audio recorder in MATLAB or Simulink. The procedure presented
here allows you to tune certain parameters that affect latency and observe the effect
in a simple measurement. The specific parameters are discussed in detail later in the
example.
Introduction
In general terms, latency is defined as the time it takes for the audio to be heard or
recorded after it has been played. There are multiple factors that influence latency. For
example:
1
Hardware: CPU, memory, and sound card.
2
Audio drivers that communicate with the system's sound card.
3
Algorithmic complexity of any audio processing between playback and recording.
4
Software used to process the audio: MATLAB or Simulink in this example.
This example shows you how to measure the overall latency with a focus on what
parameters determine the latency effect of using MATLAB or Simulink. There are two
variants of this example: one uses the audio System objects in MATLAB and the other
uses the Simulink audio input and output blocks.
Set-up Experiment
In this example, measure the latency by playing an audio signal through
dsp.AudioPlayer (or the To Audio Device block), recording the audio through
dsp.AudioRecorder (or the From Audio Device block), and measuring the delay by
the cross-correlation of the two signals. No other processing is done on the audio signal.
A loopback cable is used to physically connect the audio-out port of the sound card to its
audio-in port. The set-up is shown in the following illustration.
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DSP Tutorials
The set-up for another common application is to record live audio with a microphone,
process the audio on the computer, and play the audio back in a streaming fashion. In
that set-up, the hardware interface latency is the same as the set-up involving the audio
System objects or blocks: a sum of latencies due to the player and the recorder.
Measure Latency
The audioLatencyMeasurementBasicExampleApp function measures the latency for
the set-up where an audio signal is played and recorded with System objects or Simulink
blocks. Inputs to this function are:
• plotFlag: Set this to true to visualize the input to the dsp.AudioPlayer object and
the output from the dsp.AudioRecorder object.
• frameSize: Number of audio samples that constitute a single frame. This sets the
SamplesPerFrame property of the dsp.AudioFileReader object.
• bufferSize: The value of this parameter is copied to the BufferSize property of the
dsp.AudioPlayer and the dsp.AudioRecorder System objects.
• useSimulink: Set this to true to use the Simulink model
audiolatencybasicmeasurement.slx to measure the latency.
Most of these inputs are parameters that affect audio latency in MATLAB or Simulink.
You can try different values and measure the latency for each set. The various sections in
the MATLAB code for the audioLatencyMeasurementBasicExampleApp function are:
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Measure Audio Latency in MATLAB and Simulink
1
Initialization: The default values for the input parameters are assigned. The audio
System objects are created with appropriate parameter values.
2
Loopback simulation: For a duration of 10 seconds, audio is read from a
file and sent to the computer's audio-out port through dsp.AudioPlayer.
Through the loopback cable and audio-in port, the audio is read in using
the dsp.AudioRecorder object. When the useSimulink input is
true, the loopback simulation is performed through the Simulink model
audiolatencybasicmeasurement.slx. The signal read from the file and the
recorded signal are stored in a signal sink.
3
Cross-correlation: Using the xcorr function, the cross-correlation sequence is
computed between the audio signal sent to the player and the one received by the
recorder. The received signal lags the played signal. The time shift corresponding to
the maximum value of the cross-correlation sequence is the latency. Additionally, if
the plotFlag input is true, the two audio signals are plotted in a figure so you can
observe the lag.
If the queue is overrun or underrun, a corresponding message is displayed in the
command window for the MATLAB version of this example. For the Simulink version,
you must monitor the logged variables APunderrun and ARoverrun to determine
overrun or underrun.
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Parameters in MATLAB/Simulink Affecting Latency
Frame size
This is not an explicit property of the audio player or audio recorder System objects. The
frame size is the number of samples passed to those objects in each call to their step
methods. The bigger the frame size, the longer you must wait to collect the samples.
BufferSize
The BufferSize is a property of both the dsp.AudioPlayer and dsp.AudioRecorder
System objects. The buffer size value is half the size of the sound card buffer. The smaller
the BufferSize, the quicker you can send samples to the sound card. However, there is a
trade-off because a small buffer can also easily underrun (for the player) or overrun (for
the recorder).
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Measure Audio Latency in MATLAB and Simulink
QueueDuration
Both dsp.AudioPlayer and dsp.AudioRecorder System objects have the property,
QueueDuration. The queue is a storage space between the System object and the
sound card buffer. The main use of QueueDuration is to match the throughput of the
algorithm in MATLAB and the device. A proper setting for QueueDuration can help
prevent buffer underruns and overruns. QueueDuration should be set to a value as
small as possible to maintain acceptable latency while not introducing glitches in the
audio. The optimal value for the queue size is typically twice the size of the audio frame.
Based on this, the QueueDuration is kept to a value of (2*FrameSize+1)/SampleRate.
The same parameters are also applicable in the Simulink version that uses audio
blocks instead of System objects. More details about BufferSize and QueueDuration
can be found in the documentation for the System objects dsp.AudioPlayer and
dsp.AudioRecorder, and the blocks To Audio Device and From Audio Device.
Sound Card and Drivers
Additionally, latency is affected by the sound card and drivers. For low-latency
applications, use a low-latency sound card. Drivers can also have an impact on latency.
For example, on the Windows™ platform, DirectSound creates an additional virtual
device layer between the application and the sound card, increasing latency. On the
other hand, ASIO™ drivers communicate with the device directly, which helps to reduce
delays.
Obtain Parameter Values for Low Latency
The latency of your system can depend on multiple parameters. In order to discover the
set of parameter values that provides the smallest latency, first fix an audio frame size.
Typically, this is 1024 or 512 samples for a sample rate of 44.1 kHz. Initially set the
buffer size the same value as the frame size and keep reducing it until the queue starts to
overrun or underrun. The smallest buffer size that satisfies this criterion is generally 64
or 128 samples for an audio frame size of 512 or 1024 at 44.1 kHz. Repeat the experiment
by starting with a smaller frame size.
Sample Results
Here are some results obtained by running
audioLatencyMeasurementBasicExampleApp with different input parameters
on a Mac OS X 10.8.5 system with a 3.4 GHz Core i7 processor and 16 GB of RAM.
Measurements were made using the built in audio I/O. The audio is stereo sampled at
44.1 kHz.
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DSP Tutorials
Decrease in latency on decreasing buffer size for constant frame size:
latency = audioLatencyMeasurementBasicExampleApp(0,1024,1024,0);
Result: Latency of 43 ms
latency = audioLatencyMeasurementBasicExampleApp(0,1024,512,0);
Result: Latency of 34 ms
latency = audioLatencyMeasurementBasicExampleApp(0,1024,64,0);
Result: Latency of 14.3 ms
Decreasing the frame size further:
latency = audioLatencyMeasurementBasicExampleApp(0,512,512,0);
Result: Latency of 28 ms
latency = audioLatencyMeasurementBasicExampleApp(0,512,64,0);
Result: Latency of 13.9 ms
Running the Simulink version:
latency = audioLatencyMeasurementBasicExampleApp(0,512,64,1);
Result: Latency of 13.9 ms
Plotting the player and recorder audio signals along with latency
measurement:
latency = audioLatencyMeasurementBasicExampleApp(1,512,64,0);
Result: Latency of 13.9 ms.
You can also zoom into the plot to see the delay between the player and recorder
waveforms.
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Measure Audio Latency in MATLAB and Simulink
Summary
This example discussed the concept of latency in audio signals and demonstrated a
way in MATLAB and Simulink to quantify latency. The example also described various
parameters that influence audio latency. Some sample results obtained on a specific
computer were presented. Note that results vary based on machine configuration. You
can follow the advice in this example and experiment with different values to find the
combination that best suits your system and application.
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2
Input, Output, and Display
Learn how to input, output and display data and signals with DSP System Toolbox™.
• “Discrete-Time Signals” on page 2-2
• “Continuous-Time Signals” on page 2-11
• “Create Sample-Based Signals” on page 2-12
• “Sample-Based Row Vector Processing Changes” on page 2-17
• “Create Frame-Based Signals” on page 2-19
• “Create Multichannel Sample-Based Signals” on page 2-26
• “Create Multichannel Frame-Based Signals” on page 2-32
• “Deconstruct Multichannel Sample-Based Signals” on page 2-36
• “Deconstruct Multichannel Frame-Based Signals” on page 2-43
• “Import and Export Sample-Based Signals” on page 2-52
• “Import and Export Frame-Based Signals” on page 2-64
• “Musical Instrument Digital Interface” on page 2-72
• “Display Time-Domain Data” on page 2-77
• “Display Frequency-Domain Data in Spectrum Analyzer” on page 2-93
• “Visualize Central Limit Theorem in Array Plot” on page 2-100
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2
Input, Output, and Display
Discrete-Time Signals
In this section...
“Time and Frequency Terminology” on page 2-2
“Recommended Settings for Discrete-Time Simulations” on page 2-3
“Other Settings for Discrete-Time Simulations” on page 2-6
Time and Frequency Terminology
Simulink models can process both discrete-time and continuous-time signals. Models
built with DSP System Toolbox software are often intended to process discrete-time
signals only. A discrete-time signal is a sequence of values that correspond to particular
instants in time. The time instants at which the signal is defined are the signal's sample
times, and the associated signal values are the signal's samples. Traditionally, a discretetime signal is considered to be undefined at points in time between the sample times. For
a periodically sampled signal, the equal interval between any pair of consecutive sample
times is the signal's sample period, Ts. The sample rate, Fs, is the reciprocal of the sample
period, or 1/Ts. The sample rate is the number of samples in the signal per second.
The 7.5-second triangle wave segment below has a sample period of 0.5 second,
and sample times of 0.0, 0.5, 1.0, 1.5, ...,7.5. The sample rate of the sequence is
therefore 1/0.5, or 2 Hz.
A number of different terms are used to describe the characteristics of discrete-time
signals found in Simulink models. These terms, which are listed in the following table,
are frequently used to describe the way that various blocks operate on sample-based and
frame-based signals.
Term
Symbol
Units
Notes
Sample period
Ts
Tsi
Seconds
The time interval between consecutive samples in a
sequence, as the input to a block (Tsi) or the output
from a block (Tso).
2-2
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Discrete-Time Signals
Term
Symbol
Tso
Units
Notes
Frame period
Tf
Tfi
Tfo
Seconds
The time interval between consecutive frames in a
sequence, as the input to a block (Tfi) or the output
from a block (Tfo).
Signal period
T
Seconds
The time elapsed during a single repetition of a
periodic signal.
Sample frequency Fs
Hz (samples
per second)
The number of samples per unit time, Fs = 1/Ts.
Frequency
Hz (cycles per The number of repetitions per unit time of a periodic
second)
signal or signal component, f = 1/T.
f
Nyquist rate
Hz (cycles per The minimum sample rate that avoids aliasing,
second)
usually twice the highest frequency in the signal being
sampled.
Nyquist
frequency
fnyq
Hz (cycles per Half the Nyquist rate.
second)
Normalized
frequency
fn
Two cycles
per sample
Frequency (linear) of a periodic signal normalized to
half the sample rate, fn = ω/π = 2f/Fs.
Angular
frequency
Ω
Radians per
second
Frequency of a periodic signal in angular units,
Ω = 2πf.
Digital
(normalized
angular)
frequency
ω
Radians per
sample
Frequency (angular) of a periodic signal normalized to
the sample rate, ω = Ω/Fs = πfn.
Note In the Block Parameters dialog boxes, the term sample time is used to refer to
the sample period, Ts. For example, the Sample time parameter in the Signal From
Workspace block specifies the imported signal's sample period.
Recommended Settings for Discrete-Time Simulations
Simulink allows you to select from several different simulation solver algorithms. You
can access these solver algorithms from a Simulink model:
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Input, Output, and Display
1
In the Simulink model window, from the Simulation menu, select Model
Configuration Parameters. The Configuration Parameters dialog box opens.
2
In the Select pane, click Solver.
The selections that you make here determine how discrete-time signals are processed
in Simulink. The recommended Solver options settings for signal processing
simulations are
• Type: Fixed-step
• Solver: Discrete (no continuous states)
• Fixed step size (fundamental sample time): auto
• Tasking mode for periodic sample times: SingleTasking
2-4
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Discrete-Time Signals
You can automatically set the above solver options for all new models by running the
dspstartup.m file. See “Configure the Simulink Environment for Signal Processing
Models” in the DSP System Toolbox Getting Started Guide for more information.
In Fixed-step SingleTasking mode, discrete-time signals differ from the prototype
described in “Time and Frequency Terminology” on page 2-2 by remaining defined
between sample times. For example, the representation of the discrete-time triangle
wave looks like this.
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Input, Output, and Display
The above signal's value at t=3.112 seconds is the same as the signal's value at t=3
seconds. In Fixed-step SingleTasking mode, a signal's sample times are the
instants where the signal is allowed to change values, rather than where the signal is
defined. Between the sample times, the signal takes on the value at the previous sample
time.
As a result, in Fixed-step SingleTasking mode, Simulink permits cross-rate
operations such as the addition of two signals of different rates. This is explained further
in “Cross-Rate Operations” on page 2-7.
Other Settings for Discrete-Time Simulations
It is useful to know how the other solver options available in Simulink affect discretetime signals. In particular, you should be aware of the properties of discrete-time signals
under the following settings:
• Type: Fixed-step, Mode: MultiTasking
• Type: Variable-step (the Simulink default solver)
• Type: Fixed-step, Mode: Auto
When the Fixed-step MultiTasking solver is selected, discrete signals in Simulink
are undefined between sample times. Simulink generates an error when operations
attempt to reference the undefined region of a signal, as, for example, when signals with
different sample rates are added.
When the Variable-step solver is selected, discrete time signals remain defined
between sample times, just as in the Fixed-step SingleTasking case described in
“Recommended Settings for Discrete-Time Simulations” on page 2-3. When the
Variable-step solver is selected, cross-rate operations are allowed by Simulink.
In the Fixed-step Auto setting, Simulink automatically selects a tasking mode, singletasking or multitasking, that is best suited to the model. See“Simulink Tasking Mode”
2-6
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Discrete-Time Signals
for a description of the criteria that Simulink uses to make this decision. For the typical
model containing multiple rates, Simulink selects the multitasking mode.
Cross-Rate Operations
When the Fixed-step MultiTasking solver is selected, discrete signals in Simulink
are undefined between sample times. Therefore, to perform cross-rate operations like the
addition of two signals with different sample rates, you must convert the two signals to
a common sample rate. Several blocks in the Signal Operations and Multirate Filters
libraries can accomplish this task. See “Convert Sample and Frame Rates in Simulink”
for more information. Rate change can happen implicitly, depending on diagnostic
settings. See “Multitask rate transition”, “Single task rate transition”. However, this
is not recommended. By requiring explicit rate conversions for cross-rate operations in
discrete mode, Simulink helps you to identify sample rate conversion issues early in the
design process.
When the Variable-step solver or Fixed-step SingleTasking solver is selected,
discrete time signals remain defined between sample times. Therefore, if you sample the
signal with a rate or phase that is different from the signal's own rate and phase, you will
still measure meaningful values:
1
At the MATLAB command line, type ex_sum_tut1.
The Cross-Rate Sum Example model opens. This model sums two signals with
different sample periods.
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2-7
2
Input, Output, and Display
2
Double-click the upper Signal From Workspace block. The Block Parameters:
Signal From Workspace dialog box opens.
3
Set the Sample time parameter to 1.
This creates a fast signal, (Ts=1), with sample times 1, 2, 3, ...
2-8
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Discrete-Time Signals
4
Double-click the lower Signal From Workspace block
5
Set the Sample time parameter to 2.
This creates a slow signal, (Ts=2), with sample times 1, 3, 5, ...
6
From the Display menu choose Sample Time > Colors.
Checking the Colors option allows you to see the different sampling rates in action.
For more information about the color coding of the sample times see “View Sample
Time Information” in the Simulink documentation.
7
Run the model.
Note Using the dspstartup configurations with cross-rate operations generates
errors even though the Fixed-step SingleTasking solver is selected. This is due
to the fact that Single task rate transition is set to error in the Sample Time
pane of the Diagnostics section of the Configuration Parameters dialog box.
8
At the MATLAB command line, type dsp_examples_yout.
The following output is displayed:
dsp_examples_yout =
1
1
2
2
1
3
3
2
5
4
2
6
5
3
8
6
3
9
7
4
11
8
4
12
9
5
14
10
5
15
0
6
6
The first column of the matrix is the fast signal, (Ts=1). The second column of the
matrix is the slow signal (Ts=2). The third column is the sum of the two signals.
As expected, the slow signal changes once every 2 seconds, half as often as the fast
signal. Nevertheless, the slow signal is defined at every moment because Simulink
holds the previous value of the slower signal during time instances that the block
doesn't run.
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Input, Output, and Display
In general, for Variable-step and Fixed-step SingleTasking modes, when you
measure the value of a discrete signal between sample times, you are observing the value
of the signal at the previous sample time.
2-10
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Continuous-Time Signals
Continuous-Time Signals
In this section...
“Continuous-Time Source Blocks” on page 2-11
“Continuous-Time Nonsource Blocks” on page 2-11
Continuous-Time Source Blocks
Most signals in a signal processing model are discrete-time signals. However, many
blocks can also operate on and generate continuous-time signals, whose values vary
continuously with time. Source blocks are those blocks that generate or import signals
in a model. Most source blocks appear in the Sources library. The sample period for
continuous-time source blocks is set internally to zero. This indicates a continuous-time
signal. The Simulink Signal Generator and Constant blocks are examples of continuoustime source blocks. Continuous-time signals are rendered in black when, from the
Display menu, you point to Sample Time and select Colors.
When connecting continuous-time source blocks to discrete-time blocks, you might need
to interpose a Zero-Order Hold block to discretize the signal. Specify the desired sample
period for the discrete-time signal in the Sample time parameter of the Zero-Order Hold
block.
Continuous-Time Nonsource Blocks
Most nonsource blocks in DSP System Toolbox software accept continuous-time signals,
and all nonsource blocks inherit the sample period of the input. Therefore, continuoustime inputs generate continuous-time outputs. Blocks that are not capable of accepting
continuous-time signals include the Biquad Filter, Discrete FIR Filter, FIR Decimation,
and FIR Interpolation blocks.
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2
Input, Output, and Display
Create Sample-Based Signals
Note: Starting in R2010b, many DSP System Toolbox blocks received a new parameter to
control whether they perform sample- or frame-based processing. The following content
has not been updated to reflect this change. For more information, see the “Frame-Based
Processing” section of the Release Notes.
In this section...
“Create Signals Using Constant Block” on page 2-12
“Create Signals Using Signal from Workspace Block” on page 2-14
Create Signals Using Constant Block
A constant sample-based signal has identical successive samples. The Sources library
provides the following blocks for creating constant sample-based signals:
• Constant Diagonal Matrix
• Constant
• Identity Matrix
The most versatile of the blocks listed above is the Constant block. This topic discusses
how to create a constant sample-based signal using the Constant block:
1
Create a new Simulink model.
2
From the Sources library, click-and-drag a Constant block into the model.
3
From the Sinks library, click-and-drag a Display block into the model.
4
Connect the two blocks.
5
Double-click the Constant block, and set the block parameters as follows:
• Constant value = [1 2 3; 4 5 6]
• Interpret vector parameters as 1–D = Clear this check box
• Sampling Mode = Sample based
• Sample time = 1
2-12
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Create Sample-Based Signals
Based on these parameters, the Constant block outputs a constant, discrete-valued,
sample-based matrix signal with a sample period of 1 second.
The Constant block's Constant value parameter can be any valid MATLAB
variable or expression that evaluates to a matrix.
6
Save these parameters and close the dialog box by clicking OK.
7
From the Display menu, point to Signals & Ports and select Signal Dimensions.
8
Run the model and expand the Display block so you can view the entire signal.
You have now successfully created a six-channel, constant sample-based signal with
a sample period of 1 second.
To view the model you just created, and to learn how to create a 1–D vector signal
from the block diagram you just constructed, continue to the next section.
Create an Unoriented Vector Signal
You can create an unoriented vector by modifying the block diagram you constructed in
the previous section:
1
To add another sample-based signal to your model, copy the block diagram you
created in the previous section and paste it below the existing sample-based signal in
your model.
2
Double-click the Constant1 block, and set the block parameters as follows:
• Constant value = [1 2 3 4 5 6]
• Interpret vector parameters as 1–D = Check this box
• Sample time = 1
3
Save these parameters and close the dialog box by clicking OK.
4
Run the model and expand the Display1 block so you can view the entire signal.
Your model should now look similar to the following figure. You can also open this
model by typing ex_usingcnstblksb at the MATLAB command line.
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2-13
2
Input, Output, and Display
The Constant1 block generates a length-6 unoriented vector signal. This means that the
output is not a matrix. However, most nonsource signal processing blocks interpret a
length-M unoriented vector as an M-by-1 matrix (column vector).
Create Signals Using Signal from Workspace Block
This topic discusses how to create a four-channel sample-based signal with a sample
period of 1 second using the Signal From Workspace block:
2-14
1
Create a new Simulink model.
2
From the Sources library, click-and-drag a Signal From Workspace block into the
model.
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Create Sample-Based Signals
3
From the Simulink Sinks library, click-and-drag a To Workspace block into the
model.
4
Connect the two blocks.
5
Double-click the Signal From Workspace block, and set the block parameters as
follows:
• Signal = cat(3,[1 -1;0 5],[2 -2;0 5],[3 -3;0 5])
• Sample time = 1
• Samples per frame = 1
• Form output after final data value by = Setting to zero
Based on these parameters, the Signal From Workspace block outputs a four-channel
sample-based signal with a sample period of 1 second. After the block has output the
signal, all subsequent outputs have a value of zero. The four channels contain the
following values:
• Channel 1: 1, 2, 3, 0, 0,...
• Channel 2: -1, -2, -3, 0, 0,...
• Channel 3: 0, 0, 0, 0, 0,...
• Channel 4: 5, 5, 5, 0, 0,...
6
Save these parameters and close the dialog box by clicking OK.
7
From the Display menu, point to Signals & Ports, and select Signal Dimensions.
8
Run the model.
The following figure is a graphical representation of the model's behavior during
simulation. You can also open the model by typing ex_usingsfwblksb at the
MATLAB command line.
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2-15
2
Input, Output, and Display
9
At the MATLAB command line, type yout.
The following is a portion of the output:
yout(:,:,1) =
1
0
-1
5
yout(:,:,2) =
2
0
-2
5
yout(:,:,3) =
3
0
-3
5
yout(:,:,4) =
0
0
0
0
You have now successfully created a four-channel sample-based signal with sample
period of 1 second using the Signal From Workspace block.
2-16
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Sample-Based Row Vector Processing Changes
Sample-Based Row Vector Processing Changes
There are DSP System Toolbox blocks that handle sample-based row vector inputs in a
special way.
One category of these blocks have a Treat sample-based row input as a column
check box which allows you to explicitly specify how the block should treat sample-based
row vector inputs. Expand the following section for a full list of these blocks.
Blocks with a Check Box
• Maximum
• Mean
• Median
• Minimum
• Normalization
• RMS
• Standard Deviation
• Variance
In a future release these blocks will produce a warning when you provide them with a
sample-based row vector input, and eventually, their behavior will change.
You can prepare your models for the upcoming change by using slupdate. If the
function detects any blocks that have a Treat sample-based row input as a column
check box, it performs the following actions:
• If the input to the block is a sample-based row vector, and the Treat sample-based
row input as a column check box is selected, the slupdate function places a
Transpose block in front of the affected block. The Transpose block transposes the
sample-based row vector into a column vector, which is then input into the affected
block. Transposing the input signal ensures that your model will produce the same
results in future releases.
• If the Treat sample-based row input as a column check box is not selected, or if
the input to the block is not a sample-based row vector, function takes no action. Your
model will continue to work as expected in future releases.
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Input, Output, and Display
If the slupdate function detects any blocks that automatically treat sample-based row
vectors as a column, it performs the following actions:
• If the input to the block is a sample-based row vector, the slupdate function places
a Transpose block in front of the affected block. The Transpose block transposes the
sample-based row vector into a column vector, which is then input into the affected
block. Transposing the input signal ensures that your model will produce the same
results in future releases.
• If the input to the block is not a sample-based row vector, the slupdate function
takes no action. Your model will continue to work as expected in future releases.
2-18
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Create Frame-Based Signals
Create Frame-Based Signals
Note: Starting in R2010b, many DSP System Toolbox blocks received a new parameter to
control whether they perform sample- or frame-based processing. The following content
has not been updated to reflect this change. For more information, see the “Frame-Based
Processing” section of the Release Notes.
In this section...
“Create Signals Using Sine Wave Block” on page 2-19
“Create Signals Using Signal from Workspace Block” on page 2-22
Create Signals Using Sine Wave Block
A frame-based signal is propagated through a model in batches of samples called frames.
Frame-based processing can significantly improve the performance of your model by
decreasing the amount of time it takes your simulation to run.
One of the most commonly used blocks in the Sources library is the Sine Wave block. This
topic describes how to create a three-channel frame-based signal using the Sine Wave
block:
1
Create a new Simulink model.
2
From the Sources library, click-and-drag a Sine Wave block into the model.
3
From the Matrix Operations library, click-and-drag a Matrix Sum block into the
model.
4
From the Simulink Sinks library, click-and-drag a To Workspace block into the
model.
5
Connect the blocks in the order in which you added them to your model.
6
Double-click the Sine Wave block, and set the block parameters as follows:
• Amplitude = [1 3 2]
• Frequency = [100 250 500]
• Sample time = 1/5000
• Samples per frame = 64
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2-19
2
Input, Output, and Display
Based on these parameters, the Sine Wave block outputs three sinusoids with
amplitudes 1, 3, and 2 and frequencies 100, 250, and 500 hertz, respectively. The
sample period, 1/5000, is 10 times the highest sinusoid frequency, which satisfies the
Nyquist criterion. The frame size is 64 for all sinusoids, and, therefore, the output
has 64 rows.
7
Save these parameters and close the dialog box by clicking OK.
You have now successfully created a three-channel frame-based signal using the Sine
Wave block. The rest of this procedure describes how to add these three sinusoids
together.
8
Double-click the Matrix Sum block. Set the Sum over parameter to Specified
dimension, and set the Dimension parameter to 2. Click OK.
9
From the Display menu, point to Signals & Ports, and select Signal Dimensions.
10 Run the model.
Your model should now look similar to the following figure. You can also open the
model by typing ex_usingsinwaveblkfb at the MATLAB command line.
2-20
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Create Frame-Based Signals
The three signals are summed point-by-point by a Matrix Sum block. Then, they are
exported to the MATLAB workspace.
11 At the MATLAB command line, type plot(yout(1:100)).
Your plot should look similar to the following figure.
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2-21
2
Input, Output, and Display
This figure represents a portion of the sum of the three sinusoids. You have now added
the channels of a three-channel frame-based signal together and displayed the results in
a figure window.
Create Signals Using Signal from Workspace Block
A frame-based signal is propagated through a model in batches of samples called frames.
Frame-based processing can significantly improve the performance of your model by
decreasing the amount of time it takes your simulation to run. This topic describes how
to create a two-channel frame-based signal with a sample period of 1 second, a frame
period of 4 seconds, and a frame size of 4 samples using the Signal From Workspace
block:
2-22
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Create Frame-Based Signals
1
Create a new Simulink model.
2
From the Sources library, click-and-drag a Signal From Workspace block into the
model.
3
From the Simulink Sinks library, click-and-drag a To Workspace block into the
model.
4
Connect the two blocks.
5
Double-click the Signal From Workspace block, and set the block parameters as
follows:
• Signal = [1:10; 1 1 0 0 1 1 0 0 1 1]'
• Sample time = 1
• Samples per frame = 4
• Form output after final data value by = Setting to zero
Based on these parameters, the Signal From Workspace block outputs a twochannel, frame-based signal has a sample period of 1 second, a frame period of 4
seconds, and a frame size of four samples. After the block outputs the signal, all
subsequent outputs have a value of zero. The two channels contain the following
values:
• Channel 1: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 0, 0,...
• Channel 2: 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0,...
6
Save these parameters and close the dialog box by clicking OK.
7
From the Display menu, point to Signals & Ports, and select Signal Dimensions.
8
Run the model.
The following figure is a graphical representation of the model's behavior during
simulation. You can also open the model by typing ex_usingsfwblkfb at the
MATLAB command line.
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2-23
2
Input, Output, and Display
9
At the MATLAB command line, type yout.
The following is the output displayed at the MATLAB command line.
yout =
1
2
3
4
5
6
7
8
9
10
0
2-24
1
1
0
0
1
1
0
0
1
1
0
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Create Frame-Based Signals
0
0
Note that zeros were appended to the end of each channel. You have now successfully
created a two-channel frame-based signal and exported it to the MATLAB workspace.
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2-25
2
Input, Output, and Display
Create Multichannel Sample-Based Signals
In this section...
“Multichannel Sample-Based Signals” on page 2-26
“Create Multichannel Signals by Combining Single-Channel Signals” on page 2-26
“Create Multichannel Signals by Combining Multichannel Signals” on page 2-29
Multichannel Sample-Based Signals
When you want to perform the same operations on several independent signals, you can
group those signals together as a multichannel signal. For example, if you need to filter
each of four independent signals using the same direct-form II transpose filter, you can
combine the signals into a multichannel signal, and connect the signal to a single Digital
Filter Design block. The block applies the filter to each channel independently.
A sample-based signal with M*N channels is represented by a sequence of M-by-N
matrices. Multiple sample-based signals can be combined into a single multichannel
sample-based signal using the Concatenate block. In addition, several multichannel
sample-based signals can be combined into a single multichannel sample-based signal
using the same technique.
Create Multichannel Signals by Combining Single-Channel Signals
You can combine individual sample-based signals into a multichannel signal by using the
Matrix Concatenate block in the Simulink Math Operations library:
1
Open the Matrix Concatenate Example 1 model by typing
ex_cmbsnglchsbsigs
at the MATLAB command line.
2-26
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Create Multichannel Sample-Based Signals
2
Double-click the Signal From Workspace block, and set the Signal parameter to
1:10. Click OK.
3
Double-click the Signal From Workspace1 block, and set the Signal parameter to
-1:-1:-10. Click OK.
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2-27
2
Input, Output, and Display
4
Double-click the Signal From Workspace2 block, and set the Signal parameter to
zeros(10,1). Click OK.
5
Double-click the Signal From Workspace3 block, and set the Signal parameter to
5*ones(10,1). Click OK.
6
Double-click the Matrix Concatenate block. Set the block parameters as follows, and
then click OK:
• Number of inputs = 4
• Mode = Multidimensional array
• Concatenate dimension = 1
7
Double-click the Reshape block. Set the block parameters as follows, and then click
OK:
• Output dimensionality = Customize
• Output dimensions = [2,2]
8
Run the model.
Four independent sample-based signals are combined into a 2-by-2 multichannel
matrix signal.
Each 4-by-1 output from the Matrix Concatenate block contains one sample from
each of the four input signals at the same instant in time. The Reshape block
rearranges the samples into a 2-by-2 matrix. Each element of this matrix is a
separate channel.
Note that the Reshape block works columnwise, so that a column vector input is
reshaped as shown below.
The 4-by-1 matrix output by the Matrix Concatenate block and the 2-by-2 matrix
output by the Reshape block in the above model represent the same four-channel
sample-based signal. In some cases, one representation of the signal may be more
useful than the other.
2-28
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Create Multichannel Sample-Based Signals
9
At the MATLAB command line, type dsp_examples_yout.
The four-channel, sample-based signal is displayed as a series of matrices in the
MATLAB Command Window. Note that the last matrix contains only zeros. This
is because every Signal From Workspace block in this model has its Form output
after final data value by parameter set to Setting to Zero.
Create Multichannel Signals by Combining Multichannel Signals
You can combine existing multichannel sample-based signals into larger multichannel
signals using the Simulink Matrix Concatenate block:
1
Open the Matrix Concatenate Example 2 model by typing
ex_cmbmltichsbsigs
at the MATLAB command line.
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2-29
2
Input, Output, and Display
2-30
2
Double-click the Signal From Workspace block, and set the Signal parameter to
[1:10;-1:-1:-10]'. Click OK.
3
Double-click the Signal From Workspace1 block, and set the Signal parameter to
[zeros(10,1) 5*ones(10,1)]. Click OK.
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Create Multichannel Sample-Based Signals
4
Double-click the Matrix Concatenate block. Set the block parameters as follows, and
then click OK:
• Number of inputs = 2
• Mode = Multidimensional array
• Concatenate dimension = 1
5
Run the model.
The model combines both two-channel sample-based signals into a four-channel
signal.
Each 2-by-2 output from the Matrix Concatenate block contains both samples from
each of the two input signals at the same instant in time. Each element of this
matrix is a separate channel.
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Input, Output, and Display
Create Multichannel Frame-Based Signals
In this section...
“Multichannel Frame-Based Signals” on page 2-32
“Create Multichannel Signals Using Concatenate Block” on page 2-32
Multichannel Frame-Based Signals
When you want to perform the same operations on several independent signals, you can
group those signals together as a multichannel signal. For example, if you need to filter
each of four independent signals using the same direct-form II transpose filter, you can
combine the signals into a multichannel signal, and connect the signal to a single Digital
Filter Design block. The block applies the filter to each channel independently.
A frame-based signal with N channels and frame size M is represented by a sequence of
M-by-N matrices. Multiple individual frame-based signals, with the same frame rate and
size, can be combined into a multichannel frame-based signal using the Simulink Matrix
Concatenate block. Individual signals can be added to an existing multichannel signal in
the same way.
Create Multichannel Signals Using Concatenate Block
2-32
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Create Multichannel Frame-Based Signals
You can combine existing frame-based signals into a larger multichannel signal by
using the Simulink Concatenate block. All signals must have the same frame rate and
frame size. In this example, a single-channel frame-based signal is combined with a twochannel frame-based signal to produce a three-channel frame-based signal:
1
Open the Matrix Concatenate Example 3 model by typing
ex_combiningfbsigs
at the MATLAB command line.
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2-33
2
Input, Output, and Display
2
Double-click the Signal From Workspace block. Set the block parameters as follows:
• Signal = [1:10;-1:-1:-10]'
• Sample time = 1
2-34
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Create Multichannel Frame-Based Signals
• Samples per frame = 4
Based on these parameters, the Signal From Workspace block outputs a frame-based
signal with a frame size of four.
3
Save these parameters and close the dialog box by clicking OK.
4
Double-click the Signal From Workspace1 block. Set the block parameters as follows,
and then click OK:
• Signal = 5*ones(10,1)
• Sample time = 1
• Samples per frame = 4
The Signal From Workspace1 block has the same sample time and frame size as
the Signal From Workspace block. When you combine frame-based signals into
multichannel signals, the original signals must have the same frame rate and frame
size.
5
Double-click the Matrix Concatenate block. Set the block parameters as follows, and
then click OK:
• Number of inputs = 2
• Mode = Multidimensional array
• Concatenate dimension = 2
6
Run the model.
The 4-by-3 matrix output from the Matrix Concatenate block contains all three input
channels, and preserves their common frame rate and frame size.
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2
Input, Output, and Display
Deconstruct Multichannel Sample-Based Signals
Note: Starting in R2010b, many DSP System Toolbox blocks received a new parameter to
control whether they perform sample- or frame-based processing. The following content
has not been updated to reflect this change. For more information, see the “Frame-Based
Processing” section of the Release Notes.
In this section...
“Split Multichannel Signals into Individual Signals” on page 2-36
“Split Multichannel Signals into Several Multichannel Signals” on page 2-39
Split Multichannel Signals into Individual Signals
Multichannel signals, represented by matrices in the Simulink environment, are
frequently used in signal processing models for efficiency and compactness. Though
most of the signal processing blocks can process multichannel signals, you may need
to access just one channel or a particular range of samples in a multichannel signal.
You can access individual channels of the multichannel signal by using the blocks in
the Indexing library. This library includes the Selector, Submatrix, Variable Selector,
Multiport Selector, and Submatrix blocks.
You can split a multichannel sample-based signal into single-channel sample-based
signals using the Multiport Selector block. This block allows you to select specific rows
and/or columns and propagate the selection to a chosen output port. In this example, a
three-channel sample-based signal is deconstructed into three independent sample-based
signals:
1
2-36
Open the Multiport Selector Example 1 model by typing
ex_splitmltichsbsigsind at the MATLAB command line.
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Deconstruct Multichannel Sample-Based Signals
2
Double-click the Signal From Workspace block, and set the block parameters as
follows:
• Signal = randn(3,1,10)
• Sample time = 1
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2-37
2
Input, Output, and Display
• Samples per frame = 1
Based on these parameters, the Signal From Workspace block outputs a threechannel, sample-based signal with a sample period of 1 second.
3
Save these parameters and close the dialog box by clicking OK.
4
Double-click the Multiport Selector block. Set the block parameters as follows, and
then click OK:
• Select = Rows
• Indices to output = {1,2,3}
Based on these parameters, the Multiport Selector block extracts the rows of the
input. The Indices to output parameter setting specifies that row 1 of the input
should be reproduced at output 1, row 2 of the input should be reproduced at
output 2, and row 3 of the input should be reproduced at output 3.
5
Run the model.
6
At the MATLAB command line, type dsp_examples_yout.
The following is a portion of what is displayed at the MATLAB command line.
Because the input signal is random, your output might be different than the output
show here.
dsp_examples_yout(:,:,1) =
-0.1199
dsp_examples_yout(:,:,2) =
-0.5955
dsp_examples_yout(:,:,3) =
-0.0793
This sample-based signal is the first row of the input to the Multiport Selector
block. You can view the other two input rows by typing dsp_examples_yout1 and
dsp_examples_yout2, respectively.
You have now successfully created three, single-channel sample-based signals from a
multichannel sample-based signal using a Multiport Selector block.
2-38
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Deconstruct Multichannel Sample-Based Signals
Split Multichannel Signals into Several Multichannel Signals
Multichannel signals, represented by matrices in the Simulink environment, are
frequently used in signal processing models for efficiency and compactness. Though
most of the signal processing blocks can process multichannel signals, you may need
to access just one channel or a particular range of samples in a multichannel signal.
You can access individual channels of the multichannel signal by using the blocks in
the Indexing library. This library includes the Selector, Submatrix, Variable Selector,
Multiport Selector, and Submatrix blocks.
You can split a multichannel sample-based signal into other multichannel sample-based
signals using the Submatrix block. The Submatrix block is the most versatile of the
blocks in the Indexing library because it allows arbitrary channel selections. Therefore,
you can extract a portion of a multichannel sample-based signal. In this example, you
extract a six-channel, sample-based signal from a 35-channel, sample-based signal (5by-7 matrix):
1
Open the Submatrix Example model by typing ex_splitmltichsbsigsev at the
MATLAB command line.
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2-39
2
Input, Output, and Display
2
Double-click the Constant block, and set the block parameters as follows:
• Constant value = rand(5,7)
• Interpret vector parameters as 1–D = Clear this check box
• Sampling mode = Sample based
• Sample Time = 1
2-40
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Deconstruct Multichannel Sample-Based Signals
Based on these parameters, the Constant block outputs a constant-valued, samplebased signal.
3
Save these parameters and close the dialog box by clicking OK.
4
Double-click the Submatrix block. Set the block parameters as follows, and then click
OK:
• Row span = Range of rows
• Starting row = Index
• Starting row index = 3
• Ending row = Last
• Column span = Range of columns
• Starting column = Offset from last
• Starting column offset = 1
• Ending column = Last
Based on these parameters, the Submatrix block outputs rows three to five, the last
row of the input signal. It also outputs the second to last column and the last column
of the input signal.
5
Run the model.
The model should now look similar to the following figure.
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2-41
2
Input, Output, and Display
Notice that the output of the Submatrix block is equivalent to the matrix created by
rows three through five and columns six through seven of the input matrix.
You have now successfully created a six-channel, sample-based signal from a 35-channel
sample-based signal using a Submatrix block.
2-42
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Deconstruct Multichannel Frame-Based Signals
Deconstruct Multichannel Frame-Based Signals
Note: Starting in R2010b, many DSP System Toolbox blocks received a new parameter to
control whether they perform sample- or frame-based processing. The following content
has not been updated to reflect this change. For more information, see the “Frame-Based
Processing” section of the Release Notes.
In this section...
“Split Multichannel Signals into Individual Signals” on page 2-43
“Reorder Channels in Multichannel Frame-Based Signals” on page 2-47
Split Multichannel Signals into Individual Signals
Multichannel signals, represented by matrices in the Simulink environment, are
frequently used in signal processing models for efficiency and compactness. Though
most of the signal processing blocks can process multichannel signals, you may need
to access just one channel or a particular range of samples in a multichannel signal.
You can access individual channels of the multichannel signal by using the blocks in
the Indexing library. This library includes the Selector, Submatrix, Variable Selector,
Multiport Selector, and Submatrix blocks. It is also possible to use the Permute Matrix
block, in the Matrix operations library, to reorder the channels of a frame-based signal.
You can use the Multiport Selector block in the Indexing library to extract the individual
channels of a multichannel frame-based signal. These signals form single-channel framebased signals that have the same frame rate and size of the multichannel signal.
The figure below is a graphical representation of this process.
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2-43
2
Input, Output, and Display
In this example, you use the Multiport Selector block to extract a single-channel and a
two channel frame-based signal from a multichannel frame-based signal:
1
Open the Multiport Selector Example 2 model by typing
ex_splitmltichfbsigsind
at the MATLAB command line.
2-44
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Deconstruct Multichannel Frame-Based Signals
2
Double-click the Signal From Workspace block, and set the block parameters as
follows:
• Signal = [1:10;-1:-1:-10;5*ones(1,10)]'
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2-45
2
Input, Output, and Display
• Samples per frame = 4
Based on these parameters, the Signal From Workspace block outputs a threechannel, frame-based signal with a frame size of four.
3
Save these parameters and close the dialog box by clicking OK.
4
Double-click the Multiport Selector block. Set the block parameters as follows, and
then click OK:
• Select = Columns
• Indices to output = {[1 3],2}
Based on these parameters, the Multiport Selector block outputs the first and third
columns at the first output port and the second column at the second output port of
the block. Setting the Select parameter to Columns ensures that the block preserves
the frame rate and frame size of the input.
5
Run the model.
The figure below is a graphical representation of how the Multiport Selector block
splits one frame of the three-channel frame-based signal into a single-channel signal
and a two-channel signal.
2-46
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Deconstruct Multichannel Frame-Based Signals
The Multiport Selector block outputs a two-channel frame-based signal, comprised of the
first and third column of the input signal, at the first port. It outputs a single-channel
frame-based signal, comprised of the second column of the input signal, at the second
port.
You have now successfully created a single-channel and a two-channel frame-based
signal from a multichannel frame-based signal using the Multiport Selector block.
Reorder Channels in Multichannel Frame-Based Signals
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2-47
2
Input, Output, and Display
Multichannel signals, represented by matrices in Simulink, are frequently used in signal
processing models for efficiency and compactness. Though most of the signal processing
blocks can process multichannel signals, you may need to access just one channel or a
particular range of samples in a multichannel signal. You can access individual channels
of the multichannel signal by using the blocks in the Indexing library. This library
includes the Selector, Submatrix, Variable Selector, Multiport Selector, and Submatrix
blocks. It is also possible to use the Permute Matrix block, in the Matrix operations
library, to reorder the channels of a frame-based signal.
Some DSP System Toolbox blocks have the ability to process the interaction of channels.
Typically, DSP System Toolbox blocks compare channel one of signal A to channel one
of signal B. However, you might want to correlate channel one of signal A with channel
three of signal B. In this case, in order to compare the correct signals, you need to use
the Permute Matrix block to rearrange the channels of your frame-based signals. This
example explains how to accomplish this task:
1
2-48
Open the Permute Matrix Example model by typing ex_reordermltichfbsigs at
the MATLAB command line.
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Deconstruct Multichannel Frame-Based Signals
2
Double-click the Signal From Workspace block, and set the block parameters as
follows:
• Signal = [1:10;-1:-1:-10;5*ones(1,10)]'
• Sample time = 1
• Samples per frame = 4
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2-49
2
Input, Output, and Display
Based on these parameters, the Signal From Workspace block outputs a threechannel, frame-based signal with a sample period of 1 second and a frame size of 4.
The frame period of this block is 4 seconds.
3
Save these parameters and close the dialog box by clicking OK.
4
Double-click the Constant block. Set the block parameters as follows, and then click
OK:
• Constant value = [1 3 2]
• Interpret vector parameters as 1–D = Clear this check box
• Sampling mode = Frame based
• Frame period = 4
The discrete-time, frame-based vector output by the Constant block tells the
Permute Matrix block to swap the second and third columns of the input signal.
Note that the frame period of the Constant block must match the frame period of the
Signal From Workspace block.
5
Double-click the Permute Matrix block. Set the block parameters as follows, and
then click OK:
• Permute = Columns
• Index mode = One-based
Based on these parameters, the Permute Matrix block rearranges the columns of the
input signal, and the index of the first column is now one.
6
Run the model.
The figure below is a graphical representation of what happens to the first input
frame during simulation.
2-50
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Deconstruct Multichannel Frame-Based Signals
The second and third channel of the frame-based input signal are swapped.
7
At the MATLAB command line, type yout.
You can now verify that the second and third columns of the input signal are
rearranged.
You have now successfully reordered the channels of a frame-based signal using the
Permute Matrix block.
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2-51
2
Input, Output, and Display
Import and Export Sample-Based Signals
Note: Starting in R2010b, many DSP System Toolbox blocks received a new parameter to
control whether they perform sample- or frame-based processing. The following content
has not been updated to reflect this change. For more information, see the “Frame-Based
Processing” section of the Release Notes.
In this section...
“Import Sample-Based Vector Signals” on page 2-52
“Import Sample-Based Matrix Signals” on page 2-55
“Export Sample-Based Signals” on page 2-59
Import Sample-Based Vector Signals
The Signal From Workspace block generates a sample-based vector signal when the
variable or expression in the Signal parameter is a matrix and the Samples per frame
parameter is set to 1. Each column of the input matrix represents a different channel.
Beginning with the first row of the matrix, the block outputs one row of the matrix at
each sample time. Therefore, if the Signal parameter specifies an M-by-N matrix, the
output of the Signal From Workspace block is M 1-by-N row vectors representing N
channels.
The figure below is a graphical representation of this process for a 6-by-4 workspace
matrix, A.
2-52
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Import and Export Sample-Based Signals
In the following example, you use the Signal From Workspace block to import a samplebased vector signal into your model:
1
Open the Signal From Workspace Example 3 model by typing
ex_importsbvectorsigs at the MATLAB command line.
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2-53
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Input, Output, and Display
2
At the MATLAB command line, type A = [1:100;-1:-1:-100]';
The matrix A represents a two column signal, where each column is a different
channel.
3
At the MATLAB command line, type B = 5*ones(100,1);
The vector B represents a single-channel signal.
4
Double-click the Signal From Workspace block, and set the block parameters as
follows:
• Signal = [A B]
• Sample time = 1
2-54
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Import and Export Sample-Based Signals
• Samples per frame = 1
• Form output after final data value = Setting to zero
The Signal expression [A B] uses the standard MATLAB syntax for horizontally
concatenating matrices and appends column vector B to the right of matrix A. The
Signal From Workspace block outputs a sample-based signal with a sample period of
1 second. After the block has output the signal, all subsequent outputs have a value
of zero.
5
Save these parameters and close the dialog box by clicking OK.
6
Run the model.
The following figure is a graphical representation of the model's behavior during
simulation.
The first row of the input matrix [A B] is output at time t=0, the second row of the
input matrix is output at time t=1, and so on.
You have now successfully imported a sample-based vector signal into your signal
processing model using the Signal From Workspace block.
Import Sample-Based Matrix Signals
The Signal From Workspace block generates a sample-based matrix signal when the
variable or expression in the Signal parameter is a three-dimensional array and the
Samples per frame parameter is set to 1. Beginning with the first page of the array,
the block outputs a single page of the array to the output at each sample time. Therefore,
if the Signal parameter specifies an M-by-N-by-P array, the output of the Signal From
Workspace block is P M-by-N matrices representing M*N channels.
The following figure is a graphical illustration of this process for a 6-by-4-by-5 workspace
array A.
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Input, Output, and Display
In the following example, you use the Signal From Workspace block to import a fourchannel, sample-based matrix signal into a Simulink model:
1
2-56
Open the Signal From Workspace Example 4 model by typing
ex_importsbmatrixsigs at the MATLAB command line.
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Import and Export Sample-Based Signals
Also, the following variables are loaded into the MATLAB workspace:
Fs
1x1
8
double array
dsp_examples_A
2x2x100
3200
double array
dsp_examples_sig1
1x1x100
800
double array
dsp_examples_sig12
1x2x100
1600
double array
dsp_examples_sig2
1x1x100
800
double array
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2
Input, Output, and Display
2
dsp_examples_sig3
1x1x100
800
double array
dsp_examples_sig34
1x2x100
1600
double array
dsp_examples_sig4
1x1x100
800
double array
mtlb
4001x1
32008
double array
Double-click the Signal From Workspace block. Set the block parameters as follows,
and then click OK:
• Signal = dsp_examples_A
• Sample time = 1
• Samples per frame = 1
• Form output after final data value = Setting to zero
The dsp_examples_A array represents a four-channel, sample-based signal with
100 samples in each channel. This is the signal that you want to import, and it was
created in the following way:
dsp_examples_sig1 = reshape(1:100,[1 1 100])
dsp_examples_sig2 = reshape(-1:-1:-100,[1 1 100])
dsp_examples_sig3 = zeros(1,1,100)
dsp_examples_sig4 = 5*ones(1,1,100)
dsp_examples_sig12 = cat(2,sig1,sig2)
dsp_examples_sig34 = cat(2,sig3,sig4)
dsp_examples_A = cat(1,sig12,sig34) % 2-by-2-by-100 array
3
Run the model.
The figure below is a graphical representation of the model's behavior during
simulation.
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Import and Export Sample-Based Signals
The Signal From Workspace block imports the four-channel sample based signal
from the MATLAB workspace into the Simulink model one matrix at a time.
You have now successfully imported a sample-based matrix signal into your model using
the Signal From Workspace block.
Export Sample-Based Signals
The To Workspace and Triggered To Workspace blocks are the primary blocks for
exporting signals of all dimensions from a Simulink model to the MATLAB workspace.
A sample-based signal, with M*N channels, is represented in Simulink as a sequence of
M-by-N matrices. When the input to the To Workspace block is a sample-based signal,
the block creates an M-by-N-by-P array in the MATLAB workspace containing the P
most recent samples from each channel. The number of pages, P, is specified by the
Limit data points to last parameter. The newest samples are added at the end of the
array.
The following figure is the graphical illustration of this process using a 6-by-4 samplebased signal exported to workspace array A.
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2
Input, Output, and Display
The workspace array always has time running along its third dimension, P. Samples
are saved along the P dimension whether the input is a matrix, vector, or scalar (single
channel case).
In the following example you use a To Workspace block to export a sample-based matrix
signal to the MATLAB workspace:
1
2-60
Open the Signal From Workspace Example 6 model by typing ex_exportsbsigs at
the MATLAB command line.
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Import and Export Sample-Based Signals
Also, the following variables are loaded into the MATLAB workspace:
dsp_examples_A
2x2x100
3200
double array
dsp_examples_sig1
1x1x100
800
double array
dsp_examples_sig12
1x2x100
1600
double array
dsp_examples_sig2
1x1x100
800
double array
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Input, Output, and Display
dsp_examples_sig3
1x1x100
800
double array
dsp_examples_sig34
1x2x100
1600
double array
dsp_examples_sig4
1x1x100
800
double array
In this model, the Signal From Workspace block imports a four-channel samplebased signal called dsp_examples_A. This signal is then exported to the MATLAB
workspace using a To Workspace block.
2
Double-click the Signal From Workspace block. Set the block parameters as follows,
and then click OK:
• Signal = dsp_examples_A
• Sample time = 1
• Samples per frame = 1
• Form output after final data value = Setting to zero
Based on these parameters, the Signal From Workspace block outputs a samplebased signal with a sample period of 1 second. After the block has output the signal,
all subsequent outputs have a value of zero.
3
Double-click the To Workspace block. Set the block parameters as follows, and then
click OK:
• Variable name = dsp_examples_yout
• Limit data points to last parameter to inf
• Decimation = 1
Based on these parameters, the To Workspace block exports its sample-based input
signal to a variable called dsp_examples_yout in the MATLAB workspace. The
workspace variable can grow indefinitely large in order to capture all of the input
data. The signal is not decimated before it is exported to the MATLAB workspace.
4
Run the model.
5
At the MATLAB command line, type dsp_examples_yout.
The four-channel sample-based signal, dsp_examples_A, is output at the MATLAB
command line. The following is a portion of the output that is displayed.
dsp_examples_yout(:,:,1) =
1
2-62
-1
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Import and Export Sample-Based Signals
0
5
dsp_examples_yout(:,:,2) =
2
0
-2
5
dsp_examples_yout(:,:,3) =
3
0
-3
5
dsp_examples_yout(:,:,4) =
4
0
-4
5
Each page of the output represents a different sample time, and each element of the
matrices is in a separate channel.
You have now successfully exported a four-channel sample-based signal from a Simulink
model to the MATLAB workspace using the To Workspace block.
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Input, Output, and Display
Import and Export Frame-Based Signals
Note: Starting in R2010b, many DSP System Toolbox blocks received a new parameter to
control whether they perform sample- or frame-based processing. The following content
has not been updated to reflect this change. For more information, see the “Frame-Based
Processing” section of the Release Notes.
In this section...
“Import Frame-Based Signals” on page 2-64
“Export Frame-Based Signals” on page 2-67
Import Frame-Based Signals
The Signal From Workspace block creates a frame-based multichannel signal when the
Signal parameter is a matrix, and the Samples per frame parameter, M, is greater
than 1. Beginning with the first M rows of the matrix, the block releases M rows of the
matrix (that is, one frame from each channel) to the output port every M*Ts seconds.
Therefore, if the Signal parameter specifies a W-by-N workspace matrix, the Signal
From Workspace block outputs a series of M-by-N matrices representing N channels.
The workspace matrix must be oriented so that its columns represent the channels of the
signal.
The figure below is a graphical illustration of this process for a 6-by-4 workspace
matrix, A, and a frame size of 2.
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Import and Export Frame-Based Signals
Note: Although independent channels are generally represented as columns, a singlechannel signal can be represented in the workspace as either a column vector or row
vector. The output from the Signal From Workspace block is a column vector in both
cases.
In the following example, you use the Signal From Workspace block to create a threechannel frame-based signal and import it into the model:
1
Open the Signal From Workspace Example 5 model by typing
ex_importfbsigs
at the MATLAB command line.
dsp_examples_A = [1:100;-1:-1:-100]'; % 100-by-2 matrix
dsp_examples_B = 5*ones(100,1);
% 100-by-1 column vector
The variable called dsp_examples_A represents a two-channel signal with 100
samples, and the variable called dsp_examples_B represents a one-channel signal
with 100 samples.
Also, the following variables are defined in the MATLAB workspace:
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2
Input, Output, and Display
2
Double-click the Signal From Workspace block. Set the block parameters as follows,
and then click OK:
• Signal parameter to [dsp_examples_A dsp_examples_B]
• Sample time parameter to 1
• Samples per frame parameter to 4
• Form output after final data value parameter to Setting to zero
Based on these parameters, the Signal From Workspace block outputs a frame-based
signal with a frame size of 4 and a sample period of 1 second. The signal's frame
period is 4 seconds. The Signal parameter uses the standard MATLAB syntax for
horizontally concatenating matrices to append column vector dsp_examples_B
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Import and Export Frame-Based Signals
to the right of matrix dsp_examples_A. After the block has output the signal, all
subsequent outputs have a value of zero.
3
Run the model.
The figure below is a graphical representation of how your three-channel, framebased signal is imported into your model.
You have now successfully imported a three-channel frame-based signal into your model
using the Signal From Workspace block.
Export Frame-Based Signals
The To Workspace and Triggered To Workspace blocks are the primary blocks for
exporting signals of all dimensions from a Simulink model to the MATLAB workspace.
A frame-based signal with N channels and frame size M is represented by a sequence
of M-by-N matrices. When the input to the To Workspace block is a frame-based signal,
the block creates a P-by-N array in the MATLAB workspace containing the P most
recent samples from each channel. The number of rows, P, is specified by the Limit data
points to last parameter. The newest samples are added at the bottom of the matrix.
The following figure is a graphical illustration of this process for three consecutive
frames of a frame-based signal with a frame size of 2 that is exported to matrix A in the
MATLAB workspace.
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2
Input, Output, and Display
In the following example, you use a To Workspace block to export a frame-based signal to
the MATLAB workspace:
1
2-68
Open the Signal From Workspace Example 7 model by typing ex_exportfbsigs at
the MATLAB command line.
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Import and Export Frame-Based Signals
Also, the following variables are defined in the MATLAB workspace:
The variable called dsp_examples_A represents a two-channel signal with 100
samples, and the variable called dsp_examples_B represents a one-channel signal
with 100 samples.
dsp_examples_A = [1:100;-1:-1:-100]'; % 100-by-2 matrix
dsp_examples_B = 5*ones(100,1);
% 100-by-1 column vector
2
Double-click the Signal From Workspace block. Set the block parameters as follows,
and then click OK:
• Signal = [dsp_examples_A dsp_examples_B]
• Sample time = 1
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Input, Output, and Display
• Samples per frame = 4
• Form output after final data value = Setting to zero
Based on these parameters, the Signal From Workspace block outputs a frame-based
signal with a frame size of 4 and a sample period of 1 second. The signal's frame
period is 4 seconds. The Signal parameter uses the standard MATLAB syntax for
horizontally concatenating matrices to append column vector dsp_examples_B
to the right of matrix dsp_examples_A. After the block has output the signal, all
subsequent outputs have a value of zero.
3
Double-click the To Workspace block. Set the block parameters as follows, and then
click OK:
• Variable name = dsp_examples_yout
• Limit data points to last = inf
• Decimation = 1
• Frames = Concatenate frames (2-D array)
Based on these parameters, the To Workspace block exports its frame-based input
signal to a variable called dsp_examples_yout in the MATLAB workspace. The
workspace variable can grow indefinitely large in order to capture all of the input
data. The signal is not decimated before it is exported to the MATLAB workspace,
and each input frame is vertically concatenated to the previous frame to produce a 2D array output.
4
Run the model.
The following figure is a graphical representation of the model's behavior during
simulation.
2-70
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Import and Export Frame-Based Signals
5
At the MATLAB command line, type dsp_examples_yout.
The output is shown below:
dsp_examples_yout =
1
2
3
4
5
6
7
8
9
10
11
12
-1
-2
-3
-4
-5
-6
-7
-8
-9
-10
-11
-12
5
5
5
5
5
5
5
5
5
5
5
5
The frames of the signal are concatenated to form a two-dimensional array.
You have now successfully output a frame-based signal to the MATLAB workspace using
the To Workspace block.
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2
Input, Output, and Display
Musical Instrument Digital Interface
In this section...
“About MIDI” on page 2-72
“MIDI Control Surfaces” on page 2-72
“Using MIDI Control Surfaces with MATLAB and Simulink” on page 2-73
About MIDI
The Musical Instrument Digital Interface (MIDI) was originally developed to
interconnect electronic musical instruments. This interface is very flexible and has many
uses in many applications far beyond musical instruments. Its simple unidirectional
messaging protocol supports many different kinds of messaging.
Windows, Macintosh, and Linux platforms all have native support for MIDI, so software
on any of these platforms can send and receive MIDI messages. See http://www.midi.org
for more information about MIDI.
MIDI Control Surfaces
One kind of MIDI message is the Control Change message, used to communicate changes
in controls, such as knobs, sliders, and buttons. A MIDI Control Surface is a device
with controls that sends MIDI Control Change messages when you turn a knob, move
a slider, or push a button on a MIDI control surface. This Control Change message
indicates which control changed and what its new position is. MIDI control surfaces are
quite generic because the interpretation of the Control Change message is entirely up
to the message recipient. Even though some control surfaces are tailored for particular
applications, the messages they send can be used to control anything.
Hardware MIDI control surfaces are widely available in a range of configurations and
prices. MIDI control apps can turn a smartphone or tablet into a virtual MIDI control
surface. For custom applications, MIDI control surfaces are not difficult to build using,
for example, Arduino boards.
Because the MIDI messaging protocol is unidirectional, determining a particular
control’s position requires that the receiver listen for Control Change messages that
control sends. The protocol does not support querying the control for its position.
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Musical Instrument Digital Interface
The simplest MIDI control surfaces are unidirectional; they end MIDI Control Change
messages, but do not receive them. More sophisticated control surfaces are bidirectional:
They can both send and receive Control Change messages. These control surfaces have
knobs or sliders that can be operated automatically. For example, a control surface can
have sliders or knobs that are motorized. When it receives a Control Change message,
the appropriate control is moved to the position in the message. You can use this feature
to synchronize software GUI with MIDI control surface. For example, moving a slider on
the MIDI control surface sends a Control Change message to a GUI slider, which then
moves to match the control surface. Similarly, moving the GUI slider sends a Control
Change message to the MIDI control surface, which then moves to match the GUI slider.
Using MIDI Control Surfaces with MATLAB and Simulink
The DSP System Toolbox product enables you to use MIDI control surfaces to control
MATLAB programs and Simulink models by providing the capability to listen to Control
Change messages. The toolbox also provides a limited capability to send Control Change
messages to support synchronizing MIDI controls. The DSP System Toolbox interface to
MIDI control surfaces includes five functions and one block:
• midiid function
• midicontrols function
• midiread function
• midisync function
• midicallback function
• MIDI Controls block
Initial Setup
Your MIDI control surface should be connected to your computer, and turned on, before
starting MATLAB. Instructions for connecting your MIDI device to your computer vary
from device to device. See the instructions that came with your particular device. If you
start MATLAB before connecting your device, MATLAB may not recognize your device
when you connect it. To correct the problem, restart MATLAB with the device already
connected.
Next, set the MATLAB preference, specifying the name of the default MIDI device.
Use midiid to determine the name of the device, and then use setpref to set the
preference:
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2
Input, Output, and Display
>> [control, device] = midiid
Move the control you wish to identify; type ^C to abort.
Waiting for control message... done
control =
1082
device =
BCF2000
>> setpref('midi', 'DefaultDevice', device)
>>
This preference persists across MATLAB sessions, so you only have to set it once, unless
you want to change devices.
If you do not set this preference, MATLAB and the host operating system choose a device
for you. However, such autoselection can cause unpredictable results because many
computers have “virtual” (software) MIDI devices installed that you may not be aware of.
For predictable behavior, you should set the preference.
You can always override this default and explicitly specify a device name. Thus, you can
use multiple MIDI devices simultaneously.
Identifying Controls
Before you can connect a MIDI control with MATLAB or Simulink, you must know the
identifiers for that particular control:
• Control number
• Device name
The control number is a fixed integer assigned by the device manufacturer. Some devices
may change the assigned number based on various modes, or you can reprogram the
number. The device name is determined by the manufacturer and the host operating
system. You use midiid to determine both.
You do not usually have to use midiid repeatedly. If you use a single device in most
cases, then specify that device as the default hardware. the You can save the control
numbers in a function, a .mat file, or whatever form you find convenient. This example
shows a function returning a struct with all the control numbers for a Behringer
BCF2000:
function ctls = BCF2000
% BCF2000 return MIDI control number assignments
% for Behringer BCF2000 MIDI control surface
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Musical Instrument Digital Interface
ctls.knobs = 1001:1008;
ctls.buttons = [1065:1072;1073:1080];
ctls.sliders = 1081:1088;
end
MATLAB Interface
To use the MATLAB interface functions, first call midicontrols to specify any devices
or controls to listen to. midicontrols returns an object, which you pass to the other
functions for subsequent operations. You can now read the values of the specified MIDI
controls by calling midiread with that object. MATLAB can respond to changes in MIDI
controls by periodically calling midiread.
You can also set a callback on the specified MIDI controls by calling midicallback with
that object and a function handle. The next time the MIDI controls change value, the
function handle is invoked and passed to the object. The callback function typically calls
midiread to determine the new value of the MIDI controls. You can use this callback
when you want a MIDI control to trigger an action (such as update a GUI). Using this
approach prevents having a continuously running MATLAB program in the command
window.
Synchronization
If midiread is called before the MIDI control sends a Control Change message, the
midicontrols object has no information about the actual state of the MIDI control.
During this time, the midicontrols object and the actual MIDI control are out of sync
with each other. Thus, calling midiread returns the initial value that was specified in
the call to midicontrols (0 by default). You can synchronize the object with the control
by moving the MIDI control. The MIDI control responds by sending a Control Change
message causing the midicontrols object to sync to the MIDI control. If your MIDI
control surface is bidirectional, you can sync in the other direction by calling midisync
to send the midicontrols object’s initial value to the actual MIDI control. The MIDI
control responds by moving into sync with the midicontrols object.
It is generally harmless to call midisync even if the MIDI control surface is not
bidirectional, so it is usually good practice to call midisync immediately after calling
midicontrols.
Synchronization is also useful to link a MIDI control with a GUI control (a uicontrol
slider, for example), so that when one control is changed, the other control tracks it.
Typically, you implement such tracking by setting callback functions on both the MIDI
control (using midicallback) and the GUI control. The MIDI control callback sends its
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new value to the GUI control and the GUI control sends its value to the MIDI control,
using midisync.
Simulink Interface
The MIDI Controls block provides the Simulink interface. See the block reference page
MIDI Controls for more details.
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Display Time-Domain Data
Display Time-Domain Data
In this section...
“Configure the Time Scope Properties” on page 2-78
“Use the Simulation Controls” on page 2-83
“Modify the Time Scope Display” on page 2-84
“Inspect Your Data (Scaling the Axes and Zooming)” on page 2-86
“Manage Multiple Time Scopes” on page 2-89
The following tutorial shows you how to configure the Time Scope blocks in the
ex_timescope_tut model to display time-domain signals. To get started with this
tutorial, open the model by typing
ex_timescope_tut
at the MATLAB command line.
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Use the following workflow to configure the Time Scope blocks in the
ex_timescope_tut model:
1
“Configure the Time Scope Properties” on page 2-78
2
“Use the Simulation Controls” on page 2-83
3
“Modify the Time Scope Display” on page 2-84
4
“Inspect Your Data (Scaling the Axes and Zooming)” on page 2-86
5
“Manage Multiple Time Scopes” on page 2-89
Configure the Time Scope Properties
The Configuration Properties dialog box provides a central location from which you can
change the appearance and behavior of the Time Scope block. To open the Configuration
Properties dialog box, you must first open the Time Scope window by double-clicking the
Time Scope block in your model. When the window opens, select View > Configuration
Properties. Alternatively, in the Time Scope toolbar, click the Configuration Properties
button.
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Display Time-Domain Data
The Configuration Properties dialog box has four different tabs, Main, Time, Display,
and Logging, each of which offers you a different set of options. For more information
about the options available on each of the tabs, see the Time Scope block reference page.
Note: As you progress through this workflow, notice the blue question mark icon (
)
in the lower-left corner of the subsequent dialog boxes. This icon indicates that contextsensitive help is available. You can get more information about any of the parameters on
the dialog box by right-clicking the parameter name and selecting What's This?
Configure Appearance and Specify Signal Interpretation
First, you configure the appearance of the Time Scope window and specify how the Time
Scope block should interpret input signals. In the Configuration Properties dialog box,
click the Main tab. Choose the appropriate parameter settings for the Main tab, as
shown in the following table.
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Parameter
Setting
Open at
Checked
simulation start
Number of input 2
ports
Input
processing
Columns as channels (frame based)
Maximize axes
Auto
Axes scaling
Manual
In this tutorial, you want the block to treat the input signal as frame-based, so you must
set the Input processing parameter to Columns as channels (frame based).
Configure Axes Scaling and Data Alignment
The Main tab also allows you to control when and how Time Scope scales the axes. These
options also control how Time Scope aligns your data with respect to the axes. Click the
link labeled Configure... to the right of the Axes scaling parameter to see additional
options for axes scaling. After you click this button, the label changes to Hide... and new
parameters appear. The following table describes these additional options.
Parameter
Description
Axes scaling
Specify when the scope should automatically scale the axes. You can
select one of the following options:
• Manual — When you select this option, the scope does not
automatically scale the axes. You can manually scale the axes in
any of the following ways:
• Select Tools > Axes Scaling Properties.
• Press one of the Scale Axis Limits toolbar buttons.
• When the scope figure is the active window, press Ctrl and A
simultaneously.
• Auto — When you select this option, the scope scales the axes as
needed, both during and after simulation. Selecting this option
shows the Do not allow Y-axis limits to shrink check box.
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Display Time-Domain Data
Parameter
Description
• After N Updates — Selecting this option causes the scope to
scale the axes after a specified number of updates. Selecting this
option shows the Number of updates edit box.
By default, this property is set to Auto. This property is “Tunable”.
Scale axes limits Select this check box to scale the axes when the simulation stops.
The y-axis is always scaled. The x-axis limits are only scaled if you
at stop
also select the Scale X-axis limits check box.
Data range (%)
Allows you to specify how much white space surrounds your signal
in the Time Scope window. You can specify a value for both the
y- and x-axis. The higher the value you enter for the y-axis Data
range (%), the tighter the y-axis range is with respect to the
minimum and maximum values in your signal. For example, to have
your signal cover the entire y-axis range when the block scales the
axes, set this value to 100.
Align
Allows you to specify where the block should align your data with
respect to each axis. You can choose to have your data aligned with
the top, bottom, or center of the y-axis. Additionally, if you select the
Autoscale X-axis limits check box, you can choose to have your
data aligned with the right, left, or center of the x-axis.
Set the parameters to the values shown in the following table.
Parameter
Setting
Axes scaling
Manual
Scale axes limits Checked
at stop
Data range (%)
80
Align
Center
Autoscale X-axis Unchecked
limits
Set Time Domain Properties
In the Configuration Properties dialog box, click the Time tab. Set the parameters to the
values shown in the following table.
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Parameter
Setting
Time span
One frame period
Time span
overrun action
Wrap
Time units
Metric (based on Time Span)
Time display
offset
0
Time-axis labels All
Show time-axis
label
Checked
The Time span parameter allows you to enter a numeric value, a variable that evaluates
to a numeric value, or select the One frame period menu option. You can also select
the Auto menu option; in this mode, Time Scope automatically calculates the appropriate
value for time span from the difference between the simulation “Start time” and “Stop
time” parameters. The actual range of values that the block displays on the time-axis
depends on the value of both the Time span and Time display offset parameters. See
the following figure.
If the Time display offset parameter is a scalar, the value of the minimum time-axis
limit is equal to the Time display offset. In addition, the value of the maximum timeaxis limit is equal to the sum of the Time display offset parameter and the Time span
parameter. For information on the other parameters in the Time Scope window, see the
Time Scope reference page.
In this tutorial, the values on the time-axis range from 0 to One frame period, where
One frame period is 0.05 seconds (50 ms).
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Display Time-Domain Data
Set Display Properties
In the Configuration Properties dialog box, click the Display tab. Set the parameters to
the values shown in the following table.
Parameter
Setting
Active display
1
Title
Show legend
Checked
Show grid
Checked
Plot signal(s) as magnitude and phase
Unchecked
Y-limits (Minimum)
-2.5
Y-limits (Maximum)
2.5
Y-label
Amplitude
Set Logging Properties
In the Configuration Properties dialog box, click the Logging tab. Set Log data to
workspace to unchecked.
Click OK to save your changes and close the Configuration Properties dialog box.
Note: If you have not already done so, repeat all of these procedures for the Time Scope1
block (except leave the Number of input ports on the Main tab as 1) before continuing
with the other sections of this tutorial.
Use the Simulation Controls
One advantage to using the Time Scope block in your models is that you can control
model simulation directly from the Time Scope window. The buttons on the Simulation
Toolbar of the Time Scope window allow you to play, pause, stop, and take steps forward
or backward through model simulation. Alternatively, there are several keyboard
shortcuts you can use to control model simulation when the Time Scope is your active
window.
You can access a list of keyboard shortcuts for the Time Scope by selecting Help >
Keyboard Command Help. The following procedure introduces you to these features.
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1
If the Time Scope window is not open, double-click the block icon in the
ex_timescope_tut model. Start model simulation. In the Time Scope window, on
the Simulation Toolbar, click the Run button (
) on the Simulation Toolbar. You
can also use one of the following keyboard shortcuts:
• Ctrl+T
• P
• Space
2
While the simulation is running and the Time Scope is your active window, pause
the simulation. Use either of the following keyboard shortcuts:
• P
• Space
Alternatively, you can pause the simulation in one of two ways:
• In the Time Scope window, on the Simulation Toolbar, click the Pause button
(
).
• From the Time Scope menu, select Simulation > Pause.
3
With the model simulation still paused, advance the simulation by a single time step.
To do so, in the Time Scope window, on the Simulation Toolbar, click the Next Step
button (
).
Next, try using keyboard shortcuts to achieve the same result. Press the Page
Down key to advance the simulation by a single time step.
4
Resume model simulation using any of the following methods:
• From the Time Scope menu, select Simulation > Continue.
• In the Time Scope window, on the Simulation Toolbar, click the Continue button
(
).
• Use a keyboard shortcut, such as P or Space.
Modify the Time Scope Display
You can control the appearance of the Time Scope window using options from the display
or from the View menu. Among other capabilities, these options allow you to:
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Display Time-Domain Data
• Control the display of the legend
• Edit the line properties of your signals
• Show or hide the available toolbars
Change Signal Names in the Legend
You can change the name of a signal by double-clicking the signal name in the legend. By
default, the Time Scope names the signals based on the block they are coming from. For
this example, set the signal names as shown in the following table.
Block Name
Original Signal Name
New Signal Name
Time Scope
Add
Noisy Sine Wave
Time Scope
Digital Filter – Lowpass
Filtered Noisy Sine Wave
Time Scope1
Sine Wave
Original Sine Wave
Modify Axes Colors and Line Properties
Use the Style dialog box to modify the appearance of the axes and the lines for each of
the signals in your model. In the Time Scope menu, select View > Style.
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1
Change the Plot Type parameter to Auto for each Time Scope block. This setting
ensures that Time Scope displays a line graph if the signal is continuous and a
stairstep graph if the signal is discrete.
2
Change the Axes colors parameters for each Time Scope block. Leave the axes
background color as black and set the ticks, labels, and grid colors to white.
3
Set the Properties for line parameter to the name of the signal for which you
would like to modify the line properties. Set the line properties for each signal
according to the values shown in the following table.
Block Name
Signal Name
Line
Line Width Marker
Color
Time Scope
Noisy Sine
Wave
————
0.5
White
Time Scope
Filtered Noisy
Sine Wave
————
0.5
Red
Time Scope1
Original Sine
Wave
————
0.5
Yellow
none
Show and Hide Time Scope Toolbars
You can also use the options on the View menu to show or hide toolbars on the Time
Scope window. For example:
• To hide the simulation controls, select View > Toolbar. Doing so removes the
simulation toolbar from the Time Scope window and also removes the check mark
from next to the Toolbar option in the View menu.
• You can choose to show the simulation toolbar again at any time by selecting View >
Toolbar.
Verify that all toolbars are visible before moving to the next section of this tutorial.
Inspect Your Data (Scaling the Axes and Zooming)
Time Scope has plot navigation tools that allow you to scale the axes and zoom in or out
on the Time Scope window. The axes scaling tools allow you to specify when and how
often the Time Scope scales the axes.
So far in this tutorial, you have configured the Time Scope block for manual axes scaling.
Use one of the following options to manually scale the axes:
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Display Time-Domain Data
• From the Time Scope menu, select Tools > Scale Axes Limits.
• Press the Scale Axes Limits toolbar button (
).
• With the Time Scope as your active window, press Ctrl + A.
Adjust White Space Around the Signal
You can control how much space surrounds your signal and where your signal appears in
relation to the axes. To adjust the amount of space surrounding your signal and realign
it with the axes, you must first open the Tools—Plot Navigation Properties dialog box.
From the Time Scope menu, select Tools > Axes Scaling Properties .
In the Tools:Plot Navigation options dialog box, set the Data range (%) and Align
parameters. In a previous section, you set these parameters to 80 and Center,
respectively.
• To decrease the amount of space surrounding your signal, set the Data range (%)
parameter on the Tools:Plot Navigation Options dialog box to 90.
• To align your signal with the bottom of the Y-axis, set the Align parameter to
Bottom.
The next time you scale the axes of the Time Scope window, the window appears as
follows.
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‫‪2‬‬
‫‪2-88‬‬
Display Time-Domain Data
Use the Zoom Tools
The zoom tools allow you to zoom in simultaneously in the directions of both the x- and yaxes , or in either direction individually. For example, to zoom in on the signal between
5010 ms and 5020 ms, you can use the Zoom X option.
• To activate the Zoom X tool, select Tools > Zoom X, or press the corresponding
toolbar button (
). The Time Scope indicates that the Zoom X tool is active by
depressing the toolbar button and placing a check mark next to the Tools > Zoom X
menu option.
• To zoom in on the region between 5010 ms and 5020 ms, in the Time Scope window,
click and drag your cursor from the 10 ms mark to the 20 ms mark.
• While zoomed in, to activate the Pan tool, select Tools > Pan, or press the
corresponding toolbar button (
).
• To zoom out of the Time Scope window, right-click inside the window, and select
Zoom Out. Alternatively, you can return to the original view of your signal by rightclicking inside the Time Scope window and selecting Reset to Original View.
Manage Multiple Time Scopes
The Time Scope block provides tools to help you manage multiple Time Scope blocks in
your models. The model used throughout this tutorial, ex_timescope_tut, contains
two Time Scope blocks, labeled Time Scope and Time Scope1. The following sections
discuss the tools you can use to manage these Time Scope blocks.
Open All Time Scope Windows
When you have multiple windows open on your desktop, finding the one you need can
be difficult. The Time Scope block offers a View > Bring All Time Scopes Forward
menu option to help you manage your Time Scope windows. Selecting this option brings
all Time Scope windows into view. If a Time Scope window is not currently open, use this
menu option to open the window and bring it into view.
To try this menu option in the ex_timescope_tut model, open the Time Scope window,
and close the Time Scope1 window. From the View menu of the Time Scope window,
select Bring All Time Scopes Forward. The Time Scope1 window opens, along with
the already active Time Scope window. If you have any Time Scope blocks in other open
Simulink models, then these also come into view.
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Open Time Scope Windows at Simulation Start
When you have multiple Time Scope blocks in your model, you may not want all Time
Scope windows to automatically open when you start simulation. You can control
whether or not the Time Scope window opens at simulation start by selecting File >
Open at Start of Simulation from the Time Scope window. When you select this
option, the Time Scope GUI opens automatically when you start the simulation. When
you do not select this option, you must manually open the scope window by doubleclicking the corresponding Time Scope block in your model.
Find the Right Time Scope Block in Your Model
Sometimes, you have multiple Time Scope blocks in your model and need to find the
location of one that corresponds to the active Time Scope window. In such cases, you can
use the View > Highlight Simulink Block menu option or the corresponding toolbar
). When you do so, the model window becomes your active window, and the
button (
corresponding Time Scope block flashes three times in the model window. This option can
help you locate Time Scope blocks in your model and determine to which signals they are
attached.
To try this feature, open the Time Scope window, and on the simulation toolbar, click the
Highlight Simulink Block button. Doing so opens the ex_timescope_tut model. The
Time Scope block flashes three times in the model window, allowing you to see where in
your model the block of interest is located.
Docking Time Scope Windows in the Scopes Group Container
When you have multiple Time Scope blocks in your model you may want to see them in
the same window and compare them side-by-side. In such cases, you can select the Dock
Time Scope button ( ) at the top-right corner of the Time Scope window for the Time
Scope block.
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Display Time-Domain Data
The Time Scope window now appears in the Scopes group container. Next, press the Dock
Time Scope button at the top-right corner of the Time Scope window for the Time Scope1
block.
By default, the Scopes group container is situated above the MATLAB Command
Window. However, you can undock the Scopes group container by pressing the Show
Actions button ( ) at the top-right corner of the container and selecting Undock. The
Scopes group container is now independent from the MATLAB Command Window.
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Input, Output, and Display
Once docked, the Scopes group container displays the toolbar and menu bar of the Time
Scope window. If you open additional instances of Time Scope, a new Time Scope window
appears in the Scopes group container.
You can undock any instance of Time Scope by pressing the corresponding Undock button
( ) in the title bar of each docked instance. If you close the Scopes group container, all
docked instances of Time Scope close but the Simulink model continues to run.
Close All Time Scope Windows
If you save your model with Time Scope windows open, those windows will reopen the
next time you open the model. Reopening the Time Scope windows when you open your
model can increase the amount of time it takes your model to load. If you are working
with a large model, or a model containing multiple Time Scopes, consider closing all Time
Scope windows before you save and close that model. To do so, use the File > Close All
Time Scope Windows menu option.
To use this menu option in the ex_timescope_tut model, open the Time Scope or Time
Scope1 window, and select File > Close All Time Scope Windows. Both the Time
Scope and Time Scope1 windows close. If you now save and close the model, the Time
Scope windows do not automatically open the next time you open the model. You can
open Time Scope windows at any time by double-clicking a Time Scope block in your
model. Alternatively, you can choose to automatically open the Time Scope windows at
simulation start. To do so, from the Time Scope window, select File > Open at Start of
Simulation.
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Display Frequency-Domain Data in Spectrum Analyzer
Display Frequency-Domain Data in Spectrum Analyzer
You can use DSP System Toolbox blocks to work with signals in both the time and
frequency domain. To display frequency-domain signals, you can use blocks from
the Sinks library, such as the Vector Scope, Spectrum Analyzer, Matrix Viewer, and
Waterfall Scope blocks.
With the Spectrum Analyzer block, you can display the frequency spectra of time-domain
input data. In contrast to the Vector Scope block, the Spectrum Analyzer block computes
the Fast Fourier Transform (FFT) of the input signal internally, transforming the signal
into the frequency domain.
This example shows how you can use a Spectrum Analyzer block to display the frequency
content of two frame-based signals simultaneously:
1
At the MATLAB command prompt, type ex_spectrumanalyzer_tut.
The Spectrum Analyzer example opens, and the variables, Fs and mtlb, are loaded
into the MATLAB workspace.
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Input, Output, and Display
2
Double-click the Signal From Workspace block. Set the block parameters as follows,
and then click OK:
• Signal = mtlb
• Sample time = 1
• Samples per frame = 16
• Form output after final data value = Cyclic Repetition
Based on these parameters, the Signal From Workspace block repeatedly outputs the
input signal, mtlb, as a frame-based signal with a sample period of 1 second.
2-94
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Display Frequency-Domain Data in Spectrum Analyzer
3
Create two distinct signals to send to the Spectrum Analyzer block. Use the Digital
Filter Design block to filter the input signal, using the default parameters.
4
Double-click the Matrix Concatenate block. Set the block parameters as follows, and
then click OK:
• Number of inputs = 2
• Mode = Multidimensional array
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2
Input, Output, and Display
• Concatenate dimension = 2
The Matrix Concatenate block combines the two signals so that each column
corresponds to a different signal.
5
Double-click the Spectrum Analyzer block. The Spectrum Analyzer figure appears. In
the menu, select View > Spectrum Settings. The Spectrum Settings panel opens.
• Expand the Main options pane, if it is not already expanded.
• Set Type to Power.
• Select the Full frequency span check box.
• Set RBW (Hz) to 5.91e-3.
• Expand the Trace options pane, if it is not already expanded.
• Set Units to dBW.
• Set Averages to 2.
• Expand the Window options pane, if it is not already expanded.
• Set Overlap (%) to 50.
• Set Window to Hann.
Based on these parameters, the Spectrum Analyzer uses 128 samples from each
input channel to calculate a new windowed data segment, as shown in the following
equation.
D=
NENBW ¥ Fs
1 .512 ¥ 1 Hz
=
= 128 samples
RBW
11 .8125 ¥ 10 -3 Hz
There are also 128 frequency points in the FFT. Also, because Overlap (%) is set to
50, there is a buffer overlap length of 64 samples in each spectral estimate, as shown
in the following equation.
OL =
OP
100
¥L=
50
¥ 128 = 64 samples
100
Every time the scope updates the display, 64 points are plotted for each channel. At
16 samples per frame, Spectrum Analyzer waits for 3 frames or 48 samples before
displaying the first power spectral estimate.
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Display Frequency-Domain Data in Spectrum Analyzer
6
Fit all the calculated data points into the display. In the Spectrum Analyzer menu,
select Tools > Automatically Scale Axes Limits.
7
In the Spectrum Analyzer menu, select View > Configuration Properties. Then,
select the Show legend check box.
8
Run the model. The Spectrum Analyzer block computes the FFT of each of the input
signals. It then displays the power spectra of the frequency-domain signals in the
Spectrum Analyzer window.
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‫‪2-98‬‬
Display Frequency-Domain Data in Spectrum Analyzer
The power spectrum of the first input signal, from column one, is the yellow line. The
power spectrum of the second input signal, from column two, is the blue line.
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2
Input, Output, and Display
Visualize Central Limit Theorem in Array Plot
In this section...
“Display a Uniform Distribution” on page 2-100
“Display the Sum of Many Uniform Distributions” on page 2-101
“Inspect Your Data by Zooming” on page 2-103
Display a Uniform Distribution
This example shows how to use and configure the dsp.ArrayPlot to visualize
the Central Limit Theorem. This theorem states that the mean of a large number
of independent random variables with finite mean and variance exhibits a normal
distribution.
First, generate uniformly distributed random variables in MATLAB using the rand
function. Find their distributions using the hist function. At the MATLAB command
line, type:
numsamples = 1e4;
numbins
= 20;
r = rand(numsamples,1);
hst = hist(r,numbins);
Create a new Array Plot object.
hap3 = dsp.ArrayPlot;
Configure the properties of the Array Plot object to plot a histogram.
hap3 = dsp.ArrayPlot;
hap3.XOffset = 0;
hap3.SampleIncrement = 1/numbins;
hap3.PlotType = 'Stem';
hap3.YLimits = [0, max(hst)+1];
Call the step method to plot the uniform distribution.
step(hap3,hst');
The following Array Plot figure appears, showing a uniform distribution.
2-100
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Visualize Central Limit Theorem in Array Plot
Display the Sum of Many Uniform Distributions
Next, calculate the mean of multiple uniformly distributed random variables. As the
number of random variables increases, the distribution more closely resembles a normal
curve. Run the release method to let property values and input characteristics change.
At the MATLAB command line, type:
release(hap3);
Change the configuration of the Array Plot properties for the display of a distribution
function.
numbins
= 201;
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Input, Output, and Display
numtrials = 100;
r = zeros(numsamples,1);
hap3.SampleIncrement = 1/numbins;
hap3.PlotType = 'Stairs';
Call the step method repeatedly to plot the uniform distribution.
for ii = 1:numtrials
r = rand(numsamples,1)+r;
hst = hist(r/ii,0:1/numbins:1);
hap3.YLimits = [min(hst)-1, max(hst)+1];
step(hap3,hst');
pause(0.1);
end
When the simulation has finished, the Array Plot figure displays a bell curve, indicating
a distribution that is close to normal.
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Visualize Central Limit Theorem in Array Plot
Inspect Your Data by Zooming
The zoom tools allow you to zoom in simultaneously in the directions of both the x- and
y-axes or in either direction individually. For example, to zoom in on the distribution
between 0.3 and 0.7, you can use the Zoom X option.
• To activate the Zoom X tool, select Tools > Zoom X, or press the corresponding
toolbar button (
). You can determine if the Zoom X tool is active by looking for an
indented toolbar button or a check mark next to the Tools > Zoom X menu option.
• Next, zoom in on the region between 0.3 and 0.7. In the Array Plot window, click on
the 0.3-second mark, and drag to the 0.7-second mark. The display reflects this new xaxis setting, as shown in the following figure.
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3
Data and Signal Management
Learn concepts such as sample- and frame-based processing, sample rate, delay and
latency.
• “Sample- and Frame-Based Concepts” on page 3-2
• “Inspect Sample and Frame Rates in Simulink” on page 3-8
• “Convert Sample and Frame Rates in Simulink” on page 3-19
• “Buffering and Frame-Based Processing” on page 3-43
• “Delay and Latency” on page 3-59
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Data and Signal Management
Sample- and Frame-Based Concepts
In this section...
“Sample- and Frame-Based Signals” on page 3-2
“Model Sample- and Frame-Based Signals in MATLAB and Simulink” on page 3-3
“What Is Sample-Based Processing?” on page 3-4
“What Is Frame-Based Processing?” on page 3-4
Sample- and Frame-Based Signals
Sample-based signals are the most basic type of signal and are the easiest to construct
from a real-world (physical) signal. You can create a sample-based signal by sampling
a physical signal at a given sample rate, and outputting each individual sample as it is
received. In general, most Digital-to-Analog converters output sample-based signals.
You can create frame-based signals from sample-based signals. When you buffer a batch
of N samples, you create a frame of data. You can then output sequential frames of data
at a rate that is 1/N times the sample rate of the original sample-based signal. The rate
at which you output the frames of data is also known as the frame rate of the signal.
Frame-based data is a common format in real-time systems. Data acquisition hardware
often operates by accumulating a large number of signal samples at a high rate. The
hardware then propagates those samples to the real-time system as a block of data.
Doing so maximizes the efficiency of the system by distributing the fixed process
overhead across many samples. The faster data acquisition is suspended by slower
interrupt processes after each frame is acquired, rather than after each individual
sample. See “Benefits of Frame-Based Processing” on page 3-6 for more information.
DSP System Toolbox Source
Blocks
3-2
Create Sample-Based Signals Create Frame-Based Signals
Chirp
X
X
Constant
X
X
Constant Diagonal Matrix
X
Discrete Impulse
X
DSP Constant (Obsolete)
X
From Audio Device
X
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X
X
Sample- and Frame-Based Concepts
DSP System Toolbox Source
Blocks
Create Sample-Based Signals Create Frame-Based Signals
From Multimedia File
X
X
Identity Matrix
X
MIDI Controls
X
Multiphase Clock
X
X
N-Sample Enable
X
X
Random Source
X
Signal From Workspace
X
X
Sine Wave
X
X
UDP Receive
X
Model Sample- and Frame-Based Signals in MATLAB and Simulink
When you process signals using DSP System Toolbox software, you can do so in either
a sample- or frame-based manner. When you are working with blocks in Simulink, you
can specify, on a block-by-block basis, which type of processing the block performs. In
most cases, you specify the processing mode by setting the Input processing parameter.
Alternatively, when you are using System objects in MATLAB, you specify the processing
mode using the FrameBasedProcessing property. The following table shows the
common parameter settings you can use to perform sample- and frame-based processing
in MATLAB and Simulink.
Sample-Based Processing
Frame-Based Processing
MATLAB — System
objects
FrameBasedProcessing = FrameBasedProcessing =
False
True
Simulink — Blocks
Input processing =
Elements as channels
(sample based)
Input processing =
Columns as channels
(frame based)
Set the FrameBasedProcessing Property of a System object
All System objects support sample-based processing and some System objects support
both sample- and frame-based processing. To specify how your System object should
process input data, you set the FrameBasedProcessing property. The property has a
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3-3
3
Data and Signal Management
default value of true, which enables frame-based processing. To specify sample-based
processing, set the FrameBasedProcessing property to false.
What Is Sample-Based Processing?
In sample-based processing, blocks process signals one sample at a time. Each element
of the input signal represents one sample in a distinct channel. For example, from a
sample-based processing perspective, the following 3-by-2 matrix contains the first
sample in each of six independent channels.
When you configure a block to perform sample-based processing, the block interprets
scalar input as a single-channel signal. Similarly, the block interprets an M-by-N matrix
as multichannel signal with M*N independent channels. For example, in sample-based
processing, blocks interpret the following sequence of 3-by-2 matrices as a six-channel
signal.
For more information about the recent changes to frame-based processing, see the
“Frame-Based Processing” section of the DSP System Toolbox Release Notes.
What Is Frame-Based Processing?
In frame-based processing, blocks process data one frame at a time. Each frame of data
contains sequential samples from an independent channel. Each channel is represented
3-4
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Sample- and Frame-Based Concepts
by a column of the input signal. For example, from a frame-based processing perspective,
the following 3-by-2 matrix has two channels, each of which contains three samples.
When you configure a block to perform frame-based processing, the block interprets an
M-by-1 vector as a single-channel signal containing M samples per frame. Similarly,
the block interprets an M-by-N matrix as a multichannel signal with N independent
channels and M samples per channel. For example, in frame-based processing, blocks
interpret the following sequence of 3-by-2 matrices as a two-channel signal with a frame
size of 3.
Using frame-based processing is advantageous for many signal processing applications
because you can process multiple samples at once. By buffering your data into frames
and processing multisample frames of data, you can often improve the computational
time of your signal processing algorithms. To perform frame-based processing, you must
have a DSP System Toolbox license.
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Data and Signal Management
For more information about the recent changes to frame-based processing, see the
“Frame-Based Processing” section of the DSP System Toolbox Release Notes.
Benefits of Frame-Based Processing
Frame-based processing is an established method of accelerating both real-time systems
and model simulations.
Accelerate Real-Time Systems
Frame-based data is a common format in real-time systems. Data acquisition hardware
often operates by accumulating a large number of signal samples at a high rate, and
then propagating those samples to the real-time system as a block of data. This type
of propagation maximizes the efficiency of the system by distributing the fixed process
overhead across many samples; the faster data acquisition is suspended by slower
interrupt processes after each frame is acquired, rather than after each individual
sample is acquired.
The following figure illustrates how frame-based processing increases throughput. The
thin blocks each represent the time elapsed during acquisition of a sample. The thicker
blocks each represent the time elapsed during the interrupt service routine (ISR) that
reads the data from the hardware.
In this example, the frame-based operation acquires a frame of 16 samples between each
ISR. Thus, the frame-based throughput rate is many times higher than the sample-based
alternative.
3-6
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Sample- and Frame-Based Concepts
Be aware that frame-based processing introduces a certain amount of latency into
a process due to the inherent lag in buffering the initial frame. In many instances,
however, you can select frame sizes that improve throughput without creating
unacceptable latencies. For more information, see “Delay and Latency” on page 3-59.
Accelerate Model Simulations
The simulation of your model also benefits from frame-based processing. In this case,
you reduce the overhead of block-to-block communications by propagating frames of data
rather than individual samples.
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3-7
3
Data and Signal Management
Inspect Sample and Frame Rates in Simulink
Note: Starting in R2010b, many DSP System Toolbox blocks received a new parameter to
control whether they perform sample- or frame-based processing. The following content
has not been updated to reflect this change. For more information, see the “Frame-Based
Processing” section of the Release Notes.
In this section...
“Sample Rate and Frame Rate Concepts” on page 3-8
“Inspect Sample-Based Signals Using Probe Block” on page 3-9
“Inspect Frame-Based Signals Using Probe Block” on page 3-11
“Inspect Sample-Based Signals Using Color Coding” on page 3-13
“Inspect Frame-Based Signals Using Color Coding” on page 3-15
Sample Rate and Frame Rate Concepts
Sample rates and frame rates are important issues in most signal processing models.
This is especially true with systems that incorporate rate conversions. Fortunately, in
most cases when you build a Simulink model, you only need to set sample rates for the
source blocks. Simulink automatically computes the appropriate sample rates for the
blocks that are connected to the source blocks. Nevertheless, it is important to become
familiar with the sample rate and frame rate concepts as they apply to Simulink models.
The input frame period (Tfi) of a frame-based signal is the time interval between
consecutive vector or matrix inputs to a block. Similarly, the output frame period (Tfo) is
the time interval at which the block updates the frame-based vector or matrix value at
the output port.
In contrast, the sample period, Ts, is the time interval between individual samples in a
frame, this value is shorter than the frame period when the frame size is greater than 1.
The sample period of a frame-based signal is the quotient of the frame period and the
frame size, M:
Ts = Tf / M
3-8
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Inspect Sample and Frame Rates in Simulink
More specifically, the sample periods of inputs (Tsi) and outputs (Tso) are related to their
respective frame periods by
Tsi = Tfi / M i
Tso = Tfo / M o
where Mi and Mo are the input and output frame sizes, respectively.
The illustration below shows a single-channel, frame-based signal with a frame size (Mi)
of 4 and a frame period (Tfi) of 1. The sample period, Tsi, is therefore 1/4, or 0.25 second.
The frame rate of a signal is the reciprocal of the frame period. For instance, the input
frame rate would be 1 / Tfi . Similarly, the output frame rate would be 1 / Tfo .
The sample rate of a signal is the reciprocal of the sample period. For instance, the
sample rate would be 1 / Ts .
In most cases, the sequence sample period Tsi is most important, while the frame rate
is simply a consequence of the frame size that you choose for the signal. For a sequence
with a given sample period, a larger frame size corresponds to a slower frame rate, and
vice versa.
Inspect Sample-Based Signals Using Probe Block
You can use the Probe block to display the sample period of a sample-based signal. For
sample-based signals, the Probe block displays the label Ts, the sample period of the
sequence, followed by a two-element vector. The left element is the period of the signal
being measured. The right element is the signal's sample time offset, which is usually 0.
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Data and Signal Management
Note Simulink offers the ability to shift the sample time of a signal by an arbitrary
value, which is equivalent to shifting the signal's phase by a fractional sample period.
However, sample-time offsets are rarely used in signal processing systems, and DSP
System Toolbox blocks do not support them.
In this example, you use the Probe block to display the sample period of a sample-based
signal:
1
At the MATLAB command prompt, type ex_probe_tut1.
The Probe Example 1 model opens.
2
Run the model.
The figure below illustrates how the Probe blocks display the sample period of the
signal before and after each upsample operation.
3-10
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Inspect Sample and Frame Rates in Simulink
As displayed by the Probe blocks, the output from the Signal From Workspace block
is a sample-based signal with a sample period of 1 second. The output from the first
Upsample block has a sample period of 0.5 second, and the output from the second
Upsample block has a sample period of 0.25 second.
Inspect Frame-Based Signals Using Probe Block
You can use the Probe block to display the frame period of a frame-based signal. For
frame-based signals, the block displays the label Tf, the frame period of the sequence,
followed by a two-element vector. The left element is the period of the signal being
measured. The right element is the signal's sample time offset, which is usually 0.
Note Simulink offers the ability to shift a signal's sample times by an arbitrary value,
which is equivalent to shifting the signal's phase by a fractional sample period. However,
sample-time offsets are rarely used in signal processing systems, and DSP System
Toolbox blocks do not support them.
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3
Data and Signal Management
In this example, you use the Probe block to display the frame period of a frame-based
signal:
1
At the MATLAB command prompt, type ex_probe_tut2.
The Probe Example 2 model opens.
2
Run the model.
The figure below illustrates how the Probe blocks display the frame period of the
signal before and after each upsample operation.
3-12
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Inspect Sample and Frame Rates in Simulink
As displayed by the Probe blocks, the output from the Signal From Workspace block
is a frame-based signal with a frame period of 16 seconds. The output from the first
Upsample block has a frame period of 8 seconds, and the output from the second
Upsample block has a sample period of 4 seconds.
Note that the sample rate conversion is implemented through a change in the frame
period rather than the frame size.
Inspect Sample-Based Signals Using Color Coding
In the following example, you use sample time color coding to view the sample rate of a
sample-based signal:
1
At the MATLAB command prompt, type ex_color_tut1.
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The Sample Time Color Example 1 model opens.
2
From the Display menu, point to Sample Time, and select Colors.
This selection turns on sample time color coding. Simulink now assigns each sample
rate a different color.
3
Run the model.
The model should now look similar to the following figure:
3-14
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Inspect Sample and Frame Rates in Simulink
Every sample-based signal in this model has a different sample rate. Therefore, each
signal is assigned a different color.
For more information about sample time color coding, see “View Sample Time
Information” in the Simulink documentation.
Inspect Frame-Based Signals Using Color Coding
In this example, you use sample time color coding to view the frame rate of a frame-based
signal:
1
At the MATLAB command prompt, type ex_color_tut2.
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The Sample Time Color Example 2 model opens.
2
To turn on sample time color coding, from the Display menu, point to Sample
Time, and select Colors.
Simulink now assigns each frame rate a different color.
3
Run the model.
The model should now look similar to the following figure:
3-16
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Inspect Sample and Frame Rates in Simulink
Because the Rate options parameter in the Upsample blocks is set to Allow
multirate processing, each Upsample block changes the frame rate. Therefore,
each frame-based signal in the model is assigned a different color.
4
Double-click on each Upsample block and change the Rate options parameter to
Enforce single-rate processing.
5
Run the model.
Every signal is coded with the same color. Therefore, every signal in the model now
has the same frame rate.
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For more information about sample time color coding, see “View Sample Time
Information” in the Simulink documentation.
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Convert Sample and Frame Rates in Simulink
Convert Sample and Frame Rates in Simulink
Note: Starting in R2010b, many DSP System Toolbox blocks received a new parameter to
control whether they perform sample- or frame-based processing. The following content
has not been updated to reflect this change. For more information, see the “Frame-Based
Processing” section of the Release Notes.
In this section...
“Rate Conversion Blocks” on page 3-19
“Rate Conversion by Frame-Rate Adjustment” on page 3-20
“Rate Conversion by Frame-Size Adjustment” on page 3-24
“Avoid Unintended Rate Conversion” on page 3-28
“Frame Rebuffering Blocks” on page 3-34
“Buffer Signals by Preserving the Sample Period” on page 3-36
“Buffer Signals by Altering the Sample Period” on page 3-39
Rate Conversion Blocks
There are two common types of operations that impact the frame and sample rates of
a signal: direct rate conversion and frame rebuffering. Direct rate conversions, such as
upsampling and downsampling, can be implemented by altering either the frame rate
or the frame size of a signal. Frame rebuffering, which is used alter the frame size of a
signal in order to improve simulation throughput, usually changes either the sample rate
or frame rate of the signal as well.
The following table lists the principal rate conversion blocks in DSP System Toolbox
software. Blocks marked with an asterisk (*) offer the option of changing the rate by
either adjusting the frame size or frame rate.
Block
Library
Downsample *
Signal Operations
Dyadic Analysis Filter Bank
Filtering / Multirate Filters
Dyadic Synthesis Filter Bank
Filtering / Multirate Filters
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Block
Library
FIR Decimation *
Filtering / Multirate Filters
FIR Interpolation *
Filtering / Multirate Filters
FIR Rate Conversion
Filtering / Multirate Filters
Repeat *
Signal Operations
Upsample *
Signal Operations
Direct Rate Conversion
Rate conversion blocks accept an input signal at one sample rate, and propagate the
same signal at a new sample rate. Several of these blocks contain a Rate options
parameter offering two options for multirate versus single-rate processing:
• Enforce single-rate processing: When you select this option, the block
maintains the input sample rate.
• Allow multirate processing: When you select this option, the block
downsamples the signal such that the output sample rate is K times slower than the
input sample rate.
Note: When a Simulink model contains signals with various frame rates, the model is
called multirate. You can find a discussion of multirate models in “Excess Algorithmic
Delay (Tasking Latency)” on page 3-67. Also see “Scheduling ” in the Simulink Coder
documentation.
Rate Conversion by Frame-Rate Adjustment
One way to change the sample rate of a signal, 1/Tso, is to change the output frame rate
(Tfo ≠ Tfi), while keeping the frame size constant (Mo = Mi). Note that the sample rate of a
signal is defined as 1/Tso = Mo/Tfo:
1
At the MATLAB command prompt, type ex_downsample_tut1.
The Downsample Example T1 model opens.
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Convert Sample and Frame Rates in Simulink
2
From the Display menu, point to Signals & Ports, and select Signal Dimensions.
When you run the model, the dimensions of the signals appear next to the lines
connecting the blocks.
3
Double-click the Signal From Workspace block. The Source Block Parameters:
Signal From Workspace dialog box opens.
4
Set the block parameters as follows:
• Sample time = 0.125
• Samples per frame = 8
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Based on these parameters, the Signal From Workspace block outputs a frame-based
signal with a sample period of 0.125 second and a frame size of 8.
5
Save these parameters and close the dialog box by clicking OK.
6
Double-click the Downsample block. The Function Block Parameters:
Downsample dialog box opens.
7
Set the Rate options parameter to Allow multirate processing, and then
click OK.
The Downsample block is configured to downsample the signal by changing the
frame rate rather than the frame size.
8
Run the model.
After the simulation, the model should look similar to the following figure.
3-22
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Convert Sample and Frame Rates in Simulink
Because Tfi = M i ¥ Tsi , the input frame period, Tfi , is Tfi = 8 ¥ 0.125 = 1 second. This
value is displayed by the first Probe block. Therefore the input frame rate, 1 / Tfi , is
also 1 second.
The second Probe block in the model verifies that the output from the Downsample
block has a frame period, Tfo , of 2 seconds, twice the frame period of the input.
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However, because the frame rate of the output, 1 Tfo , is 0.5 second, the Downsample
block actually downsampled the original signal to half its original rate. As a result,
the output sample period, Tso = Tfo / M o , is doubled to 0.25 second without any
change to the frame size. The signal dimensions in the model confirm that the frame
size did not change.
Rate Conversion by Frame-Size Adjustment
One way to change the sample rate of a signal is by changing the frame size (that is
Mo ≠ Mi), but keep the frame rate constant (Tfo = Tfi). Note that the sample rate of a
signal is defined as 1/Tso = Mo/Tfo:
1
At the MATLAB command prompt, type ex_downsample_tut2.
The Downsample Example T2 model opens.
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Convert Sample and Frame Rates in Simulink
2
From the Display menu, point to Signals & Ports, and select Signal Dimensions.
When you run the model, the dimensions of the signals appear next to the lines
connecting the blocks.
3
Double-click the Signal From Workspace block. The Source Block Parameters:
Signal From Workspace dialog box opens.
4
Set the block parameters as follows:
• Sample time = 0.125
• Samples per frame = 8
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Based on these parameters, the Signal From Workspace block outputs a frame-based
signal with a sample period of 0.125 second and a frame size of 8.
5
Save these parameters and close the dialog box by clicking OK.
6
Double-click the Downsample block. The Function Block Parameters:
Downsample dialog box opens.
7
Set the Rate options parameter to Enforce single-rate processing, and
then click OK.
The Downsample block is configured to downsample the signal by changing the
frame size rather than the frame rate.
8
Run the model.
After the simulation, the model should look similar to the following figure.
3-26
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Convert Sample and Frame Rates in Simulink
Because Tfi = M i ¥ Tsi , the input frame period, Tfi , is Tfi = 8 ¥ 0.125 = 1 second. This
value is displayed by the first Probe block. Therefore the input frame rate, 1 / Tfi , is
also 1 second.
The Downsample block downsampled the input signal to half its original frame
size. The signal dimensions of the output of the Downsample block confirm that the
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downsampled output has a frame size of 4, half the frame size of the input. As a
result, the sample period of the output, Tso = Tfo / M o , now has a sample period of
0.25 second. This process occurred without any change to the frame rate ( Tfi = Tfo ).
Avoid Unintended Rate Conversion
It is important to be aware of where rate conversions occur in a model. In a few cases,
unintentional rate conversions can produce misleading results:
1
At the MATLAB command prompt, type ex_vectorscope_tut1.
The Vector Scope Example model opens.
2
Double-click the upper Sine Wave block. The Source Block Parameters: Sine
Wave dialog box opens.
3
Set the block parameters as follows:
• Frequency (Hz) = 1
• Sample time = 0.1
• Samples per frame = 128
Based on the Sample time and the Samples per frame parameters, the Sine Wave
outputs a sinusoid with a frame period of 128*0.1 or 12.8 seconds.
4
Save these parameters and close the dialog box by clicking OK.
5
Double-click the lower Sine Wave block.
6
Set the block parameters as follows, and then click OK:
• Frequency (Hz) = 2
• Sample time = 0.1
• Samples per frame = 128
Based on the Sample time and the Samples per frame parameters, the Sine Wave
outputs a sinusoid with a frame period of 128*0.1 or 12.8 seconds.
3-28
7
Double-click the Magnitude FFT block. The Function Block Parameters:
Magnitude FFT dialog box opens.
8
Select the Inherit FFT length from input dimensions check box, and then click
OK.
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Convert Sample and Frame Rates in Simulink
This setting instructs the block to use the input frame size (128) as the FFT length
(which is also the output size).
9
Double-click the Vector Scope block. The Sink Block Parameters: Vector Scope
dialog box opens.
10 Set the block parameters as follows, and then click OK:
• Click the Scope Properties tab.
• Input domain = Frequency
• Click the Axis Properties tab.
• Minimum Y-limit = -10
• Maximum Y-limit = 40
11 Run the model.
The model should now look similar to the following figure. Note that the signal
leaving the Magnitude FFT block is 128-by-1.
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The Vector Scope window displays the magnitude FFT of a signal composed of two
sine waves, with frequencies of 1 Hz and 2 Hz.
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Convert Sample and Frame Rates in Simulink
The Vector Scope block uses the input frame size (128) and period (12.8) to deduce
the original signal's sample period (0.1), which allows it to correctly display the
peaks at 1 Hz and 2 Hz.
12 Double-click the Magnitude FFT block. The Function Block Parameters:
Magnitude FFT dialog box opens.
13 Set the block parameters as follows:
• Clear the Inherit FFT length from input dimensions check box.
• Set the FFT length parameter to 256.
Based on these parameters, the Magnitude FFT block zero-pads the length-128 input
frame to a length of 256 before performing the FFT.
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14 Run the model.
The model should now look similar to the following figure. Note that the signal
leaving the Magnitude FFT block is 256-by-1.
The Vector Scope window displays the magnitude FFT of a signal composed of two
sine waves, with frequencies of 2 Hz and 4 Hz.
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Convert Sample and Frame Rates in Simulink
In this case, based on the input frame size (256) and frame period (12.8), the Vector
Scope block incorrectly calculates the original signal's sample period to be (12.8/256)
or 0.05 second. As a result, the spectral peaks appear incorrectly at 2 Hz and 4 Hz
rather than 1 Hz and 2 Hz.
The source of the error described above is unintended rate conversion. The zeropad operation performed by the Magnitude FFT block halves the sample period of
the sequence by appending 128 zeros to each frame. To calculate the spectral peaks
correctly, the Vector Scope block needs to know the sample period of the original
signal.
15 To correct for the unintended rate conversion, double-click the Vector Scope block.
16 Set the block parameters as follows:
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• Click the Axis Properties tab.
• Clear the Inherit sample time from input check box.
• Set the Sample time of original time series parameter to the actual sample
period of 0.1.
17 Run the model.
The Vector Scope block now accurately plots the spectral peaks at 1 Hz and 2 Hz.
In general, when you zero-pad or overlap buffers, you are changing the sample period
of the signal. If you keep this in mind, you can anticipate and correct problems such as
unintended rate conversion.
Frame Rebuffering Blocks
There are two common types of operations that impact the frame and sample rates of
a signal: direct rate conversion and frame rebuffering. Direct rate conversions, such as
upsampling and downsampling, can be implemented by altering either the frame rate
or the frame size of a signal. Frame rebuffering, which is used alter the frame size of a
signal in order to improve simulation throughput, usually changes either the sample rate
or frame rate of the signal as well.
Sometimes you might need to rebuffer a signal to a new frame size at some point in a
model. For example, your data acquisition hardware may internally buffer the sampled
signal to a frame size that is not optimal for the signal processing algorithm in the model.
In this case, you would want to rebuffer the signal to a frame size more appropriate for
the intended operations without introducing any change to the data or sample rate.
The following table lists the principal DSP System Toolbox buffering blocks.
Block
Library
Buffer
Signal Management/ Buffers
Delay Line
Signal Management/ Buffers
Unbuffer
Signal Management/ Buffers
Variable Selector
Signal Management/ Indexing
Blocks for Frame Rebuffering with Preservation of the Signal
Buffering operations provide another mechanism for rate changes in signal processing
models. The purpose of many buffering operations is to adjust the frame size of the
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Convert Sample and Frame Rates in Simulink
signal, M, without altering the signal's sample rate Ts. This usually results in a change to
the signal's frame rate, Tf, according to the following equation:
Tf = MTs
However, the equation above is only true if no samples are added or deleted from the
original signal. Therefore, the equation above does not apply to buffering operations that
generate overlapping frames, that only partially unbuffer frames, or that alter the data
sequence by adding or deleting samples.
There are two blocks in the Buffers library that can be used to change a signal's frame
size without altering the signal itself:
• Buffer — redistributes signal samples to a larger or smaller frame size
• Unbuffer — unbuffers a frame-based signal to a sample-based signal (frame size = 1)
The Buffer block preserves the signal's data and sample period only when its Buffer
overlap parameter is set to 0. The output frame period, Tfo, is
Tfo =
M o Tfi
Mi
where Tfi is the input frame period, Mi is the input frame size, and Mo is the output frame
size specified by the Output buffer size (per channel) parameter.
The Unbuffer block unbuffers a frame-based signal to its sample-based equivalent, and
always preserves the signal's data and sample period
Tso = Tfi / M i
where Tfi and Mi are the period and size, respectively, of the frame-based input.
Both the Buffer and Unbuffer blocks preserve the sample period of the sequence in the
conversion (Tso = Tsi).
Blocks for Frame Rebuffering with Alteration of the Signal
Some forms of buffering alter the signal's data or sample period in addition to adjusting
the frame size. This type of buffering is desirable when you want to create sliding
windows by overlapping consecutive frames of a signal, or select a subset of samples from
each input frame for processing.
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The blocks that alter a signal while adjusting its frame size are listed below. In this list,
Tsi is the input sequence sample period, and Tfi and Tfo are the input and output frame
periods, respectively:
• The Buffer block adds duplicate samples to a sequence when the Buffer overlap
parameter, L, is set to a nonzero value. The output frame period is related to the
input sample period by
Tfo = ( M o - L) Tsi
where Mo is the output frame size specified by the Output buffer size (per
channel) parameter. As a result, the new output sample period is
Tso =
( M o - L) Tsi
Mo
• The Delay Line block adds duplicate samples to the sequence when the Delay line
size parameter, Mo, is greater than 1. The output and input frame periods are the
same, Tfo = Tfi = Tsi, and the new output sample period is
Tso =
Tsi
Mo
• The Variable Selector block can remove, add, and/or rearrange samples in the input
frame when Select is set to Rows. The output and input frame periods are the same,
Tfo = Tfi, and the new output sample period is
Tso =
M i Tsi
Mo
where Mo is the length of the block's output, determined by the Elements vector.
In all of these cases, the sample period of the output sequence is not equal to the sample
period of the input sequence.
Buffer Signals by Preserving the Sample Period
In the following example, a signal with a sample period of 0.125 second is rebuffered
from a frame size of 8 to a frame size of 16. This rebuffering process doubles the
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Convert Sample and Frame Rates in Simulink
frame period from 1 to 2 seconds, but does not change the sample period of the signal
(Tso = Tsi = 0.125). The process also does not add or delete samples from the original
signal:
1
At the MATLAB command prompt, type ex_buffer_tut1.
The Buffer Example T1 model opens.
2
Double-click the Signal From Workspace block. The Source Block Parameters:
Signal From Workspace dialog box opens.
3
Set the parameters as follows:
• Signal = 1:1000
• Sample time = 0.125
• Samples per frame = 8
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• Form output after final data value = Setting to zero
Based on these parameters, the Signal from Workspace block outputs a framebased signal with a sample period of 0.125 second. Each output frame contains eight
samples.
4
Save these parameters and close the dialog box by clicking OK.
5
Double-click the Buffer block. The Function Block Parameters: Buffer dialog box
opens.
6
Set the parameters as follows, and then click OK:
• Output buffer size (per channel) = 16
• Buffer overlap = 0
• Initial conditions = 0
Based on these parameters, the Buffer block rebuffers the signal from a frame size
of 8 to a frame size of 16.
7
Run the model.
The following figure shows the model after simulation.
3-38
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Convert Sample and Frame Rates in Simulink
Note that the input to the Buffer block has a frame size of 8 and the output of the
block has a frame size of 16. As shown by the Probe blocks, the rebuffering process
doubles the frame period from 1 to 2 seconds.
Buffer Signals by Altering the Sample Period
Some forms of buffering alter the signal's data or sample period in addition to adjusting
the frame size. In the following example, a signal with a sample period of 0.125 second is
rebuffered from a frame size of 8 to a frame size of 16 with a buffer overlap of 4:
1
At the MATLAB command prompt, type ex_buffer_tut2.
The Buffer Example T2 model opens.
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Data and Signal Management
2
Double-click the Signal From Workspace block. The Source Block Parameters:
Signal From Workspace dialog box opens.
3
Set the parameters as follows:
• Signal = 1:1000
• Sample time = 0.125
• Samples per frame = 8
• Form output after final data value = Setting to zero
Based on these parameters, the Signal from Workspace block outputs a framebased signal with a sample period of 0.125 second. Each output frame contains eight
samples.
4
3-40
Save these parameters and close the dialog box by clicking OK.
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Convert Sample and Frame Rates in Simulink
5
Double-click the Buffer block. The Function Block Parameters: Buffer dialog box
opens.
6
Set the parameters as follows, and then click OK:
• Output buffer size (per channel) = 16
• Buffer overlap = 4
• Initial conditions = 0
Based on these parameters, the Buffer block rebuffers the signal from a frame size
of 8 to a frame size of 16. Also, after the initial output, the first four samples of each
output frame are made up of the last four samples from the previous output frame.
7
Run the model.
The following figure shows the model after the simulation has stopped.
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Data and Signal Management
Note that the input to the Buffer block has a frame size of 8 and the output of the
block has a frame size of 16. The relation for the output frame period for the Buffer
block is
Tfo = ( M o - L) Tsi
Tfo is (16-4)*0.125, or 1.5 seconds, as confirmed by the second Probe block. The
sample period of the signal at the output of the Buffer block is no longer 0.125
second. It is now Tso = Tfo / M o = 1.5 / 16 = 0 .0938 second. Thus, both the signal's
data and the signal's sample period have been altered by the buffering operation.
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Buffering and Frame-Based Processing
Buffering and Frame-Based Processing
Note: Starting in R2010b, many DSP System Toolbox blocks received a new parameter to
control whether they perform sample- or frame-based processing. The following content
has not been updated to reflect this change. For more information, see the “Frame-Based
Processing” section of the Release Notes.
In this section...
“Frame Status” on page 3-43
“Buffer Sample-Based Signals into Frame-Based Signals” on page 3-43
“Buffer Sample-Based Signals into Frame-Based Signals with Overlap” on page 3-46
“Buffer Frame-Based Signals into Other Frame-Based Signals” on page 3-51
“Buffer Delay and Initial Conditions” on page 3-54
“Unbuffer Frame-Based Signals into Sample-Based Signals” on page 3-54
Frame Status
The frame status of a signal refers to whether the signal is sample based or frame
based. In a Simulink model, the frame status is symbolized by a single line ,→, for a
sample-based signal and a double line, ⇒ for a frame-based signal. One way to convert a
sample-based signal to a frame-based signal is by using the Buffer block. You can convert
a frame-based signal to a sample-based signal using the Unbuffer block. To change
the frame status of a signal without performing a buffering operation, use the Frame
Conversion block in the Signal Attributes library.
Buffer Sample-Based Signals into Frame-Based Signals
Multichannel sample-based and frame-based signals can be buffered into multichannel
frame-based signals using the Buffer block.
The following figure is a graphical representation of a sample-based signal being
converted into a frame-based signal by the Buffer block.
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Data and Signal Management
In the following example, a two-channel sample-based signal is buffered into a twochannel frame-based signal using a Buffer block:
1
At the MATLAB command prompt, type ex_buffer_tut.
The Buffer Example model opens.
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Buffering and Frame-Based Processing
2
Double-click the Signal From Workspace block. The Source Block Parameters:
Signal From Workspace dialog box opens.
3
Set the parameters as follows:
• Signal = [1:10;-1:-1:-10]'
• Sample time = 1
• Samples per frame = 1
• Form output after final data value = Setting to zero
Based on these parameters, the Signal from Workspace block outputs a samplebased signal with a sample period of 1 second. Because you set the Samples per
frame parameter setting to 1, the Signal From Workspace block outputs one twochannel sample at each sample time.
4
Save these parameters and close the dialog box by clicking OK.
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Data and Signal Management
5
Double-click the Buffer block. The Function Block Parameters: Buffer dialog box
opens.
6
Set the parameters as follows:
• Output buffer size (per channel) = 4
• Buffer overlap = 0
• Initial conditions = 0
Because you set the Output buffer size parameter to 4, the Buffer block outputs a
frame-based signal with frame size 4.
7
Run the model.
Note that the input to the Buffer block is sample based (represented as a single line)
while the output is frame-based (represented by a double line).
The figure below is a graphical interpretation of the model behavior during
simulation.
[4 -4]
[3 -3]
[2 -2]
[1 -1]
t=3
t=2
t=1
t=0
Four consecutive samples from a
2-channel sample-based signal
1
2
3
4
-1
-2
-3
-4
2-channel frame-based signal
Note: Alternatively, you can set the Samples per frame parameter of the Signal From
Workspace block to 4 and create the same frame-based signal shown above without using
a Buffer block. The Signal From Workspace block performs the buffering internally, in
order to output a two-channel frame-based signal.
Buffer Sample-Based Signals into Frame-Based Signals with Overlap
In some cases it is useful to work with data that represents overlapping sections of an
original sample-based or frame-based signal. For example, in estimating the power
spectrum of a signal, it is often desirable to compute the FFT of overlapping sections of
3-46
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Buffering and Frame-Based Processing
data. Overlapping buffers are also needed in computing statistics on a sliding window, or
for adaptive filtering.
The Buffer overlap parameter of the Buffer block specifies the number of overlap
points, L. In the overlap case (L > 0), the frame period for the output is (Mo-L)*Tsi, where
Tsi is the input sample period and Mo is the Buffer size.
Note: Set the Buffer overlap parameter to a negative value to achieve output frame
rates slower than in the nonoverlapping case. The output frame period is still Tsi*(Mo-L),
but now with L < 0. Only the Mo newest inputs are included in the output buffers. The
previous L inputs are discarded.
In the following example, a four-channel sample-based signal with sample period 1 is
buffered to a frame-based signal with frame size 3 and frame period 2. Because of the
buffer overlap, the input sample period is not conserved, and the output sample period
is 2/3:
1
At the MATLAB command prompt, type ex_buffer_tut3.
The Buffer Example T3 model opens.
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Data and Signal Management
Also, the variable sp_examples_src is loaded into the MATLAB workspace. This
variable is defined as follows:
sp_examples_src=[1 1 5 -1; 2 1 5 -2; 3 0 5 -3; 4 0 5 -4; 5 1 5 -5; 6 1 5 -6];
2
Double-click the Signal From Workspace block. The Source Block Parameters:
Signal From Workspace dialog box opens.
3
Set the block parameters as follows:
• Signal = sp_examples_src
• Sample time = 1
• Samples per frame = 1
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Buffering and Frame-Based Processing
• Form output after final data value by = Setting to zero
Based on these parameters, the Signal from Workspace block outputs a samplebased signal with a sample period of 1 second. Because you set the Samples per
frame parameter setting to 1, the Signal From Workspace block outputs one fourchannel sample at each sample time.
4
Save these parameters and close the dialog box by clicking OK.
5
Double-click the Buffer block. The Function Block Parameters: Buffer dialog box
opens.
6
Set the block parameters as follows, and then click OK:
• Output buffer size (per channel) = 3
• Buffer overlap = 1
• Initial conditions = 0
Because you set the Output buffer size parameter to 3, the Buffer block outputs
a frame-based signal with frame size 3. Also, because you set the Buffer overlap
parameter to 1, the last sample from the previous output frame is the first sample in
the next output frame.
7
Run the model.
Note that the input to the Buffer block is sample based (represented as a single line)
while the output is frame based (represented by a double line).
The following figure is a graphical interpretation of the model's behavior during
simulation.
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Data and Signal Management
8
At the MATLAB command prompt, type sp_examples_yout.
The following is displayed in the MATLAB Command Window.
sp_examples_yout =
0
0
0
0
1
2
2
3
4
4
5
6
6
0
0
0
0
0
3-50
0
0
0
0
1
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
5
5
5
5
5
5
5
5
5
0
0
0
0
0
0
0
0
0
-1
-2
-2
-3
-4
-4
-5
-6
-6
0
0
0
0
0
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Buffering and Frame-Based Processing
Notice that the inputs do not begin appearing at the output until the fifth row, the
second row of the second frame. This is due to the block's latency.
See “Excess Algorithmic Delay (Tasking Latency)” on page 3-67 for general
information about algorithmic delay. For instructions on how to calculate buffering delay,
see “Buffer Delay and Initial Conditions” on page 3-54.
Buffer Frame-Based Signals into Other Frame-Based Signals
In the following example, a two-channel frame-based signal with frame size 4 is
rebuffered to a frame-based signal with frame size 3 and frame period 2. Because of the
overlap, the input sample period is not conserved, and the output sample period is 2/3:
1
At the MATLAB command prompt, type ex_buffer_tut4.
The Buffer Example T4 model opens.
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Data and Signal Management
Also, the variable sp_examples_src is loaded into the MATLAB workspace. This
variable is defined as
sp_examples_src = [1 1; 2 1; 3 0; 4 0; 5 1; 6 1; 7 0; 8 0]
2
Double-click the Signal From Workspace block. The Source Block Parameters:
Signal From Workspace dialog box opens.
3
Set the block parameters as follows:
• Signal = sp_examples_src
• Sample time = 1
3-52
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Buffering and Frame-Based Processing
• Samples per frame = 4
Based on these parameters, the Signal From Workspace block outputs a twochannel, frame-based signal with a sample period of 1 second and a frame size of 4.
4
Save these parameters and close the dialog box by clicking OK.
5
Double-click the Buffer block. The Function Block Parameters: Buffer dialog box
opens.
6
Set the block parameters as follows, and then click OK:
• Output buffer size (per channel) = 3
• Buffer overlap = 1
• Initial conditions = 0
Based on these parameters, the Buffer block outputs a two-channel, frame-based
signal with a frame size of 3.
7
Run the model.
The following figure is a graphical representation of the model's behavior during
simulation.
Note that the inputs do not begin appearing at the output until the last row of the
third output matrix. This is due to the block's latency.
See “Excess Algorithmic Delay (Tasking Latency)” on page 3-67 for general
information about algorithmic delay. For instructions on how to calculate buffering delay,
and see “Buffer Delay and Initial Conditions” on page 3-54.
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Data and Signal Management
Buffer Delay and Initial Conditions
In the examples “Buffer Sample-Based Signals into Frame-Based Signals with Overlap”
on page 3-46 and “Buffer Frame-Based Signals into Other Frame-Based Signals” on
page 3-51, the input signal is delayed by a certain number of samples. The initial
output samples correspond to the value specified for the Initial condition parameter.
The initial condition is zero in both examples mentioned above.
Under most conditions, the Buffer and Unbuffer blocks have some amount of delay or
latency. This latency depends on both the block parameter settings and the Simulink
tasking mode. You can use the rebuffer_delay function to determine the length of the
block's latency for any combination of frame size and overlap.
The syntax rebuffer_delay(f,n,v) returns the delay, in samples, introduced by the
buffering and unbuffering blocks during multitasking operations, where f is the input
frame size, n is the Output buffer size parameter setting, and v is the Buffer overlap
parameter setting.
For example, you can calculate the delay for the model discussed in the “Buffer FrameBased Signals into Other Frame-Based Signals” on page 3-51 using the following
command at the MATLAB command line:
d = rebuffer_delay(4,3,1)
d = 8
This result agrees with the block's output in that example. Notice that this model was
simulated in Simulink multitasking mode.
For more information about delay, see “Excess Algorithmic Delay (Tasking Latency)” on
page 3-67. For delay information about a specific block, see the “Latency” section of
the block reference page. For more information about the rebuffer_delay function, see
rebuffer_delay.
Unbuffer Frame-Based Signals into Sample-Based Signals
You can unbuffer multichannel frame-based signals into multichannel sample-based
signals using the Unbuffer block. The Unbuffer block performs the inverse operation of
the Buffer block's “sample-based to frame-based” buffering process, and generates an Nchannel sample-based output from an N-channel frame-based input. The first row in each
input matrix is always the first sample-based output.
3-54
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Buffering and Frame-Based Processing
The following figure is a graphical representation of this process.
The sample period of the sample-based output, Tso, is related to the input frame
period, Tfi, by the input frame size, Mi.
Tso = Tfi / M i
The Unbuffer block always preserves the signal's sample period (Tso = Tsi). See “Convert
Sample and Frame Rates in Simulink” on page 3-19 for more information about rate
conversions.
In the following example, a two-channel frame-based signal is unbuffered into a twochannel sample-based signal:
1
At the MATLAB command prompt, type ex_unbuffer_tut.
The Unbuffer Example model opens.
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3
Data and Signal Management
2
Double-click the Signal From Workspace block. The Source Block Parameters:
Signal From Workspace dialog box opens.
3
Set the block parameters as follows:
• Signal = [1:10;-1:-1:-10]'
• Sample time = 1
• Samples per frame = 4
• Form output after final data value by = Setting to zero
Based on these parameters, the Signal From Workspace block outputs a twochannel, frame based-signal with frame size 4.
3-56
4
Save these parameters and close the dialog box by clicking OK.
5
Double-click the Unbuffer block. The Function Block Parameters: Unbuffer
dialog box opens.
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Buffering and Frame-Based Processing
6
Set the Initial conditions parameter to 0, and then click OK.
The Unbuffer block unbuffers the frame-based signal into a two-channel samplebased signal.
7
Run the model.
The following figures is a graphical representation of what happens during the model
simulation.
1
2
3
4
-1
-2
-3
-4
2-channel frame-based signal
[4 -4]
[3 -3]
[2 -2]
[1 -1]
t=7
t=6
t=5
t=4
Four consecutive samples from a
2-channel sample-based signal
Note: The Unbuffer block generates initial conditions not shown in the figure below
with the value specified by the Initial conditions parameter. See the Unbuffer
reference page for information about the number of initial conditions that appear in
the output.
8
At the MATLAB command prompt, type sp_examples_yout.
The following is a portion of the output.
sp_examples_yout(:,:,1) =
0
0
sp_examples_yout(:,:,2) =
0
0
sp_examples_yout(:,:,3) =
0
0
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Data and Signal Management
sp_examples_yout(:,:,4) =
0
0
sp_examples_yout(:,:,5) =
1
-1
sp_examples_yout(:,:,6) =
2
-2
sp_examples_yout(:,:,7) =
3
-3
The Unbuffer block unbuffers the frame-based signal into a two-channel, samplebased signal. Each page of the output matrix represents a different sample time.
3-58
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Delay and Latency
Delay and Latency
Note: Starting in R2010b, many DSP System Toolbox blocks received a new parameter to
control whether they perform sample- or frame-based processing. The following content
has not been updated to reflect this change. For more information, see the “Frame-Based
Processing” section of the Release Notes.
In this section...
“Computational Delay” on page 3-59
“Algorithmic Delay” on page 3-60
“Zero Algorithmic Delay” on page 3-61
“Basic Algorithmic Delay” on page 3-64
“Excess Algorithmic Delay (Tasking Latency)” on page 3-67
“Predict Tasking Latency” on page 3-69
Computational Delay
The computational delay of a block or subsystem is related to the number of operations
involved in executing that block or subsystem. For example, an FFT block operating
on a 256-sample input requires Simulink software to perform a certain number of
multiplications for each input frame. The actual amount of time that these operations
consume depends heavily on the performance of both the computer hardware and
underlying software layers, such as the MATLAB environment and the operating system.
Therefore, computational delay for a particular model can vary from one computer
platform to another.
The simulation time represented on a model's status bar, which can be accessed via the
Simulink Digital Clock block, does not provide any information about computational
delay. For example, according to the Simulink timer, the FFT mentioned above executes
instantaneously, with no delay whatsoever. An input to the FFT block at simulation time
t=25.0 is processed and output at simulation time t=25.0, regardless of the number of
operations performed by the FFT algorithm. The Simulink timer reflects only algorithmic
delay, not computational delay.
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Data and Signal Management
Reduce Computational Delay
There are a number of ways to reduce computational delay without actually running
the simulation on faster hardware. To begin with, you should familiarize yourself with
“Manual Performance Optimization” in the Simulink documentation, which describes
some basic strategies. The following information discusses several options for improving
performance.
A first step in improving performance is to analyze your model, and eliminate or simplify
elements that are adding excessively to the computational load. Such elements might
include scope displays and data logging blocks that you had put in place for debugging
purposes and no longer require. In addition to these model-specific adjustments, there
are a number of more general steps you can take to improve the performance of any
model:
• Use frame-based processing wherever possible. It is advantageous for the entire
model to be frame based. See “Benefits of Frame-Based Processing” for more
information.
• Use the dspstartup file to tailor Simulink for signal processing models, or manually
make the adjustments described in “Settings in dspstartup.m” in the DSP System
Toolbox Getting Started Guide.
• Turn off the Simulink status bar by deselecting the Status bar option in the View
menu. Simulation speed will improve, but the time indicator will not be visible.
• Run your simulation from the MATLAB command line by typing
sim(gcs)
This method of starting a simulation can greatly increase the simulation speed, but
also has several limitations:
• You cannot interact with the simulation (to tune parameters, for instance).
• You must press Ctrl+C to stop the simulation, or specify start and stop times.
• There are no graphics updates in M-file S-functions, which include blocks such as
Vector Scope, etc.
• Use Simulink Coder code generation software to generate generic real-time (GRT)
code targeted to your host platform, and run the model using the generated
executable file. See the Simulink Coder documentation for more information.
Algorithmic Delay
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Delay and Latency
Algorithmic delay is delay that is intrinsic to the algorithm of a block or subsystem and
is independent of CPU speed. In this guide, the algorithmic delay of a block is referred to
simply as the block's delay. It is generally expressed in terms of the number of samples
by which a block's output lags behind the corresponding input. This delay is directly
related to the time elapsed on the Simulink timer during that block's execution.
The algorithmic delay of a particular block may depend on both the block parameter
settings and the general Simulink settings. To simplify matters, it is helpful to categorize
a block's delay using the following categories:
• “Zero Algorithmic Delay” on page 3-61
• “Basic Algorithmic Delay” on page 3-64
• “Excess Algorithmic Delay (Tasking Latency)” on page 3-67
The following topics explain the different categories of delay, and how the simulation and
parameter settings can affect the level of delay that a particular block experiences.
Zero Algorithmic Delay
The FFT block is an example of a component that has no algorithmic delay. The Simulink
timer does not record any passage of time while the block computes the FFT of the input,
and the transformed data is available at the output in the same time step that the input
is received. There are many other blocks that have zero algorithmic delay, such as the
blocks in the Matrices and Linear Algebra libraries. Each of those blocks processes its
input and generates its output in a single time step.
The Normalization block is an example of a block with zero algorithmic delay:
1
At the MATLAB command prompt, type ex_normalization_tut.
The Normalization Example T1 model opens.
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2
Double-click the Signal From Workspace block. The Source Block Parameters:
Signal From Workspace dialog box opens.
3
Set the block parameters as follows:
• Signal = 1:100
• Sample time = 1/4
• Samples per frame = 4
3-62
4
Save these parameters and close the dialog box by clicking OK.
5
Double-click the Frame Conversion block. The Function Block Parameters:
Frame Conversion dialog box opens.
6
Set the Sampling mode of output signal parameter to Sample based, and then
click OK.
7
Run the model.
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Delay and Latency
The model prepends the current value of the Simulink timer output from the Digital
Clock block to each output frame. The Frame Conversion block converts the framebased signal to a sample-based signal so that the output in the MATLAB Command
Window is more easily readable.
The Signal From Workspace block generates a new frame containing four samples
once every second (Tfo = π*4). The first few output frames are:
(t=0)
(t=1)
(t=2)
(t=3)
(t=4)
8
[ 1 2 3 4]'
[ 5 6 7 8]'
[ 9 10 11 12]'
[13 14 15 16]'
[17 18 19 20]'
At the MATLAB command prompt, type squeeze(dsp_examples_yout)'.
The normalized output, dsp_examples_yout, is converted to an easier-to-read
matrix format. The result, ans, is shown in the following figure:
ans =
0
1.0000
2.0000
3.0000
4.0000
5.0000
0.0333
0.0287
0.0202
0.0154
0.0124
0.0103
0.0667
0.0345
0.0224
0.0165
0.0131
0.0108
0.1000
0.0402
0.0247
0.0177
0.0138
0.0113
0.1333
0.0460
0.0269
0.0189
0.0146
0.0118
The first column of ans is the Simulink time provided by the Digital Clock block. You
can see that the squared 2-norm of the first input,
[1 2 3 4]' ./ sum([1 2 3 4]'.^2)
appears in the first row of the output (at time t=0), the same time step that the input
was received by the block. This indicates that the Normalization block has zero
algorithmic delay.
Zero Algorithmic Delay and Algebraic Loops
When several blocks with zero algorithmic delay are connected in a feedback loop,
Simulink may report an algebraic loop error and performance may generally suffer.
You can prevent algebraic loops by injecting at least one sample of delay into a feedback
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3
Data and Signal Management
loop , for example, by including a Delay block with Delay > 0. For more information, see
“Algebraic Loops” in the Simulink documentation.
Basic Algorithmic Delay
The Variable Integer Delay block is an example of a block with algorithmic delay. In the
following example, you use this block to demonstrate this concept:
1
At the MATLAB command prompt, type ex_variableintegerdelay_tut.
The Variable Integer Delay Example T1 opens.
2
Double-click the Signal From Workspace block. The Source Block Parameters:
Signal From Workspace dialog box opens.
3
Set the block parameters as follows:
• Signal = 1:100
• Sample time = 1
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Delay and Latency
• Samples per frame = 1
4
Save these parameters and close the dialog box by clicking OK.
5
Double-click the Constant block. The Source Block Parameters: Constant dialog
box opens.
6
Set the block parameters as follows:
• Constant value = 3
• Interpret vector parameters as 1–D = Clear this check box
• Sampling mode = Sample based
• Sample time = 1
Click OK to save these parameters and close the dialog box.
The input to the Delay port of the Variable Integer Delay block specifies the number
of sample periods that should elapse before an input to the In port is released to the
output. This value represents the block's algorithmic delay. In this example, since
the input to the Delay port is 3, and the sample period at the In and Delay ports
is 1, then the sample that arrives at the block's In port at time t=0 is released to the
output at time t=3.
7
Double-click the Variable Integer Delay block. The Function Block Parameters:
Variable Integer Delay dialog box opens.
8
Set the Initial conditions parameter to -1, and then click OK.
9
From the Display menu, point to Signals & Ports, and select Signal Dimensions
and Wide Nonscalar Lines.
10 Run the model.
The model should look similar to the following figure.
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Data and Signal Management
11 At the MATLAB command prompt, type dsp_examples_yout
The output is shown below:
dsp_examples_yout =
0
1
2
3
4
5
-1
-1
-1
1
2
3
The first column is the Simulink time provided by the Digital Clock block. The
second column is the delayed input. As expected, the input to the block at t=0 is
delayed three samples and appears as the fourth output sample, at t=3. You can also
see that the first three outputs from the Variable Integer Delay block inherit the
value of the block's Initial conditions parameter, -1. This period of time, from the
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Delay and Latency
start of the simulation until the first input is propagated to the output, is sometimes
called the initial delay of the block.
Many DSP System Toolbox blocks have some degree of fixed or adjustable algorithmic
delay. These include any blocks whose algorithms rely on delay or storage elements, such
as filters or buffers. Often, but not always, such blocks provide an Initial conditions
parameter that allows you to specify the output values generated by the block during the
initial delay. In other cases, the initial conditions are internally set to 0.
Consult the block reference pages for the delay characteristics of specific DSP System
Toolbox blocks.
Excess Algorithmic Delay (Tasking Latency)
Under certain conditions, Simulink may force a block to delay inputs longer than is
strictly required by the block's algorithm. This excess algorithmic delay is called tasking
latency, because it arises from synchronization requirements of the Simulink tasking
mode. A block's overall algorithmic delay is the sum of its basic delay and tasking
latency.
Algorithmic delay = Basic algorithmic delay + Tasking latency
The tasking latency for a particular block may be dependent on the following block and
model characteristics:
• “Simulink Tasking Mode” on page 3-67
• “Block Rate Type” on page 3-68
• “Model Rate Type” on page 3-68
• “Block Sample Mode” on page 3-68
Simulink Tasking Mode
Simulink has two tasking modes:
• Single-tasking
• Multitasking
To select a mode, from the Simulation menu, select Model Configuration
Parameters. In the Select pane, click Solver. From the Type list, select Fixed-step.
From the Tasking mode for periodic sample times list, choose SingleTasking
or MultiTasking. If, from the Tasking mode for periodic sample times list you
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Data and Signal Management
select Auto, the simulation runs in single-tasking mode if the model is single-rate, or
multitasking mode if the model is multirate.
Note: Many multirate blocks have reduced latency in the Simulink single-tasking mode.
Check the “Latency” section of a multirate block's reference page for details. Also see
“Scheduling ” in the Simulink Coder User's Guide.
Block Rate Type
A block is called single-rate when all of its input and output ports operate at the same
frame rate. A block is called multirate when at least one input or output port has a
different frame rate than the others.
Many blocks are permanently single-rate. This means that all input and output ports
always have the same frame rate. For other blocks, the block parameter settings
determine whether the block is single-rate or multirate. Only multirate blocks are subject
to tasking latency.
Note: Simulink may report an algebraic loop error if it detects a feedback loop composed
entirely of multirate blocks. To break such an algebraic loop, insert a single-rate block
with nonzero delay, such as a Unit Delay block. See the Simulink documentation for
more information about “Algebraic Loops”.
Model Rate Type
When all ports of all blocks in a model operate at a single frame rate, the model is called
single-rate. When the model contains blocks with differing frame rates, or at least one
multirate block, the model is called multirate. Note that Simulink prevents a single-rate
model from running in multitasking mode by generating an error.
Block Sample Mode
Many blocks can operate in either sample-based or frame-based modes. In source blocks,
the mode is usually determined by the Samples per frame parameter. If, for the
Samples per frame parameter, you enter 1, the block operates in sample-based mode.
If you enter a value greater than 1, the block operates in frame-based mode. In nonsource
blocks, the sample mode is determined by the input signal. See the block reference pages
for additional information about specific blocks.
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Delay and Latency
Predict Tasking Latency
The specific amount of tasking latency created by a particular combination of block
parameter and simulation settings is discussed in the “Latency” section of a block's
reference page. In this topic, you use the Upsample block's reference page to predict the
tasking latency of a model:
1
At the MATLAB command prompt, type ex_upsample_tut1.
The Upsample Example T1 model opens.
2
From the Simulation menu, select Model Configuration Parameters.
3
In the Solver pane, from the Type list, select Fixed-step. From the Solver list,
select discrete (no continuous states).
4
From the Tasking mode for periodic sample times list, select MultiTasking,
and then click OK.
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Data and Signal Management
Most multirate blocks experience tasking latency only in the Simulink multitasking
mode.
5
Double-click the Signal From Workspace block. The Source Block Parameters:
Signal From Workspace dialog box opens.
6
Set the block parameters as follows, and then click OK:
• Signal = 1:100
• Sample time = 1/4
• Samples per frame = 4
• Form output after final data value by = Setting to zero
7
Double-click the Upsample block. The Function Block Parameters: Upsample
dialog box opens.
8
Set the block parameters as follows, and then click OK:
• Upsample factor, L = 4
• Sample offset (0 to L-1) = 0
• Input processing = Columns as channels (frame based)
• Rate options = Allow multirate processing
• Initial condition = -1
The Rate options parameter makes the model multirate, since the input and output
frame rates will not be equal.
9
Double-click the Digital Clock block. The Source Block Parameters: Digital
Clock dialog box opens.
10 Set the Sample time parameter to 0.25, and then click OK.
This matches the sample period of the Upsample block's output.
11 Double-click the Frame Conversion block. The Function Block Parameters:
Frame Conversion dialog box opens.
12 Set the Sampling mode of output signal parameter to Sample based, and then
click OK.
13 Run the model.
The model should now look similar to the following figure.
3-70
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Delay and Latency
The model prepends the current value of the Simulink timer, from the Digital Clock
block, to each output frame. The Frame Conversion block converts the frame-based
signal into a sample-based signal so that the output in the MATLAB Command
Window is easily readable.
In the example, the Signal From Workspace block generates a new frame containing
four samples once every second (Tfo = π*4). The first few output frames are:
(t=0)
(t=1)
(t=2)
(t=3)
(t=4)
[ 1 2 3 4]
[ 5 6 7 8]
[ 9 10 11 12]
[13 14 15 16]
[17 18 19 20]
The Upsample block upsamples the input by a factor of 4, inserting three zeros
between each input sample. The change in rates is confirmed by the Probe blocks in
the model, which show a decrease in the frame period from Tfi = 1 to Tfo = 0.25.
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Data and Signal Management
14 At the MATLAB command prompt, type squeeze(dsp_examples_yout)'.
The output from the simulation is displayed in a matrix format. The first few
samples of the result, ans, are:
“Latency and Initial Conditions” in the Upsample block's reference page indicates
that when Simulink is in multitasking mode, the first sample of the block's framebased input appears in the output as sample MiL+D+1, where Mi is the input frame
size, L is the Upsample factor, and D is the Sample offset. This formula predicts
that the first input in this example should appear as output sample 17 (that is,
4*4+0+1).
The first column of the output is the Simulink time provided by the Digital Clock
block. The four values to the right of each time are the values in the output frame at
that time. You can see that the first sample in each of the first four output frames
inherits the value of the Upsample block's Initial conditions parameter. As a result
of the tasking latency, the first input value appears as the first sample of the 5th
output frame (at t=1). This is sample 17.
Now try running the model in single-tasking mode.
15 From the Simulation menu, select Model Configuration Parameters.
16 In the Solver pane, from the Type list, select Fixed-step. From the Solver list,
select Discrete (no continuous states).
17 From the Tasking mode for periodic sample times list, select SingleTasking.
18 Run the model.
The model now runs in single-tasking mode.
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Delay and Latency
19 At the MATLAB command prompt, type squeeze(dsp_examples_yout)'.
The first few samples of the result, ans, are:
“Latency and Initial Conditions” in the Upsample block's reference page indicates
that the block has zero latency for all multirate operations in the Simulink singletasking mode.
The first column of the output is the Simulink time provided by the Digital Clock
block. The four values to the right of each time are the values in the output frame
at that time. The first input value appears as the first sample of the first output
frame (at t=0). This is the expected behavior for the zero-latency condition. For the
particular parameter settings used in this example, running upsample_tut1 in
single-tasking mode eliminates the 17-sample delay that is present when you run the
model in multitasking mode.
You have now successfully used the Upsample block's reference page to predict the
tasking latency of a model.
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‫‪3-74‬‬
4
Filter Analysis, Design, and
Implementation
• “Design a Filter in Fdesign — Process Overview” on page 4-2
• “Design a Filter in the Filterbuilder GUI” on page 4-10
• “Use FDATool with DSP System Toolbox Software” on page 4-14
• “Digital Frequency Transformations” on page 4-77
• “Digital Filter Design Block” on page 4-111
• “Filter Realization Wizard” on page 4-121
• “Digital Filter Implementations” on page 4-133
• “Analog Filter Design Block” on page 4-143
• “Removing High-Frequency Noise from an ECG Signal” on page 4-145
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4
Filter Analysis, Design, and Implementation
Design a Filter in Fdesign — Process Overview
Process Flow Diagram and Filter Design Methodology
• “Exploring the Process Flow Diagram” on page 4-2
• “Select a Response” on page 4-4
• “Select a Specification” on page 4-4
• “Select an Algorithm” on page 4-6
• “Customize the Algorithm” on page 4-7
• “Design the Filter” on page 4-8
• “Design Analysis” on page 4-9
• “Realize or Apply the Filter to Input Data” on page 4-9
Note: You must minimally have the Signal Processing Toolbox™ installed to use
fdesign and design. Some of the features described below may be unavailable if your
installation does not additionally include the DSP System Toolbox license. The DSP
System Toolbox significantly expands the functionality available for the specification,
design, and analysis of filters. You can verify the presence of both toolboxes by typing
ver at the command prompt.
Exploring the Process Flow Diagram
The process flow diagram shown in the following figure lists the steps and shows the
order of the filter design process.
4-2
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Design a Filter in Fdesign — Process Overview
The first four steps of the filter design process relate to the filter Specifications Object,
while the last two steps involve the filter Implementation Object. Both of these objects
are discussed in more detail in the following sections. Step 5 - the design of the filter, is
the transition step from the filter Specifications Object to the Implementation object. The
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4-3
4
Filter Analysis, Design, and Implementation
analysis and verification step is completely optional. It provides methods for the filter
designer to ensure that the filter complies with all design criteria. Depending on the
results of this verification, you can loop back to steps 3 and 4, to either choose a different
algorithm, or to customize the current one. You may also wish to go back to steps 3 or 4
after you filter the input data with the designed filter (step 7), and find that you wish to
tweak the filter or change it further.
The diagram shows the help command for each step. Enter the help line at the MATLAB
command prompt to receive instructions and further documentation links for the
particular step. Not all of the steps have to be executed explicitly. For example, you could
go from step 1 directly to step 5, and the interim three steps are done for you by the
software.
The following are the details for each of the steps shown above.
Select a Response
If you type:
help fdesign/responses
at the MATLAB command prompt, you see a list of all available filter responses. The
responses marked with an asterisk require the DSP System Toolbox.
You must select a response to initiate the filter. In this example, a bandpass filter
Specifications Object is created by typing the following:
d = fdesign.bandpass
Select a Specification
A specification is an array of design parameters for a given filter. The specification is a
property of the Specifications Object.
Note: A specification is not the same as the Specifications Object. A Specifications Object
contains a specification as one of its properties.
When you select a filter response, there are a number of different specifications available.
Each one contains a different combination of design parameters. After you create a
filter Specifications Object, you can query the available specifications for that response.
Specifications marked with an asterisk require the DSP System Toolbox.
4-4
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Design a Filter in Fdesign — Process Overview
>> d = fdesign.bandpass; % step 1 - choose the response
>> set (d, 'specification')
ans =
'Fst1,Fp1,Fp2,Fst2,Ast1,Ap,Ast2'
'N,F3dB1,F3dB2'
'N,F3dB1,F3dB2,Ap'
'N,F3dB1,F3dB2,Ast'
'N,F3dB1,F3dB2,Ast1,Ap,Ast2'
'N,F3dB1,F3dB2,BWp'
'N,F3dB1,F3dB2,BWst'
'N,Fc1,Fc2'
'N,Fp1,Fp2,Ap'
'N,Fp1,Fp2,Ast1,Ap,Ast2'
'N,Fst1,Fp1,Fp2,Fst2'
'N,Fst1,Fp1,Fp2,Fst2,Ap'
'N,Fst1,Fst2,Ast'
'Nb,Na,Fst1,Fp1,Fp2,Fst2'
>> d=fdesign.arbmag;
>> set(d,'specification')
ans =
'N,F,A'
'N,B,F,A'
The set command can be used to select one of the available specifications as follows:
>> d = fdesign.lowpass; % step 1
>> % step 2: get a list of available specifications
>> set (d, 'specification')
ans =
'Fp,Fst,Ap,Ast'
'N,F3dB'
'N,F3dB,Ap'
'N,F3dB,Ap,Ast'
'N,F3dB,Ast'
'N,F3dB,Fst'
'N,Fc'
'N,Fc,Ap,Ast'
'N,Fp,Ap'
'N,Fp,Ap,Ast'
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4-5
4
Filter Analysis, Design, and Implementation
'N,Fp,F3dB'
'N,Fp,Fst'
'N,Fp,Fst,Ap'
'N,Fp,Fst,Ast'
'N,Fst,Ap,Ast'
'N,Fst,Ast'
'Nb,Na,Fp,Fst'
>> %step 2: set the required specification
>> set (d, 'specification', 'N,Fc')
If you do not perform this step explicitly, fdesign returns the default specification for
the response you chose in “Select a Response” on page 4-4, and provides default
values for all design parameters included in the specification.
Select an Algorithm
The availability of algorithms depends the chosen filter response, the design parameters,
and the availability of the DSP System Toolbox. In other words, for the same lowpass
filter, changing the specification string also changes the available algorithms. In the
following example, for a lowpass filter and a specification of 'N, Fc', only one algorithm
is available—window.
>> %step 2: set the required specification
>> set (d, 'specification', 'N,Fc')
>> designmethods (d) %step3: get available algorithms
Design Methods for class fdesign.lowpass (N,Fc):
window
However, for a specification of 'Fp,Fst,Ap,Ast', a number of algorithms are available.
If the user has only the Signal Processing Toolbox installed, the following algorithms are
available:
>>set (d, 'specification', 'Fp,Fst,Ap,Ast')
>>designmethods(d)
Design Methods for class fdesign.lowpass (Fp,Fst,Ap,Ast):
butter
cheby1
4-6
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Design a Filter in Fdesign — Process Overview
cheby2
ellip
equiripple
kaiserwin
If the user additionally has the DSP System Toolbox installed, the number of available
algorithms for this response and specification string increases:
>>set(d,'specification','Fp,Fst,Ap,Ast')
>>designmethods(d)
Design Methods for class fdesign.lowpass (Fp,Fst,Ap,Ast):
butter
cheby1
cheby2
ellip
equiripple
ifir
kaiserwin
multistage
The user chooses a particular algorithm and implements the filter with the design
function.
>>Hd=design(d,'butter');
The preceding code actually creates the filter, where Hd is the filter Implementation
Object. This concept is discussed further in the next step.
If you do not perform this step explicitly, design automatically selects the optimum
algorithm for the chosen response and specification.
Customize the Algorithm
The customization options available for any given algorithm depend not only on the
algorithm itself, selected in “Select an Algorithm” on page 4-6, but also on the
specification selected in “Select a Specification” on page 4-4. To explore all the
available options, type the following at the MATLAB command prompt:
help (d, 'algorithm-name')
where d is the Filter Specification Object, and algorithm-name is the name of the
algorithm in single quotes, such as 'butter' or 'cheby1'.
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4-7
4
Filter Analysis, Design, and Implementation
The application of these customization options takes place while “Design the Filter”
on page 4-8, because these options are the properties of the filter Implementation
Object, not the Specification Object.
If you do not perform this step explicitly, the optimum algorithm structure is selected.
Design the Filter
This next task introduces a new object, the Filter Object, or dfilt. To create a filter, use
the design command:
>> % design filter w/o specifying the algorithm
>> Hd = design(d);
where Hd is the Filter Object and d is the Specifications Object. This code creates a filter
without specifying the algorithm. When the algorithm is not specified, the software
selects the best available one.
To apply the algorithm chosen in “Select an Algorithm” on page 4-6, use the same
design command, but specify the Butterworth algorithm as follows:
>> Hd = design(d, 'butter');
where Hd is the new Filter Object, and d is the Specifications Object.
To obtain help and see all the available options, type:
>> help fdesign/design
This help command describes not only the options for the design command itself, but
also options that pertain to the method or the algorithm. If you are customizing the
algorithm, you apply these options in this step. In the following example, you design a
bandpass filter, and then modify the filter structure:
>> Hd = design(d, 'butter', 'filterstructure', 'df2sos')
f =
FilterStructure:
Arithmetic:
sosMatrix:
ScaleValues:
PersistentMemory:
'Direct-Form II, Second-Order Sections'
'double'
[7x6 double]
[8x1 double]
false
The filter design step, just like the first task of choosing a response, must be performed
explicitly. A Filter Object is created only when design is called.
4-8
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Design a Filter in Fdesign — Process Overview
Design Analysis
After the filter is designed you may wish to analyze it to determine if the filter satisfies
the design criteria. Filter analysis is broken into three main sections:
• Frequency domain analysis — Includes the magnitude response, group delay, and
pole-zero plots.
• Time domain analysis — Includes impulse and step response
• Implementation analysis — Includes quantization noise and cost
To display help for analysis of a discrete-time filter, type:
>> help dfilt/analysis
To display help for analysis of a multirate filter, type:
>> help mfilt/functions
To analyze your filter, you must explicitly perform this step.
Realize or Apply the Filter to Input Data
After the filter is designed and optimized, it can be used to filter actual input data. The
basic filter command takes input data x, filters it through the Filter Object, and produces
output y:
>> y = filter (FilterObj, x)
This step is never automatically performed for you. To filter your data, you must
explicitly execute this step. To understand how the filtering commands work, type:
>> help dfilt/filter
Note: If you have Simulink, you have the option of exporting this filter to a Simulink
block using the realizemdl command. To get help on this command, type:
>> help realizemdl
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4-9
4
Filter Analysis, Design, and Implementation
Design a Filter in the Filterbuilder GUI
The Graphical Interface to Fdesign
• “Introduction to Filterbuilder” on page 4-10
• “Filterbuilder Design Process” on page 4-10
• “Select a Response” on page 4-11
• “Select a Specification” on page 4-11
• “Select an Algorithm” on page 4-12
• “Customize the Algorithm” on page 4-12
• “Analyze the Design” on page 4-12
• “Realize or Apply the Filter to Input Data” on page 4-13
Introduction to Filterbuilder
The filterbuilder function provides a graphical interface to the fdesign objectoriented filter design paradigm and is intended to reduce development time during the
filter design process. filterbuilder uses a specification-centered approach to find the
best filter for the desired response.
Note: filterbuilder requires the Signal Processing Toolbox. The functionality of
filterbuilder is greatly expanded by the DSP System Toolbox. Some of the features
described or displayed below are only available if the DSP System Toolbox is installed.
You may verify your installation by typing ver at the command prompt.
Filterbuilder Design Process
The design process when using filterbuilder is similar to the process outlined in
the section titled “Process Flow Diagram and Filter Design Methodology” in the Getting
Started guide. The idea is to choose the constraints and specifications of the filter, and
to use those as a starting point in the design. Postponing the choice of algorithm for
the filter allows the best design method to be determined automatically, based upon
the desired performance criteria. The following are the details of each of the steps for
designing a filter with filterbuilder.
4-10
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Design a Filter in the Filterbuilder GUI
Select a Response
When you open the filterbuilder tool by typing:
filterbuilder
at the MATLAB command prompt, the Response Selection dialog box appears, listing
all possible filter responses available in the software. If you have the DSP System
Toolbox software installed, you have access to the full complement of filter responses.
Note: This step cannot be skipped because it is not automatically completed for you by
the software. You must select a response to initiate the filter design process.
After you choose a response, say bandpass, you start the design of the Specifications
Object, and the Bandpass Design dialog box appears. This dialog box contains a Main
pane, a Data Types pane and a Code Generation pane. The specifications of your filter
are generally set in the Main pane of the dialog box.
The Data Types pane provides settings for precision and data types, and the Code
Generation pane contains options for various implementations of the completed filter
design.
For the initial design of your filter, you will mostly use the Main pane.
The Bandpass Design dialog box contains all the parameters you need to determine
the specifications of a bandpass filter. The parameters listed in the Main pane depend
upon the type of filter you are designing. However, no matter what type of filter you have
chosen in the Response Selection dialog box, the filter design dialog box contains the
Main, Data Types, and Code Generation panes.
Select a Specification
To choose the specification for the bandpass filter, you can begin by selecting an Impulse
Response, Order Mode, and Filter Type in the Filter Specifications frame of the
Main Pane. You can further specify the response of your filter by setting frequency and
magnitude specifications in the appropriate frames on the Main Pane.
Note: Frequency, Magnitude, and Algorithm specifications are interdependent
and may change based upon your Filter Specifications selections. When choosing
specifications for your filter, select your Filter Specifications first and work your
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4-11
4
Filter Analysis, Design, and Implementation
way down the dialog box- this approach ensures that the best settings for dependent
specifications display as available in the dialog box.
Select an Algorithm
The algorithms available for your filter depend upon the filter response and design
parameters you have selected in the previous steps. For example, in the case of a
bandpass filter, if the impulse response selected is IIR and the Order Mode field is set
toMinimum, the design methods available are Butterworth, Chebyshev type I or II,
or Elliptic, whereas if the Order Mode field is set to Specify, the design method
available is IIR least p-norm.
Customize the Algorithm
By expanding the Design options section of the Algorithm frame, you can further
customize the algorithm specified. The options available will depend upon the algorithm
and settings that have already been selected in the dialog box. In the case of a bandpass
IIR filter using the Butterworth method, design options such as Match Exactly are
available.
Analyze the Design
To analyze the filter response, click on the View Filter Response button. The Filter
Visualization Tool opens displaying the magnitude plot of the filter response.
4-12
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Design a Filter in the Filterbuilder GUI
Realize or Apply the Filter to Input Data
When you have achieved the desired filter response through design iterations and
analysis using the Filter Visualization Tool, apply the filter to the input data. Again,
this step is never automatically performed for you by the software. To filter your data,
you must explicitly execute this step. In the Filter Visualization Tool, click OK and
DSP System Toolbox software creates the filter object with the name specified in the
Save variable as field and exports it to the MATLAB workspace.
The filter is then ready to be used to filter actual input data. The basic filter command
takes input data x, filters it through the Filter Object, and produces output y:
>> y = filter (FilterObj, x)
To understand how the filtering commands work, type:
>> help dfilt/filter
Tip If you have Simulink, you have the option of exporting this filter to a Simulink block
using the realizemdl command. To get help on this command, type:
>> help realizemdl
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4-13
4
Filter Analysis, Design, and Implementation
Use FDATool with DSP System Toolbox Software
In this section...
“Design Advanced Filters in FDATool” on page 4-14
“Access the Quantization Features of FDATool” on page 4-18
“Quantize Filters in FDATool” on page 4-20
“Analyze Filters with a Noise-Based Method” on page 4-28
“Scale Second-Order Section Filters” on page 4-33
“Reorder the Sections of Second-Order Section Filters” on page 4-37
“View SOS Filter Sections” on page 4-42
“Import and Export Quantized Filters” on page 4-47
“Generate MATLAB Code” on page 4-52
“Import XILINX Coefficient (.COE) Files” on page 4-53
“Transform Filters Using FDATool” on page 4-53
“Design Multirate Filters in FDATool” on page 4-62
“Realize Filters as Simulink Subsystem Blocks” on page 4-74
Design Advanced Filters in FDATool
• “Overview of FDATool Features” on page 4-14
• “Use FDATool with DSP System Toolbox Software” on page 4-15
• “Design a Notch Filter” on page 4-16
Overview of FDATool Features
DSP System Toolbox software adds new dialog boxes and operating modes, and
new menu selections, to the Filter Design and Analysis Tool (FDATool) provided by
Signal Processing Toolbox software. From the additional dialog boxes, one titled Set
Quantization Parameters and one titled Frequency Transformations, you can:
• Design advanced filters that Signal Processing Toolbox software does not provide the
design tools to develop.
• View Simulink models of the filter structures available in the toolbox.
• Quantize double-precision filters you design in this GUI using the design mode.
4-14
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Use FDATool with DSP System Toolbox Software
• Quantize double-precision filters you import into this GUI using the import mode.
• Analyze quantized filters.
• Scale second-order section filters.
• Select the quantization settings for the properties of the quantized filter displayed by
the tool:
• Coefficients — select the quantization options applied to the filter coefficients
• Input/output — control how the filter processes input and output data
• Filter Internals — specify how the arithmetic for the filter behaves
• Design multirate filters.
• Transform both FIR and IIR filters from one response to another.
After you import a filter into FDATool, the options on the quantization dialog box let you
quantize the filter and investigate the effects of various quantization settings.
Options in the frequency transformations dialog box let you change the frequency
response of your filter, keeping various important features while changing the response
shape.
Use FDATool with DSP System Toolbox Software
Adding DSP System Toolbox software to your tool suite adds a number of filter design
techniques to FDATool. Use the new filter responses to develop filters that meet more
complex requirements than those you can design in Signal Processing Toolbox software.
While the designs in FDATool are available as command line functions, the graphical
user interface of FDATool makes the design process more clear and easier to accomplish.
As you select a response type, the options in the right panes in FDATool change to let
you set the values that define your filter. You also see that the analysis area includes
a diagram (called a design mask) that describes the options for the filter response you
choose.
By reviewing the mask you can see how the options are defined and how to use them.
While this is usually straightforward for lowpass or highpass filter responses, setting
the options for the arbitrary response types or the peaking/notching filters is more
complicated. Having the masks leads you to your result more easily.
Changing the filter design method changes the available response type options.
Similarly, the response type you select may change the filter design methods you can
choose.
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4-15
4
Filter Analysis, Design, and Implementation
Design a Notch Filter
Notch filters aim to remove one or a few frequencies from a broader spectrum. You
must specify the frequencies to remove by setting the filter design options in FDATool
appropriately:
• Response Type
• Design Method
• Frequency Specifications
• Magnitude Specifications
Here is how you design a notch filter that removes concert A (440 Hz) from an input
musical signal spectrum.
1
Select Notching from the Differentiator list in Response Type.
2
Select IIR in Filter Design Method and choose Single Notch from the list.
3
For the Frequency Specifications, set Units to Hz and Fs, the full scale
frequency, to 1000.
4
Set the location of the center of the notch, in either normalized frequency or Hz. For
the notch center at 440 Hz, enter 440.
5
To shape the notch, enter the bandwidth, bw, to be 40.
6
Leave the Magnitude Specification in dB (the default) and leave Apass as 1.
7
Click Design Filter.
FDATool computes the filter coefficients and plots the filter magnitude response in
the analysis area for you to review.
When you design a single notch filter, you do not have the option of setting the filter
order — the Filter Order options are disabled.
Your filter should look about like this:
4-16
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Use FDATool with DSP System Toolbox Software
For more information about a design method, refer to the online Help system. For
instance, to get further information about the Q setting for the notch filter in FDATool,
enter
doc iirnotch
at the command line. This opens the Help browser and displays the reference page for
function iirnotch.
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4-17
4
Filter Analysis, Design, and Implementation
Designing other filters follows a similar procedure, adjusting for different design
specification options as each design requires.
Any one of the designs may be quantized in FDATool and analyzed with the available
analyses on the Analysis menu.
Access the Quantization Features of FDATool
You use the quantization panel in FDATool to quantize filters. Quantization
represents the fourth operating mode for FDATool, along with the filter design, filter
transformation, and import modes. To switch to quantization mode, open FDATool from
the MATLAB command prompt by entering
fdatool
When FDATool opens, click the Set Quantization Parameters button on the side bar.
FDATool switches to quantization mode and you see the following panel at the bottom of
FDATool, with the default double-precision option shown for Filter arithmetic.
4-18
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Use FDATool with DSP System Toolbox Software
The Filter arithmetic option lets you quantize filters and investigate the effects of
changing quantization settings. To enable the quantization settings in FDATool, select
Fixed-point from the Filter Arithmetic.
The quantization options appear in the lower panel of FDATool. You see tabs that access
various sets of options for quantizing your filter.
You use the following tabs in the dialog box to perform tasks related to quantizing filters
in FDATool:
• Coefficients provides access the settings for defining the coefficient quantization.
This is the default active panel when you switch FDATool to quantization mode
without a quantized filter in the tool. When you import a fixed-point filter into
FDATool, this is the active pane when you switch to quantization mode.
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4-19
4
Filter Analysis, Design, and Implementation
• Input/Output switches FDATool to the options for quantizing the inputs and outputs
for your filter.
• Filter Internals lets you set a variety of options for the arithmetic your filter
performs, such as how the filter handles the results of multiplication operations or
how the filter uses the accumulator.
• Apply — applies changes you make to the quantization parameters for your filter.
Quantize Filters in FDATool
• “Set Quantization Parameters” on page 4-20
• “Coefficients Options” on page 4-20
• “Input/Output Options” on page 4-22
• “Filter Internals Options” on page 4-24
• “Filter Internals Options for CIC Filters” on page 4-26
Set Quantization Parameters
Quantized filters have properties that define how they quantize data you filter. Use
the Set Quantization Parameters dialog box in FDATool to set the properties. Using
options in the Set Quantization Parameters dialog box, FDATool lets you perform a
number of tasks:
• Create a quantized filter from a double-precision filter after either importing the filter
from your workspace, or using FDATool to design the prototype filter.
• Create a quantized filter that has the default structure (Direct form II transposed) or
any structure you choose, and other property values you select.
• Change the quantization property values for a quantized filter after you design the
filter or import it from your workspace.
When you click Set Quantization Parameters, and then change Filter arithmetic
to Fixed-point, the quantized filter panel opens in FDATool, with the coefficient
quantization options set to default values.
Coefficients Options
To let you set the properties for the filter coefficients that make up your quantized
filter, FDATool lists options for numerator word length (and denominator word length
4-20
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Use FDATool with DSP System Toolbox Software
if you have an IIR filter). The following table lists each coefficients option and a short
description of what the option setting does in the filter.
Option Name
When Used
Description
Numerator Word Length
FIR filters only
Sets the word length used to
represent numerator coefficients in
FIR filters.
Numerator Frac. Length
FIR/IIR
Sets the fraction length used to
interpret numerator coefficients in
FIR filters.
Numerator Range (+/-)
FIR/IIR
Lets you set the range the
numerators represent. You use this
instead of the Numerator Frac.
Length option to set the precision.
When you enter a value x, the
resulting range is -x to x. Range must
be a positive integer.
Coefficient Word Length
IIR filters only
Sets the word length used to
represent both numerator and
denominator coefficients in IIR
filters. You cannot set different
word lengths for the numerator and
denominator coefficients.
Denominator Frac. Length
IIR filters
Sets the fraction length used to
interpret denominator coefficients in
IIR filters.
Denominator Range (+/-)
IIR filters
Lets you set the range the
denominator coefficients represent.
You use this instead of the
Denominator Frac. Length option
to set the precision. When you enter a
value x, the resulting range is -x to x.
Range must be a positive integer.
Best-precision fraction
lengths
All filters
Directs FDATool to select the
fraction lengths for numerator (and
denominator where available) values
to maximize the filter performance.
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4
Filter Analysis, Design, and Implementation
Option Name
When Used
Description
Selecting this option disables all of
the fraction length options for the
filter.
Scale Values frac. length
SOS IIR filters
Sets the fraction length used to
interpret the scale values in SOS
filters.
Scale Values range (+/-)
SOS IIR filters
Lets you set the range the SOS scale
values represent. You use this with
SOS filters to adjust the scaling used
between filter sections. Setting this
value disables the Scale Values
frac. length option. When you enter
a value x, the resulting range is -x to
x. Range must be a positive integer.
Use unsigned
representation
All filters
Tells FDATool to interpret the
coefficients as unsigned values.
Scale the numerator
coefficients to fully utilize
the entire dynamic range
All filters
Directs FDATool to scale the
numerator coefficients to effectively
use the dynamic range defined by the
numerator word length and fraction
length format.
Input/Output Options
The options that specify how the quantized filter uses input and output values are listed
in the table below.
Option Name
When Used
Description
Input Word Length
All filters
Sets the word length used to represent the
input to a filter.
Input fraction length
All filters
Sets the fraction length used to interpret
input values to filter.
Input range (+/-)
All filters
Lets you set the range the inputs
represent. You use this instead of the
Input fraction length option to set the
precision. When you enter a value x, the
4-22
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Option Name
When Used
Description
resulting range is -x to x. Range must be a
positive integer.
Output word length
All filters
Sets the word length used to represent the
output from a filter.
Avoid overflow
All filters
Directs the filter to set the fraction length
for the input to prevent the output values
from exceeding the available range as
defined by the word length. Clearing
this option lets you set Output fraction
length.
Output fraction length All filters
Sets the fraction length used to represent
output values from a filter.
Output range (+/-)
All filters
Lets you set the range the outputs
represent. You use this instead of the
Output fraction length option to set the
precision. When you enter a value x, the
resulting range is -x to x. Range must be a
positive integer.
Stage input word
length
SOS filters only
Sets the word length used to represent the
input to an SOS filter section.
Avoid overflow
SOS filters only
Directs the filter to use a fraction length
for stage inputs that prevents overflows
in the values. When you clear this option,
you can set Stage input fraction length.
Stage input fraction
length
SOS filters only
Sets the fraction length used to represent
input to a section of an SOS filter.
Stage output word
length
SOS filters only
Sets the word length used to represent the
output from an SOS filter section.
Avoid overflow
SOS filters only
Directs the filter to use a fraction length
for stage outputs that prevents overflows
in the values. When you clear this option,
you can set Stage output fraction
length.
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4
Filter Analysis, Design, and Implementation
Option Name
When Used
Description
Stage output fraction
length
SOS filters only
Sets the fraction length used to represent
the output from a section of an SOS filter.
Filter Internals Options
The options that specify how the quantized filter performs arithmetic operations are
listed in the table below.
Option
Equivalent Filter Property
(Using Wildcard *)
Description
Round towards
RoundMode
Sets the mode the filter uses to quantize
numeric values when the values lie
between representable values for the data
format (word and fraction lengths). Choose
from one of:
• ceil - Round toward positive infinity.
• convergent - Round to the closest
representable integer. Ties round to the
nearest even stored integer. This is the
least biased of the methods available in
this software.
• fix/zero - Round toward zero.
• floor - Round toward negative
infinity.
• nearest - Round toward nearest. Ties
round toward positive infinity.
• round - Round toward nearest. Ties
round toward negative infinity for
negative numbers, and toward positive
infinity for positive numbers.
Overflow Mode
4-24
OverflowMode
Sets the mode used to respond to overflow
conditions in fixed-point arithmetic.
Choose from either saturate (limit
the output to the largest positive or
negative representable value) or wrap
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Option
Equivalent Filter Property
(Using Wildcard *)
Description
(set overflowing values to the nearest
representable value using modular
arithmetic.
Filter Product (Multiply) Options
Product Mode
ProductMode
Determines how the filter handles the
output of product operations. Choose
from full precision (FullPrecision),
or whether to keep the most significant
bit (KeepMSB) or least significant bit
(KeepLSB) in the result when you need to
shorten the word length. Specify all
lets you set the fraction length applied to
the results of product operations.
Product word length
*ProdWordLength
Sets the word length applied to interpret
the results of multiply operations.
Num. fraction length
NumProdFracLength
Sets the fraction length used to interpret
the results of product operations that
involve numerator coefficients.
Den. fraction length
DenProdFracLength
Sets the fraction length used to interpret
the results of product operations that
involve denominator coefficients.
Accum. mode
AccumMode
Determines how the accumulator outputs
stored values. Choose from full precision
(FullPrecision), or whether to keep the
most significant bits (KeepMSB) or least
significant bits (KeepLSB) when output
results need shorter word length than
the accumulator supports. To let you set
the word length and the precision (the
fraction length) used by the output from
the accumulator, set this to Specify all.
Accum. word length
*AccumWordLength
Sets the word length used to store data in
the accumulator/buffer.
Filter Sum Options
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4
Filter Analysis, Design, and Implementation
Option
Equivalent Filter Property
(Using Wildcard *)
Description
Num. fraction length
NumAccumFracLength
Sets the fraction length used to interpret
the numerator coefficients.
Den. fraction length
DenAccumFracLength
Sets the fraction length the filter uses to
interpret denominator coefficients.
Cast signals before
sum
CastBeforeSum
Specifies whether to cast numeric data to
the appropriate accumulator format (as
shown in the signal flow diagrams for each
filter structure) before performing sum
operations.
State word length
*StateWordLength
Sets the word length used to represent the
filter states. Applied to both numeratorand denominator-related states
Avoid overflow
None
Prevent overflows in arithmetic
calculations by setting the fraction length
appropriately.
State fraction length
*StateFracLength
Lets you set the fraction length applied
to interpret the filter states. Applied to
both numerator- and denominator-related
states
Filter State Options
Note: When you apply changes to the values in the Filter Internals pane, the plots for
the Magnitude response estimate and Round-off noise power spectrum analyses
update to reflect those changes. Other types of analyses are not affected by changes to
the values in the Filter Internals pane.
Filter Internals Options for CIC Filters
CIC filters use slightly different options for specifying the fixed-point arithmetic in the
filter. The next table shows and describes the options.
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Quantize Double-Precision Filters
When you are quantizing a double-precision filter by switching to fixed-point or singleprecision floating point arithmetic, follow these steps.
1
Click Set Quantization Parameters to display the Set Quantization
Parameters pane in FDATool.
2
Select Single-precision floating point or Fixed-point from Filter
arithmetic.
When you select one of the optional arithmetic settings, FDATool quantizes the
current filter according to the settings of the options in the Set Quantization
Parameter panes, and changes the information displayed in the analysis area to
show quantized filter data.
3
In the quantization panes, set the options for your filter. Set options for
Coefficients, Input/Output, and Filter Internals.
4
Click Apply.
FDATool quantizes your filter using your new settings.
5
Use the analysis features in FDATool to determine whether your new quantized
filter meets your requirements.
Change the Quantization Properties of Quantized Filters
When you are changing the settings for the quantization of a quantized filter, or after
you import a quantized filter from your MATLAB workspace, follow these steps to set the
property values for the filter:
1
Verify that the current filter is quantized.
2
Click Set Quantization Parameters to display the Set Quantization
Parameters panel.
3
Review and select property settings for the filter quantization: Coefficients, Input/
Output, and Filter Internals. Settings for options on these panes determine how
your filter quantizes data during filtering operations.
4
Click Apply to update your current quantized filter to use the new quantization
property settings from Step 3.
5
Use the analysis features in FDATool to determine whether your new quantized
filter meets your requirements.
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4
Filter Analysis, Design, and Implementation
Analyze Filters with a Noise-Based Method
• “Analyze Filters with the Magnitude Response Estimate Method” on page 4-28
• “Compare the Estimated and Theoretical Magnitude Responses” on page 4-31
• “Select Quantized Filter Structures” on page 4-31
• “Convert the Structure of a Quantized Filter” on page 4-32
• “Convert Filters to Second-Order Sections Form” on page 4-32
Analyze Filters with the Magnitude Response Estimate Method
After you design and quantize your filter, the Magnitude Response Estimate option
on the Analysis menu lets you apply the noise loading method to your filter. When
you select Analysis > Magnitude Response Estimate from the menu bar, FDATool
immediately starts the Monte Carlo trials that form the basis for the method and runs
the analysis, ending by displaying the results in the analysis area in FDATool.
With the noise-based method, you estimate the complex frequency response for your
filter as determined by applying a noise- like signal to the filter input. Magnitude
Response Estimate uses the Monte Carlo trials to generate a noise signal that contains
complete frequency content across the range 0 to Fs. The first time you run the analysis,
magnitude response estimate uses default settings for the various conditions that define
the process, such as the number of test points and the number of trials.
Analysis Parameter
Default Setting
Description
Number of Points
512
Number of equally spaced points
around the upper half of the unit circle.
Frequency Range
0 to Fs/2
Frequency range of the plot x-axis.
Frequency Units
Hz
Units for specifying the frequency
range.
Sampling Frequency
48000
Inverse of the sampling period.
Frequency Scale
dB
Units used for the y-axis display of the
output.
Normalized Frequency
Off
Use normalized frequency for the
display.
After your first analysis run ends, open the Analysis Parameters dialog box and adjust
your settings appropriately, such as changing the number of trials or number of points.
4-28
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To open the Analysis Parameters dialog box, use either of the next procedures when
you have a quantized filter in FDATool:
• Select Analysis > Analysis Parameters from the menu bar
• Right-click in the filter analysis area and select Analysis Parameters from the
context menu
Whichever option you choose opens the dialog box. Notice that the settings for the options
reflect the defaults.
Noise Method Applied to a Filter
To demonstrate the magnitude response estimate method, start by creating a quantized
filter. For this example, use FDATool to design a sixth-order Butterworth IIR filter.
To Use Noise-Based Analysis in FDATool
1
Enter fdatool at the MATLAB prompt to launch FDATool.
2
Under Response Type, select Highpass.
3
Select IIR in Design Method. Then select Butterworth.
4
To set the filter order to 6, select Specify order under Filter Order. Enter 6 in the
text box.
5
Click Design Filter.
In FDATool, the analysis area changes to display the magnitude response for your
filter.
6
To generate the quantized version of your filter, using default quantizer settings,
click
on the side bar.
FDATool switches to quantization mode and displays the quantization panel.
7
From Filter arithmetic, select fixed-point.
Now the analysis areas shows the magnitude response for both filters — your
original filter and the fixed-point arithmetic version.
8
Finally, to use noise-based estimation on your quantized filter, select Analysis >
Magnitude Response Estimate from the menu bar.
FDATool runs the trial, calculates the estimated magnitude response for the filter,
and displays the result in the analysis area as shown in this figure.
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4
Filter Analysis, Design, and Implementation
In the above figure you see the magnitude response as estimated by the analysis
method.
View the Noise Power Spectrum
When you use the noise method to estimate the magnitude response of a filter, FDATool
simulates and applies a spectrum of noise values to test your filter response. While the
simulated noise is essentially white, you might want to see the actual spectrum that
FDATool used to test your filter.
From the Analysis menu bar option, select Round-off Noise Power Spectrum. In the
analysis area in FDATool, you see the spectrum of the noise used to estimate the filter
response. The details of the noise spectrum, such as the range and number of data points,
appear in the Analysis Parameters dialog box.
For more information, refer to McClellan, et al., Computer-Based Exercises for Signal
Processing Using MATLAB 5, Prentice-Hall, 1998. See Project 5: Quantization Noise in
Digital Filters, page 231.
Change Your Noise Analysis Parameters
In “Noise Method Applied to a Filter” on page 4-29, you used synthetic white noise
to estimate the magnitude response for a fixed-point highpass Butterworth filter. Since
you ran the estimate only once in FDATool, your noise analysis used the default analysis
parameters settings shown in “Analyze Filters with the Magnitude Response Estimate
Method” on page 4-28.
4-30
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To change the settings, follow these steps after the first time you use the noise estimate
on your quantized filter.
1
With the results from running the noise estimating method displayed in the
FDATool analysis area, select Analysis > Analysis Parameters from the menu
bar.
To give you access to the analysis parameters, the Analysis Parameters dialog box
opens (with default settings).
2
To use more points in the spectrum to estimate the magnitude response, change
Number of Points to 1024 and click OK to run the analysis.
FDATool closes the Analysis Parameters dialog box and reruns the noise estimate,
returning the results in the analysis area.
To rerun the test without closing the dialog box, press Enter after you type your new
value into a setting, then click Apply. Now FDATool runs the test without closing
the dialog box. When you want to try many different settings for the noise-based
analysis, this is a useful shortcut.
Compare the Estimated and Theoretical Magnitude Responses
An important measure of the effectiveness of the noise method for estimating the
magnitude response of a quantized filter is to compare the estimated response to the
theoretical response.
One way to do this comparison is to overlay the theoretical response on the estimated
response. While you have the Magnitude Response Estimate displaying in FDATool,
select Analysis > Overlay Analysis from the menu bar. Then select Magnitude
Response to show both response curves plotted together in the analysis area.
Select Quantized Filter Structures
FDATool lets you change the structure of any quantized filter. Use the Convert
structure option to change the structure of your filter to one that meets your needs.
To learn about changing the structure of a filter in FDATool, refer to “Converting the
Filter Structure” in your Signal Processing Toolbox documentation.
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4
Filter Analysis, Design, and Implementation
Convert the Structure of a Quantized Filter
You use the Convert structure option to change the structure of filter. When the
Source is Designed(Quantized) or Imported(Quantized), Convert structure lets
you recast the filter to one of the following structures:
• “Direct Form II Transposed Filter Structure”
• “Direct Form I Transposed Filter Structure”
• “Direct Form II Filter Structure”
• “Direct Form I Filter Structure”
• “Direct Form Finite Impulse Response (FIR) Filter Structure”
• “Direct Form FIR Transposed Filter Structure”
• “Lattice Autoregressive Moving Average (ARMA) Filter Structure”
• dfilt.calattice
• dfilt.calatticepc
• “Direct Form Antisymmetric FIR Filter Structure (Any Order)”
Starting from any quantized filter, you can convert to one of the following representation:
• Direct form I
• Direct form II
• Direct form I transposed
• Direct form II transposed
• Lattice ARMA
Additionally, FDATool lets you do the following conversions:
• Minimum phase FIR filter to Lattice MA minimum phase
• Maximum phase FIR filter to Lattice MA maximum phase
• Allpass filters to Lattice allpass
Refer to “FilterStructure” for details about each of these structures.
Convert Filters to Second-Order Sections Form
To learn about using FDATool to convert your quantized filter to use second-order
sections, refer to “Converting to Second-Order Sections” in your Signal Processing
4-32
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Toolbox documentation. You might notice that filters you design in FDATool, rather than
filters you imported, are implemented in SOS form.
View Filter Structures in FDATool
To open the demonstration, click Help > Show filter structures. After the Help
browser opens, you see the reference page for the current filter. You find the filter
structure signal flow diagram on this reference page, or you can navigate to reference
pages for other filter.
Scale Second-Order Section Filters
• “Use the Reordering and Scaling Second-Order Sections Dialog Box” on page 4-33
• “Scale an SOS Filter” on page 4-35
Use the Reordering and Scaling Second-Order Sections Dialog Box
FDATool provides the ability to scale SOS filters after you create them. Using options on
the Reordering and Scaling Second-Order Sections dialog box, FDATool scales either or
both the filter numerators and filter scale values according to your choices for the scaling
options.
Parameter
Description and Valid Value
Scale
Apply any scaling options to the filter. Select this when
you are reordering your SOS filter and you want to scale it
at the same time. Or when you are scaling your filter, with
or without reordering. Scaling is disabled by default.
No Overflow — High
SNR slider
Lets you set whether scaling favors reducing arithmetic
overflow in the filter or maximizing the signal-to-noise
ratio (SNR) at the filter output. Moving the slider to the
right increases the emphasis on SNR at the expense of
possible overflows. The markings indicate the P-norm
applied to achieve the desired result in SNR or overflow
protection. For more information about the P-norm
settings, refer to norm for details.
Maximum Numerator
Maximum allowed value for numerator coefficients after
scaling.
Numerator Constraint
Specifies whether and how to constrain numerator
coefficient values. Options are none, normalize,
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4
Filter Analysis, Design, and Implementation
Parameter
Description and Valid Value
power of 2, and unit. Choosing none lets the
scaling use any scale value for the numerators by
removing any constraints on the numerators, except
that the coefficients will be clipped if they exceed the
Maximum Numerator. With Normalize the maximum
absolute value of the numerator is forced to equal the
Maximum Numerator value (for all other constraints,
the Maximum Numerator is only an upper limit, above
which coefficients will be clipped). The power of 2 option
forces scaling to use numerator values that are powers of
2, such as 2 or 0.5. With unit, the leading coefficient of
each numerator is forced to a value of 1.
Overflow Mode
Sets the way the filter handles arithmetic overflow
situations during scaling. Choose from either saturate
(limit the output to the largest positive or negative
representable value) or wrap (set overflowing values to the
nearest representable value using modular arithmetic.
Scale Value Constraint
Specify whether to constrain the filter scale values, and
how to constrain them. Valid options are unit, power of
2, and none. Choosing unit for the constraint disables the
Max. Scale Value setting and forces scale values to equal
1. Power of 2 constrains the scale values to be powers of
2, such as 2 or 0.5, while none removes any constraint on
the scale values, except that they cannot exceed the Max.
Scale Value.
Max. Scale Value
Sets the maximum allowed scale values. SOS filter scaling
applies the Max. Scale Value limit only when you set
Scale Value Constraint to a value other than unit (the
default setting). Setting a maximum scale value removes
any other limits on the scale values.
Revert to Original Filter
Returns your filter to the original scaling. Being able to
revert to your original filter makes it easier to assess the
results of scaling your filter.
Various combinations of settings let you scale filter numerators without changing the
scale values, or adjust the filter scale values without changing the numerators. There is
no scaling control for denominators.
4-34
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Use FDATool with DSP System Toolbox Software
Scale an SOS Filter
Start the process by designing a lowpass elliptical filter in FDATool.
1
Launch FDATool.
2
In Response Type, select Lowpass.
3
In Design Method, select IIR and Elliptic from the IIR design methods list.
4
Select Minimum Order for the filter.
5
Switch the frequency units by choosing Normalized(0 to 1) from the Units list.
6
To set the passband specifications, enter 0.45 for wpass and 0.55 for wstop.
Finally, in Magnitude Specifications, set Astop to 60.
7
Click Design Filter to design the filter.
After FDATool finishes designing the filter, you see the following plot and settings in
the tool.
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4-35
4
Filter Analysis, Design, and Implementation
You kept the Options setting for Match exactly as both, meaning the filter design
matches the specification for the passband and the stopband.
8
To switch to scaling the filter, select Edit > Reorder and Scale Second-Order
Sections from the menu bar.
9
To see the filter coefficients, return to FDATool and select Filter Coefficients from
the Analysis menu. FDATool displays the coefficients and scale values in FDATool.
With the coefficients displayed you can see the effects of scaling your filter directly in the
scale values and filter coefficients.
4-36
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Use FDATool with DSP System Toolbox Software
Now try scaling the filter in a few different ways. First scale the filter to maximize the
SNR.
1
Return to the Reordering and Scaling Second-Order Sections dialog box
and select None for Reordering in the left pane. This prevents FDATool from
reordering the filter sections when you rescale the filter.
2
Move the No Overflow—High SNR slider from No Overflow to High SNR.
3
Click Apply to scale the filter and leave the dialog box open.
After a few moments, FDATool updates the coefficients displayed so you see the new
scaling.
All of the scale factors are now 1, and the SOS matrix of coefficients shows that
none of the numerator coefficients are 1 and the first denominator coefficient of each
section is 1.
4
Click Revert to Original Filter to restore the filter to the original settings for
scaling and coefficients.
Reorder the Sections of Second-Order Section Filters
Reorder Filters Using FDATool
FDATool designs most discrete-time filters in second-order sections. Generally, SOS
filters resist the effects of quantization changes when you create fixed-point filters. After
you have a second-order section filter in FDATool, either one you designed in the tool, or
one you imported, FDATool provides the capability to change the order of the sections
that compose the filter. Any SOS filter in FDATool allows reordering of the sections.
To reorder the sections of a filter, you access the Reorder and Scaling of Second-Order
Sections dialog box in FDATool.
With your SOS filter in FDATool, select Edit > Reorder and Scale from the menu bar.
FDATool returns the reordering dialog box shown here with the default settings.
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Controls on the Reordering and Scaling of Second-Order Sections dialog box
In this dialog box, the left-hand side contains options for reordering SOS filters. On
the right you see the scaling options. These are independent — reordering your filter
does not require scaling (note the Scale option) and scaling does not require that you
reorder your filter (note the None option under Reordering). For more about scaling
SOS filters, refer to “Scale Second-Order Section Filters” on page 4-33 and to scale
in the reference section.
Reordering SOS filters involves using the options in the Reordering and Scaling of
Second-Order Sections dialog box. The following table lists each reorder option and
provides a description of what the option does.
4-38
Control Option
Description
Auto
Reorders the filter sections to minimize the output noise
power of the filter. Note that different ordering applies
to each specification type, such as lowpass or highpass.
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Control Option
Description
Automatic ordering adapts to the specification type of your
filter.
None
Does no reordering on your filter. Selecting None lets you
scale your filter without applying reordering at the same
time. When you access this dialog box with a current filter,
this is the default setting — no reordering is applied.
Least selective section
Rearranges the filter sections so the least restrictive
to most selective section (lowest Q) section is the first section and the most
restrictive (highest Q) section is the last section.
Most selective section to Rearranges the filter sections so the most restrictive
(highest Q) section is the first section and the least
least selective section
restrictive (lowest Q) section is the last section.
Custom reordering
Lets you specify the section ordering to use by enabling the
Numerator Order and Denominator Order options
Numerator Order
Specify new ordering for the sections of your SOS filter.
Enter a vector of the indices of the sections in the order in
which to rearrange them. For example, a filter with five
sections has indices 1, 2, 3, 4, and 5. To switch the second
and fourth sections, the vector would be [1,4,3,2,5].
Use Numerator Order
Rearranges the denominators in the order assigned to the
numerators.
Specify
Lets you specify the order of the denominators, rather than
using the numerator order. Enter a vector of the indices of
the sections to specify the order of the denominators to use.
For example, a filter with five sections has indices 1, 2, 3, 4,
and 5. To switch the second and fourth sections, the vector
would be [1,4,3,2,5].
Use Numerator Order
Reorders the scale values according to the order of the
numerators.
Specify
Lets you specify the order of the scale values, rather than
using the numerator order. Enter a vector of the indices of
the sections to specify the order of the denominators to use.
For example, a filter with five sections has indices 1, 2, 3, 4,
and 5. To switch the second and fourth sections, the vector
would be [1,4,3,2,5].
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Filter Analysis, Design, and Implementation
Control Option
Description
Revert to Original Filter Returns your filter to the original section ordering. Being
able to revert to your original filter makes comparing
the results of changing the order of the sections easier to
assess.
Reorder an SOS Filter
With FDATool open a second-order filter as the current filter, you use the following
process to access the reordering capability and reorder you filter. Start by launching
FDATool from the command prompt.
1
Enter fdatool at the command prompt to launch FDATool.
2
Design a lowpass Butterworth filter with order 10 and the default frequency
specifications by entering the following settings:
• Under Response Type select Lowpass.
• Under Design Method, select IIR and Butterworth from the list.
• Specify the order equal to 10 in Specify order under Filter Order.
• Keep the default Fs and Fc values in Frequency Specifications.
3
Click Design Filter.
FDATool designs the Butterworth filter and returns your filter as a Direct-Form
II filter implemented with second-order sections. You see the specifications in the
Current Filter Information area.
With the second-order filter in FDATool, reordering the filter uses the Reordering
and Scaling of Second-Order Sections feature in FDATool (also available in
Filter Visualization Tool, fvtool).
4
To reorder your filter, select Edit > Reorder and Scale Second-Order Sections
from the FDATool menus.
Now you are ready to reorder the sections of your filter. Note that FDATool performs the
reordering on the current filter in the session.
Use Least Selective to Most Selective Section Reordering
To let FDATool reorder your filter so the least selective section is first and the most
selective section is last, perform the following steps in the Reordering and Scaling of
Second-Order Sections dialog box.
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1
In Reordering, select Least selective section to most selective section.
2
To prevent filter scaling at the same time, clear Scale in Scaling.
3
In FDATool, select View > SOS View Settings from the menu bar so you see the
sections of your filter displayed in FDATool.
4
In the SOS View Settings dialog box, select Individual sections. Making this
choice configures FDATool to show the magnitude response curves for each section of
your filter in the analysis area.
5
Back in the Reordering and Scaling of Second-Order Sections dialog box, click
Apply to reorder your filter according to the Qs of the filter sections, and keep the
dialog box open. In response, FDATool presents the responses for each filter section
(there should be five sections) in the analysis area.
In the next two figures you can compare the ordering of the sections of your filter. In
the first figure, your original filter sections appear. In the second figure, the sections
have been rearranged from least selective to most selective.
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Filter Analysis, Design, and Implementation
You see what reordering does, although the result is a bit subtle. Now try custom
reordering the sections of your filter or using the most selective to least selective
reordering option.
View SOS Filter Sections
• “Using the SOS View Dialog Box” on page 4-42
• “View the Sections of SOS Filters” on page 4-44
Using the SOS View Dialog Box
Since you can design and reorder the sections of SOS filters, FDATool provides the
ability to view the filter sections in the analysis area — SOS View. Once you have a
second-order section filter as your current filter in FDATool, you turn on the SOS View
option to see the filter sections individually, or cumulatively, or even only some of the
sections. Enabling SOS View puts FDATool in a mode where all second-order section
filters display sections until you disable the SOS View option. SOS View mode applies
to any analysis you display in the analysis area. For example, if you configure FDATool
to show the phase responses for filters, enabling SOS View means FDATool displays the
phase response for each section of SOS filters.
Controls on the SOS View Dialog Box
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SOS View uses a few options to control how FDATool displays the sections, or which
sections to display. When you select View > SOS View from the FDATool menu bar, you
see this dialog box containing options to configure SOS View operation.
By default, SOS View shows the overall response of SOS filters. Options in the SOS View
dialog box let you change the display. This table lists all the options and describes the
effects of each.
Option
Description
Overall Filter
This is the familiar display in FDATool. For a secondorder section filter you see only the overall response
rather than the responses for the individual sections.
This is the default configuration.
Individual sections
When you select this option, FDATool displays the
response for each section as a curve. If your filter
has five sections you see five response curves, one for
each section, and they are independent. Compare to
Cumulative sections.
Cumulative sections
When you select this option, FDATool displays the
response for each section as the accumulated response
of all prior sections in the filter. If your filter has five
sections you see five response curves:
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Filter Analysis, Design, and Implementation
Option
Description
• The first curve plots the response for the first filter
section.
• The second curve plots the response for the
combined first and second sections.
• The third curve plots the response for the first,
second, and third sections combined.
And so on until all filter sections appear in the display.
The final curve represents the overall filter response.
Compare to Cumulative sections and Overall
Filter.
User defined
Here you define which sections to display, and in
which order. Selecting this option enables the text box
where you enter a cell array of the indices of the filter
sections. Each index represents one section. Entering
one index plots one response. Entering something like
{1:2} plots the combined response of sections 1 and
2. If you have a filter with four sections, the entry
{1:4} plots the combined response for all four sections,
whereas {1,2,3,4} plots the response for each section.
Note that after you enter the cell array, you need to
click OK or Apply to update the FDATool analysis
area to the new SOS View configuration.
Use secondary-scaling
points
This directs FDATool to use the secondary scaling
points in the sections to determine where to split the
sections. This option applies only when the filter is a
df2sos or df1tsos filter. For these structures, the
secondary scaling points refer to the scaling locations
between the recursive and the nonrecursive parts of
the section (the "middle" of the section). By default,
secondary-scaling points is not enabled. You use this
with the Cumulative sections option only.
View the Sections of SOS Filters
After you design or import an SOS filter in to FDATool, the SOS view option lets you see
the per section performance of your filter. Enabling SOS View from the View menu in
4-44
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FDATool configures the tool to display the sections of SOS filters whenever the current
filter is an SOS filter.
These next steps demonstrate using SOS View to see your filter sections displayed in
FDATool.
1
Launch FDATool.
2
Create a lowpass SOS filter using the Butterworth design method. Specify the filter
order to be 6. Using a low order filter makes seeing the sections more clear.
3
Design your new filter by clicking Design Filter.
FDATool design your filter and show you the magnitude response in the analysis
area. In Current Filter Information you see the specifications for your filter. You
should have a sixth-order Direct-Form II, Second-Order Sections filter with three
sections.
4
To enable SOS View, select View > SOS View from the menu bar.
By default the analysis area in FDATool shows the overall filter response, not the
individual filter section responses. This dialog box lets you change the display
configuration to see the sections.
5
To see the magnitude responses for each filter section, select Individual sections.
6
Click Apply to update FDATool to display the responses for each filter section. The
analysis area changes to show you something like the following figure.
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Filter Analysis, Design, and Implementation
If you switch FDATool to display filter phase responses (by selecting Analysis >
Phase Response), you see the phase response for each filter section in the analysis
area.
7
To define your own display of the sections, you use the User defined option and
enter a vector of section indices to display. Now you see a display of the first section
response, and the cumulative first, second, and third sections response:
• Select User defined to enable the text entry box in the dialog box.
• Enter the cell array {1,1:3} to specify that FDATool should display the response
of the first section and the cumulative response of the first three sections of the
filter.
8
To apply your new SOS View selection, click Apply or OK (which closes the SOS
View dialog box).
In the FDATool analysis area you see two curves — one for the response of the first
filter section and one for the combined response of sections 1, 2, and 3.
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Import and Export Quantized Filters
• “Overview and Structures” on page 4-47
• “Import Quantized Filters” on page 4-48
• “To Export Quantized Filters” on page 4-50
Overview and Structures
When you import a quantized filter into FDATool, or export a quantized filter from
FDATool to your workspace, the import and export functions use objects and you specify
the filter as a variable. This contrasts with importing and exporting nonquantized filters,
where you select the filter structure and enter the filter numerator and denominator for
the filter transfer function.
You have the option of exporting quantized filters to your MATLAB workspace, exporting
them to text files, or exporting them to MAT-files.
For general information about importing and exporting filters in FDATool, refer to
“Importing a Filter Design”, and “Exporting a Filter Design”.
FDATool imports quantized filters having the following structures:
• Direct form I
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Filter Analysis, Design, and Implementation
• Direct form II
• Direct form I transposed
• Direct form II transposed
• Direct form symmetric FIR
• Direct form antisymmetric FIR
• Lattice allpass
• Lattice AR
• Lattice MA minimum phase
• Lattice MA maximum phase
• Lattice ARMA
• Lattice coupled-allpass
• Lattice coupled-allpass power complementary
Import Quantized Filters
After you design or open a quantized filter in your MATLAB workspace, FDATool lets
you import the filter for analysis. Follow these steps to import your filter in to FDATool:
1
Open FDATool.
2
Select File > Import Filter from Workspace from the menu bar, or choose the
Import Filter from Workspace icon in the side panel:
.
In the lower region of FDATool, the Design Filter pane becomes Import Filter,
and options appear for importing quantized filters, as shown.
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3
From the Filter Structure list, select Filter object.
The options for importing filters change to include:
• Discrete filter — Enter the variable name for the discrete-time, fixed-point
filter in your workspace.
• Frequency units — Select the frequency units from the Units list under
Sampling Frequency, and specify the sampling frequency value in Fs if needed.
Your sampling frequency must correspond to the units you select. For example,
when you select Normalized (0 to 1), Fs defaults to one. But if you choose
one of the frequency options, enter the sampling frequency in your selected units.
If you have the sampling frequency defined in your workspace as a variable, enter
the variable name for the sampling frequency.
4
Click Import to import the filter.
FDATool checks your workspace for the specified filter. It imports the filter if it finds
it, displaying the magnitude response for the filter in the analysis area. If it cannot
find the filter it returns an FDATool Error dialog box.
Note: If, during any FDATool session, you switch to quantization mode and create
a fixed-point filter, FDATool remains in quantization mode. If you import a doubleprecision filter, FDATool automatically quantizes your imported filter applying the most
recent quantization parameters.
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Filter Analysis, Design, and Implementation
When you check the current filter information for your imported filter, it will indicate
that the filter is Source: imported (quantized) even though you did not import a
quantized filter.
To Export Quantized Filters
To save your filter design, FDATool lets you export the quantized filter to your MATLAB
workspace (or you can save the current session in FDATool). When you choose to save the
quantized filter by exporting it, you select one of these options:
• Export to your MATLAB workspace
• Export to a text file
• Export to a MAT-file
Export Coefficients, Objects, or System Objects to the Workspace
You can save the filter as filter coefficients variables, dfilt filter object variables, or
System object variables.
To save the filter to the MATLAB workspace:
1
Select Export from the File menu. The Export dialog box appears.
2
Select Workspace from the Export To list.
3
From the Export As list, select one of the following options:
• Select Coefficients to save the filter coefficients.
• Select Objects to save the filter in a filter object.
• Select System Objects to save the filter in a filter System object.
The System Objects option does not appear in the drop-down list when the current
filter structure is not supported by System objects.
4
Assign a variable name:
• For coefficients, assign variable names using the Numerator and Denominator
options under Variable Names.
• For objects or System objects, assign the variable name in the Discrete Filter
option.
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If you have variables with the same names in your workspace and you want to
overwrite them, select the Overwrite Variables box.
5
Click Export.
Do not try to export the filter to a variable name that exists in your workspace
without selecting Overwrite existing variables, in the previous step. If you do so,
FDATool stops the export operation. The tool returns a warning that the variable
you specified as the quantized filter name already exists in the workspace.
• To continue to export the filter to the existing variable, click OK to dismiss the
warning.
• Then select the Overwrite existing variables check box and click Export.
Getting Filter Coefficients After Exporting
To extract the filter coefficients from your quantized filter after you export the filter to
MATLAB, use the celldisp function in MATLAB. For example, create a quantized
filter in FDATool, and export the filter as Hq. To extract the filter coefficients for Hq, use
celldisp(Hq.referencecoefficients)
which returns the cell array containing the filter reference coefficients, or
celldisp(Hq.quantizedcoefficients
to return the quantized coefficients.
Export Filter Coefficients as a Text File
To save your quantized filter as a text file, follow these steps:
1
Select Export from the File menu.
2
Select Text-file under Export to.
3
Click OK to export the filter and close the dialog box. Click Apply to export the
filter without closing the Export dialog box. Clicking Apply lets you export your
quantized filter to more than one name without leaving the Export dialog box.
The Export Filter Coefficients to Text-file dialog box appears. This is the
standard Microsoft Windows® save file dialog box.
4
Choose or enter a folder and filename for the text file, and click OK.
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Filter Analysis, Design, and Implementation
FDATool exports your quantized filter as a text file with the name you provided, and
the MATLAB editor opens, displaying the file for editing.
Export Filter Coefficients as a MAT-File
To save your quantized filter as a MAT-file, follow these steps:
1
2
3
4
Select Export from the File menu.
Select MAT-file under Export to.
Assign a variable name for the filter.
Click OK to export the filter and close the dialog box. Click Apply to export the
filter without closing the Export dialog box. Clicking Apply lets you export your
quantized filter to more than one name without leaving the Export dialog box.
The Export Filter Coefficients to MAT-file dialog box appears. This dialog box is
the standard Microsoft Windows save file dialog box.
5
Choose or enter a folder and filename for the text file, and click OK.
FDATool exports your quantized filter as a MAT-file with the specified name.
Generate MATLAB Code
You can generate MATLAB code using the File > Generate MATLAB Code menu. This
menu has three options:
• Filter Design Function
This option creates MATLAB code that generates the DFILT/MFILT object currently
designed in FDATool.
• Filter Design Function (with System Objects)
This option is similar to the previous option with the difference that a System object is
generated instead of a DFILT/MFILT object. The option is disabled when the current
filter is not supported by system objects.
• Data Filtering Function (with System Objects)
This option generates MATLAB code that filters input data with the current filter
design. The MATLAB code is ready to be converted to C/C++ code using the codegen
command. This option is disabled when the current filter is not supported by system
objects.
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Import XILINX Coefficient (.COE) Files
Import XILINX .COE Files into FDATool
You can import XILINX coefficients (.coe) files into FDATool to create quantized filters
directly using the imported filter coefficients.
To use the import file feature:
1
Select File > Import Filter From XILINX Coefficient (.COE) File in FDATool.
2
In the Import Filter From XILINX Coefficient (.COE) File dialog box, find and
select the .coe file to import.
3
Click Open to dismiss the dialog box and start the import process.
FDATool imports the coefficient file and creates a quantized, single-section, directform FIR filter.
Transform Filters Using FDATool
• “Filter Transformation Capabilities of FDATool” on page 4-53
• “Original Filter Type” on page 4-54
• “Frequency Point to Transform” on page 4-57
• “Transformed Filter Type” on page 4-58
• “Specify Desired Frequency Location” on page 4-59
Filter Transformation Capabilities of FDATool
The toolbox provides functions for transforming filters between various forms. When
you use FDATool with the toolbox installed, a side bar button and a menu bar option
enable you to use the Transform Filter panel to transform filters as well as using the
command line functions.
From the selection on the FDATool menu bar — Transformations — you can transform
lowpass FIR and IIR filters to a variety of passband shapes.
You can convert your FIR filters from:
• Lowpass to lowpass.
• Lowpass to highpass.
For IIR filters, you can convert from:
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Filter Analysis, Design, and Implementation
• Lowpass to lowpass.
• Lowpass to highpass.
• Lowpass to bandpass.
• Lowpass to bandstop.
When you click the Transform Filter button,
Filter panel opens in FDATool, as shown here.
, on the side bar, the Transform
Your options for Original filter type refer to the type of your current filter to transform.
If you select lowpass, you can transform your lowpass filter to another lowpass filter or to
a highpass filter, or to numerous other filter formats, real and complex.
Note: When your original filter is an FIR filter, both the FIR and IIR transformed filter
type options appear on the Transformed filter type list. Both options remain active
because you can apply the IIR transforms to an FIR filter. If your source is as IIR filter,
only the IIR transformed filter options show on the list.
Original Filter Type
Select the magnitude response of the filter you are transforming from the list. Your
selection changes the types of filters you can transform to. For example:
• When you select Lowpass with an IIR filter, your transformed filter type can be
• Lowpass
• Highpass
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• Bandpass
• Bandstop
• Multiband
• Bandpass (complex)
• Bandstop (complex)
• Multiband (complex)
• When you select Lowpass with an FIR filter, your transformed filter type can be
• Lowpass
• Lowpass (FIR)
• Highpass
• Highpass (FIR) narrowband
• Highpass (FIR) wideband
• Bandpass
• Bandstop
• Multiband
• Bandpass (complex)
• Bandstop (complex)
• Multiband (complex)
In the following table you see each available original filter type and all the types of filter
to which you can transform your original.
Original Filter
Available Transformed Filter Types
Lowpass FIR
• Lowpass
• Lowpass (FIR)
• Highpass
• Highpass (FIR) narrowband
• Highpass (FIR) wideband
• Bandpass
• Bandstop
• Multiband
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Filter Analysis, Design, and Implementation
Original Filter
Available Transformed Filter Types
• Bandpass (complex)
• Bandstop (complex)
• Multiband (complex)
Lowpass IIR
• Lowpass
• Highpass
• Bandpass
• Bandstop
• Multiband
• Bandpass (complex)
• Bandstop (complex)
• Multiband (complex)
Highpass FIR
• Lowpass
• Lowpass (FIR) narrowband
• Lowpass (FIR) wideband
• Highpass (FIR)
• Highpass
• Bandpass
• Bandstop
• Multiband
• Bandpass (complex)
• Bandstop (complex)
• Multiband (complex)
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Original Filter
Available Transformed Filter Types
Highpass IIR
• Lowpass
• Highpass
• Bandpass
• Bandstop
• Multiband
• Bandpass (complex)
• Bandstop (complex)
• Multiband (complex)
Bandpass FIR
• Bandpass
• Bandpass (FIR)
Bandpass IIR
Bandpass
Bandstop FIR
• Bandstop
• Bandstop (FIR)
Bandstop IIR
Bandstop
Note also that the transform options change depending on whether your original filter is
FIR or IIR. Starting from an FIR filter, you can transform to IIR or FIR forms. With an
IIR original filter, you are limited to IIR target filters.
After selecting your response type, use Frequency point to transform to specify the
magnitude response point in your original filter to transfer to your target filter. Your
target filter inherits the performance features of your original filter, such as passband
ripple, while changing to the new response form.
For more information about transforming filters, refer to “Frequency Transformations for
Real Filters” on page 4-85 and “Frequency Transformations for Complex Filters” on
page 4-99.
Frequency Point to Transform
The frequency point you enter in this field identifies a magnitude response value (in dB)
on the magnitude response curve.
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Filter Analysis, Design, and Implementation
When you enter frequency values in the Specify desired frequency location option,
the frequency transformation tries to set the magnitude response of the transformed
filter to the value identified by the frequency point you enter in this field.
While you can enter any location, generally you should specify a filter passband or
stopband edge, or a value in the passband or stopband.
The Frequency point to transform sets the magnitude response at the values you
enter in Specify desired frequency location. Specify a value that lies at either the
edge of the stopband or the edge of the passband.
If, for example, you are creating a bandpass filter from a highpass filter, the
transformation algorithm sets the magnitude response of the transformed filter at
the Specify desired frequency location to be the same as the response at the
Frequency point to transform value. Thus you get a bandpass filter whose response
at the low and high frequency locations is the same. Notice that the passband between
them is undefined. In the next two figures you see the original highpass filter and the
transformed bandpass filter.
For more information about transforming filters, refer to “Digital Frequency
Transformations” on page 4-77.
Transformed Filter Type
Select the magnitude response for the target filter from the list. The complete list of
transformed filter types is:
• Lowpass
• Lowpass (FIR)
• Highpass
• Highpass (FIR) narrowband
• Highpass (FIR) wideband
• Bandpass
• Bandstop
• Multiband
• Bandpass (complex)
• Bandstop (complex)
• Multiband (complex)
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Not all types of transformed filters are available for all filter types on the Original filter
types list. You can transform bandpass filters only to bandpass filters. Or bandstop
filters to bandstop filters. Or IIR filters to IIR filters.
For more information about transforming filters, refer to “Frequency Transformations for
Real Filters” on page 4-85 and “Frequency Transformations for Complex Filters” on
page 4-99.
Specify Desired Frequency Location
The frequency point you enter in Frequency point to transform matched a magnitude
response value. At each frequency you enter here, the transformation tries to make the
magnitude response the same as the response identified by your Frequency point to
transform value.
While you can enter any location, generally you should specify a filter passband or
stopband edge, or a value in the passband or stopband.
For more information about transforming filters, refer to “Digital Frequency
Transformations” on page 4-77.
Transform Filters
To transform the magnitude response of your filter, use the Transform Filter option on
the side bar.
1
2
Design or import your filter into FDATool.
Click Transform Filter,
, on the side bar.
FDATool opens the Transform Filter panel in FDATool.
3
From the Original filter type list, select the response form of the filter you are
transforming.
When you select the type, whether is lowpass, highpass, bandpass, or bandstop,
FDATool recognizes whether your filter form is FIR or IIR. Using both your filter
type selection and the filter form, FDATool adjusts the entries on the Transformed
filter type list to show only those that apply to your original filter.
4
Enter the frequency point to transform value in Frequency point to transform.
Notice that the value you enter must be in kHz; for example, enter 0.1 for 100 Hz or
1.5 for 1500 Hz.
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Filter Analysis, Design, and Implementation
5
From the Transformed filter type list, select the type of filter you want to
transform to.
Your filter type selection changes the options here.
• When you pick a lowpass or highpass filter type, you enter one value in Specify
desired frequency location.
• When you pick a bandpass or bandstop filter type, you enter two values — one in
Specify desired low frequency location and one in Specify desired high
frequency location. Your values define the edges of the passband or stopband.
• When you pick a multiband filter type, you enter values as elements in a vector
in Specify a vector of desired frequency locations — one element for each
desired location. Your values define the edges of the passbands and stopbands.
After you click Transform Filter, FDATool transforms your filter, displays
the magnitude response of your new filter, and updates the Current Filter
Information to show you that your filter has been transformed. In the filter
information, the Source is Transformed.
For example, the figure shown here includes the magnitude response curves for
two filters. The original filter is a lowpass filter with rolloff between 0.2 and 0.25.
The transformed filter is a lowpass filter with rolloff region between 0.8 and 0.85.
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Magnitude Response
20
0
Magnitude (dB)
−20
−40
−60
−80
−100
Filter #1: Original Lowpass filter response
Filter #2: Transformed Lowpass Filter Response
−120
0
0.1
0.2
0.3
0.4
0.5
0.6
Normalized Frequency (×π rad/sample)
0.7
0.8
0.9
1
• To demonstrate the effects of selecting Narrowband Highpass or Wideband
Highpass, the next figure presents the magnitude response curves for a source
lowpass filter after it is transformed to both narrow- and wideband highpass
filters. For comparison, the response of the original filter appears as well.
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Filter Analysis, Design, and Implementation
Magnitude Response
20
0
Magnitude (dB)
−20
−40
−60
−80
−100
−120
Filter #1:Original Lowpass Filter Response
Filter #2:Narrowband Highpass Filter Response
Filter #3: Wideband Highpass Filter Response
0
0.1
0.2
0.3
0.4
0.5
0.6
Normalized Frequency (×π rad/sample)
0.7
0.8
0.9
1
For the narrowband case, the transformation algorithm essentially reverses the
magnitude response, like reflecting the curve around the y-axis, then translating
the curve to the right until the origin lies at 1 on the x-axis. After reflecting and
translating, the passband at high frequencies is the reverse of the passband of the
original filter at low frequencies with the same rolloff and ripple characteristics.
Design Multirate Filters in FDATool
• “Introduction” on page 4-63
• “Switch FDATool to Multirate Filter Design Mode” on page 4-63
• “Controls on the Multirate Design Panel” on page 4-64
• “Quantize Multirate Filters” on page 4-71
• “Export Individual Phase Coefficients of a Polyphase Filter to the Workspace” on page
4-73
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Introduction
Not only can you design multirate filters from the MATLAB command prompt, FDATool
provides the same design capability in a graphical user interface tool. By starting
FDATool and switching to the multirate filter design mode you have access to all of the
multirate design capabilities in the toolbox — decimators, interpolators, and fractional
rate changing filters, among others.
Switch FDATool to Multirate Filter Design Mode
The multirate filter design mode in FDATool lets you specify and design a wide range of
multirate filters, including decimators and interpolators.
With FDATool open, click Create a Multirate Filter,
, on the side bar. You see
FDATool switch to the design mode showing the multirate filter design options. Shown
in the following figure is the default multirate design configuration that designs an
interpolating filter with an interpolation factor of 2. The design uses the current FIR
filter in FDATool.
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Filter Analysis, Design, and Implementation
When the current filter in FDATool is not an FIR filter, the multirate filter design panel
removes the Use current FIR filter option and selects the Use default Nyquist FIR
filter option instead as the default setting.
Controls on the Multirate Design Panel
You see the options that allow you to design a variety of multirate filters. The Type
option is your starting point. From this list you select the multirate filter to design.
Based on your selection, other options change to provide the controls you need to specify
your filter.
Notice the separate sections of the design panel. On the left is the filter type area
where you choose the type of multirate filter to design and set the filter performance
specifications.
In the center section FDATool provides choices that let you pick the filter design method
to use.
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The rightmost section offers options that control filter configuration when you select
Cascaded-Integrator Comb (CIC) as the design method in the center section. Both the
Decimator type and Interpolator type filters let you use the Cascaded-Integrator
Comb (CIC) option to design multirate filters.
Here are all the options available when you switch to multirate filter design mode. Each
option listed includes a brief description of what the option does when you use it.
Select and Configure Your Filter
Option
Description
Type
Specifies the type of multirate filter to design. Choose
from Decimator, Interpolator, or Fractional-rate
convertor.
• When you choose Decimator, set Decimation Factor to
specify the decimation to apply.
• When you choose Interpolator, set Interpolation
Factor to specify the interpolation amount applied.
• When you choose Fractional-rate convertor,
set both Interpolation Factor and Decimation
Factor. FDATool uses both to determine the fractional
rate change by dividing Interpolation Factor by
Decimation Factor to determine the fractional
rate change in the signal. You should select values
for interpolation and decimation that are relatively
prime. When your interpolation factor and decimation
factor are not relatively prime, FDATool reduces the
interpolation/decimation fractional rate to the lowest
common denominator and issues a message in the status
bar in FDATool. For example, if the interpolation factor
is 6 and the decimation factor is 3, FDATool reduces
6/3 to 2/1 when you design the rate changer. But if the
interpolation factor is 8 and the decimation factor is 3,
FDATool designs the filter without change.
Interpolation Factor
Use the up-down control arrows to specify the amount of
interpolation to apply to the signal. Factors range upwards
from 2.
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Filter Analysis, Design, and Implementation
Option
Description
Decimation Factor
Use the up-down control arrows to specify the amount of
decimation to apply to the signal. Factors range upwards
from 2.
Sampling Frequency
No settings here. Just Units and Fs below.
Units
Specify whether Fs is specified in Hz, kHz, MHz, GHz, or
Normalized (0 to 1) units.
Fs
Set the full scale sampling frequency in the frequency units
you specified in Units. When you select Normalized for
Units, you do not enter a value for Fs.
Design Your Filter
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Option
Description
Use current FIR filter
Directs FDATool to use the current FIR filter to design
the multirate filter. If the current filter is an IIR form, you
cannot select this option. You cannot design multirate filters
with IIR structures.
Use a default Nyquist
Filter
Tells FDATool to use the default Nyquist design method
when the current filter in FDATool is not an FIR filter.
Cascaded IntegratorComb (CIC)
Design CIC filters using the options provided in the righthand area of the multirate design panel.
Hold Interpolator
(Zero-order)
When you design an interpolator, you can specify how
the filter sets interpolated values between signal values.
When you select this option, the interpolator applies the
most recent signal value for each interpolated value until it
processes the next signal value. This is similar to sampleand-hold techniques. Compare to the Linear Interpolator
option.
Linear Interpolator
(First-order)
When you design an interpolator, you can specify how
the filter sets interpolated values between signal values.
When you select this option, the interpolator applies linear
interpolation between signal value to set the interpolated
value until it processes the next signal value. Compare to
the Linear Interpolator option.
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To see the difference between hold interpolation and linear interpolation, the following
figure presents a sine wave signal s1 in three forms:
• The top subplot in the figure presents signal s1 without interpolation.
• The middle subplot shows signal s1 interpolated by a linear interpolator with an
interpolation factor of 5.
• The bottom subplot shows signal s1 interpolated by a hold interpolator with an
interpolation factor of 5.
You see in the bottom figure the sample and hold nature of hold interpolation, and the
first-order linear interpolation applied by the linear interpolator.
Uninterpolated Signal s1
1
0.5
0
−0.5
−1
1
2
3
4
5
6
7
8
9
10
40
45
50
40
45
50
First−Order Linear Interpolation By 5 of Signal s1
1
0.5
0
−0.5
−1
0
5
10
15
20
25
30
35
Zero−Order Hold Interpolation By 5 of Signal s1
1
0.5
0
−0.5
−1
0
5
10
15
20
25
Samples
30
35
We used FDATool to create interpolators similar to the following code for the figure:
• Linear interpolator — hm=mfilt.linearinterp(5)
• Hold interpolator — hm=mfilt.holdinterp(5)
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Filter Analysis, Design, and Implementation
Options for Designing CIC Filters Description
Differential Delay
Sets the differential delay for the CIC filter. Usually a value of one
or two is appropriate.
Number of Sections
Specifies the number of sections in a CIC decimator. The default
number of sections is 2 and the range is any positive integer.
Design a Fractional Rate Convertor
To introduce the process you use to design a multirate filter in FDATool, this example
uses the options to design a fractional rate convertor which uses 7/3 as the fractional
rate. Begin the design by creating a default lowpass FIR filter in FDATool. You do not
have to begin with this FIR filter, but the default filter works fine.
1
Launch FDATool.
2
Select the settings for a minimum-order lowpass FIR filter, using the Equiripple
design method.
3
When FDATool displays the magnitude response for the filter, click
in the side
bar. FDATool switches to multirate filter design mode, showing the multirate design
panel.
4
To design a fractional rate filter, select Fractional-rate convertor from the
Type list. The Interpolation Factor and Decimation Factor options become
available.
5
In Interpolation Factor, use the up arrow to set the interpolation factor to 7.
6
Using the up arrow in Decimation Factor, set 3 as the decimation factor.
7
Select Use a default Nyquist FIR filter. You could design the rate convertor
with the current FIR filter as well.
8
Enter 24000 to set Fs.
9
Click Create Multirate Filter.
After designing the filter, FDATool returns with the specifications for your new filter
displayed in Current Filter Information, and shows the magnitude response of
the filter.
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You can test the filter by exporting it to your workspace and using it to filter a signal. For
information about exporting filters, refer to “Import and Export Quantized Filters” on
page 4-47.
Design a CIC Decimator for 8 Bit Input/Output Data
Another kind of filter you can design in FDATool is Cascaded-Integrator Comb (CIC)
filters. FDATool provides the options needed to configure your CIC to meet your needs.
1
2
Launch FDATool and design the default FIR lowpass filter. Designing a filter at this
time is an optional step.
Switch FDATool to multirate design mode by clicking
on the side bar.
3
For Type, select Decimator, and set Decimation Factor to 3.
4
To design the decimator using a CIC implementation, select Cascaded-Integrator
Comb (CIC). This enables the CIC-related options on the right of the panel.
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Filter Analysis, Design, and Implementation
5
Set Differential Delay to 2. Generally, 1 or 2 are good values to use.
6
Enter 2 for the Number of Sections.
7
Click Create Multirate Filter.
FDATool designs the filter, shows the magnitude response in the analysis area,
and updates the current filter information to show that you designed a tenth-order
cascaded-integrator comb decimator with two sections. Notice the source is Multirate
Design, indicating you used the multirate design mode in FDATool to make the
filter. FDATool should look like this now.
Designing other multirate filters follows the same pattern.
To design other multirate filters, do one of the following depending on the filter to design:
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• To design an interpolator, select one of these options.
• Use a default Nyquist FIR filter
• Cascaded-Integrator Comb (CIC)
• Hold Interpolator (Zero-order)
• Linear Interpolator (First-order)
• To design a decimator, select from these options.
• Use a default Nyquist FIR filter
• Cascaded-Integrator Comb (CIC)
• To design a fractional-rate convertor, select Use a default Nyquist FIR filter.
Quantize Multirate Filters
After you design a multirate filter in FDATool, the quantization features enable you to
convert your floating-point multirate filter to fixed-point arithmetic.
Note: CIC filters are always fixed-point.
With your multirate filter as the current filter in FDATool, you can quantize your filter
and use the quantization options to specify the fixed-point arithmetic the filter uses.
Quantize and Configure Multirate Filters
Follow these steps to convert your multirate filter to fixed-point arithmetic and set the
fixed-point options.
1
Design or import your multirate filter and make sure it is the current filter in
FDATool.
2
Click the Set Quantization Parameters button on the side bar.
3
From the Filter Arithmetic list on the Filter Arithmetic pane, select Fixedpoint. If your filter is a CIC filter, the Fixed-point option is enabled by default
and you do not set this option.
4
In the quantization panes, set the options for your filter. Set options for
Coefficients, Input/Output, and Filter Internals.
5
Click Apply.
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Filter Analysis, Design, and Implementation
When you current filter is a CIC filter, the options on the Input/Output and Filter
Internals panes change to provide specific features for CIC filters.
Input/Output
The options that specify how your CIC filter uses input and output values are listed in
the table below.
Option Name
Description
Input Word Length
Sets the word length used to represent the input to a filter.
Input fraction length
Sets the fraction length used to interpret input values to
filter.
Input range (+/-)
Lets you set the range the inputs represent. You use this
instead of the Input fraction length option to set the
precision. When you enter a value x, the resulting range is x to x. Range must be a positive integer.
Output word length
Sets the word length used to represent the output from a
filter.
Avoid overflow
Directs the filter to set the fraction length for the input
to prevent the output values from exceeding the available
range as defined by the word length. Clearing this option
lets you set Output fraction length.
Output fraction length
Sets the fraction length used to represent output values
from a filter.
Output range (+/-)
Lets you set the range the outputs represent. You use this
instead of the Output fraction length option to set the
precision. When you enter a value x, the resulting range is x to x. Range must be a positive integer.
The available options change when you change the Filter precision setting. Moving
from Full to Specify all adds increasing control by enabling more input and output
word options.
Filter Internals
With a CIC filter as your current filter, the Filter precision option on the Filter
Internals pane includes modes for controlling the filter word and fraction lengths.
There are four usage modes for this (the same mode you select for the FilterInternals
property in CIC filters at the MATLAB prompt).
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Use FDATool with DSP System Toolbox Software
• Full — All word and fraction lengths set to Bmax + 1, called Baccum by Harris in [2].
Full Precision is the default setting.
• Minimum section word lengths — Set the section word lengths to minimum
values that meet roundoff noise and output requirements as defined by Hogenauer in
[3].
• Specify word lengths — Enables the Section word length option for you to
enter word lengths for each section. Enter either a scalar to use the same value for
every section, or a vector of values, one for each section.
• Specify all — Enables the Section fraction length option in addition to Section
word length. Now you can provide both the word and fraction lengths for each
section, again using either a scalar or a vector of values.
Export Individual Phase Coefficients of a Polyphase Filter to the Workspace
After designing a polyphase filter in Filter Design Analysis Tool (FDATool), you can
obtain the individual phase coefficients of the filter by:
1
Exporting the filter to an object in the MATLAB workspace.
2
Using the polyphase method to create a matrix of the filter's coefficients.
Export the Polyphase Filter to an Object
To export a polyphase filter to an object in the MATLAB workspace, complete the
following steps.
1
In FDATool, open the File menu and select Export.... This opens the dialog box for
exporting the filter coefficients.
2
In the Export dialog box, for Export To, select Workspace.
3
For Export As, select Object.
4
(Optional) For Variable Names, enter the name of the Multirate Filter object that
will be created in the MATLAB workspace.
5
Click the Export button. The multirate filter object, Hm in this example, appears in
the MATLAB workspace.
Create a Matrix of Coefficients Using the polyphase Method
To create a matrix of the filter's coefficients, enter p=polyphase(Hm) at the command
line. The polyphase method creates a matrix, p, of filter coefficients from the filter
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4
Filter Analysis, Design, and Implementation
object, Hm. Each row of p consists of the coefficients of an individual phase subfilter. The
first row contains to the coefficients of the first phase subfilter, the second row contains
those of the second phase subfilter, and so on.
Realize Filters as Simulink Subsystem Blocks
• “Introduction” on page 4-74
• “About the Realize Model Panel in FDATool” on page 4-74
Introduction
After you design or import a filter in FDATool, the realize model feature lets you create
a Simulink subsystem block that implements your filter. The generated filter subsystem
block uses either digital filter blocks from the DSP System Toolbox library, or the Delay,
Gain, and Sum blocks in Simulink. If you do not have a Fixed-Point Designer™ license,
FDATool still realizes your model using blocks in fixed-point mode from Simulink, but
you cannot run any model that includes your filter subsystem block in Simulink.
About the Realize Model Panel in FDATool
To access to the Realize Model panel and the options for realizing your quantized filter
as a Simulink subsystem block, switch FDATool to realize model mode by clicking
the sidebar.
The following panel shows the options for configuring how FDATool implements your
filter as a Simulink block.
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on
Use FDATool with DSP System Toolbox Software
For information on these parameters, see the descriptions on the “Filter Realization
Wizard” block reference page.
Realize a Filter Using FDATool
After your quantized filter in FDATool is performing the way you want, with your desired
phase and magnitude response, and with the right coefficients and form, follow these
steps to realize your filter as a subsystem that you can use in a Simulink model.
1
2
Click Realize Model on the sidebar to change FDATool to realize model mode.
From the Destination list under Model, select either:
• Current model — to add the realized filter subsystem to your current model
• New model — to open a new Simulink model window and add your filter
subsystem to the new window
3
4
Provide a name for your new filter subsystem in the Name field.
Decide whether to overwrite an existing block with this new one, and select or clear
the Overwrite generated ‘Filter’ block check box.
5
Select the Build model using basic elements check box to implement your filter
as a subsystem block that consists of Sum, Gain, and Delay blocks.
6
Select or clear the optimizations to apply.
• Optimize for zero gains — removes zero gain blocks from the model realization
• Optimize for unity gains — replaces unity gain blocks with direct connections
to adjacent blocks
• Optimize for negative gains — replaces negative gain blocks by a change of
sign at the nearest sum block
• Optimize delay chains — replaces cascaded delay blocks with a single delay
block that produces the equivalent gain
• Optimize for unity scale values — removes all scale value multiplications by 1
from the filter structure
7
Click Realize Model to realize your quantized filter as a subsystem block according
to the settings you selected.
If you double-click the filter block subsystem created by FDATool, you see the filter
implementation in Simulink model form. Depending on the options you chose when you
realized your filter, and the filter you started with, you might see one or more sections, or
different architectures based on the form of your quantized filter. From this point on, the
subsystem filter block acts like any other block that you use in Simulink models.
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Filter Analysis, Design, and Implementation
Supported Filter Structures
FDATool lets you realize discrete-time and multirate filters from the following forms:
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Structure
Description
firdecim
Decimators based on FIR filters
firtdecim
Decimators based on transposed FIR filters
linearinterp
Linear interpolators
firinterp
Interpolators based on FIR filters
multirate polyphase
Multirate filters
holdinterp
Interpolators that use the hold interpolation
algorithm
dfilt.allpass
Discrete-time filters with allpass structure
dfilt.cascadeallpass
dfilt.cascadewdfallpass
mfilt.iirdecim
Decimators based on IIR filters
mfilt.iirwdfdecim
mfilt.iirinterp
Interpolators based on IIR filters
mfilt.iirwdfinterp
dfilt.wdfallpass
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Digital Frequency Transformations
Digital Frequency Transformations
In this section...
“Details and Methodology” on page 4-77
“Frequency Transformations for Real Filters” on page 4-85
“Frequency Transformations for Complex Filters” on page 4-99
Details and Methodology
• “Overview of Transformations” on page 4-77
• “Select Features Subject to Transformation” on page 4-81
• “Mapping from Prototype Filter to Target Filter” on page 4-83
• “Summary of Frequency Transformations” on page 4-84
Overview of Transformations
Converting existing FIR or IIR filter designs to a modified IIR form is often done using
allpass frequency transformations. Although the resulting designs can be considerably
more expensive in terms of dimensionality than the prototype (original) filter, their ease
of use in fixed or variable applications is a big advantage.
The general idea of the frequency transformation is to take an existing prototype
filter and produce another filter from it that retains some of the characteristics of the
prototype, in the frequency domain. Transformation functions achieve this by replacing
each delaying element of the prototype filter with an allpass filter carefully designed to
have a prescribed phase characteristic for achieving the modifications requested by the
designer.
The basic form of mapping commonly used is
HT ( z) = H o[ H A ( z)]
The HA(z) is an Nth-order allpass mapping filter given by
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Filter Analysis, Design, and Implementation
N
∑ ai z −i
N ( z)
H A ( z) = S Ni = 0
= A
DA ( z)
ai z − N + i
∑
a0 = 1
i= 0
where
Ho(z) — Transfer function of the prototype filter
HA(z) — Transfer function of the allpass mapping filter
HT(z) — Transfer function of the target filter
Let's look at a simple example of the transformation given by
HT ( z) = H o ( − z)
The target filter has its poles and zeroes flipped across the origin of the real and
imaginary axes. For the real filter prototype, it gives a mirror effect against 0.5, which
means that lowpass Ho(z) gives rise to a real highpass HT(z). This is shown in the
following figure for the prototype filter designed as a third-order halfband elliptic filter.
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Digital Frequency Transformations
Target filter
0
−10
−10
−20
−20
|H(ω)| in dB
|H(ω)| in dB
Prototype filter
0
−30
−40
−50
−60
−30
−40
−50
0
0.2
0.4
0.6
0.8
1
Normalized Frequency (×π rad/sample)
−60
Prototype filter Pole−Zero plot
0
0.2
0.4
0.6
0.8
1
Normalized Frequency (×π rad/sample)
Target filter Pole−Zero plot
Example of a Simple Mirror Transformation
The choice of an allpass filter to provide the frequency mapping is necessary to provide
the frequency translation of the prototype filter frequency response to the target filter by
changing the frequency position of the features from the prototype filter without affecting
the overall shape of the filter response.
The phase response of the mapping filter normalized to π can be interpreted as a
translation function:
H (wnew ) = w old
The graphical interpretation of the frequency transformation is shown in the figure
below. The complex multiband transformation takes a real lowpass filter and converts it
into a number of passbands around the unit circle.
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Filter Analysis, Design, and Implementation
Graphical Interpretation of the Mapping Process
Most of the frequency transformations are based on the second-order allpass mapping
filter:
H A ( z) = ±
1 + a1 z−1 + a 2 z−2
a 2 + a1 z −1 + z −2
The two degrees of freedom provided by α1 and α2 choices are not fully used by the usual
restrictive set of “flat-top” classical mappings like lowpass to bandpass. Instead, any
two transfer function features can be migrated to (almost) any two other frequency
locations if α1 and α2 are chosen so as to keep the poles of HA(z) strictly outside the unit
circle (since HA(z) is substituted for z in the prototype transfer function). Moreover, as
first pointed out by Constantinides, the selection of the outside sign influences whether
the original feature at zero can be moved (the minus sign, a condition known as “DC
mobility”) or whether the Nyquist frequency can be migrated (the “Nyquist mobility” case
arising when the leading sign is positive).
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Digital Frequency Transformations
All the transformations forming the package are explained in the next sections of the
tutorial. They are separated into those operating on real filters and those generating
or working with complex filters. The choice of transformation ranges from standard
Constantinides first and second-order ones [1][2] up to the real multiband filter by Mullis
and Franchitti [3], and the complex multiband filter and real/complex multipoint ones by
Krukowski, Cain and Kale [4].
Select Features Subject to Transformation
Choosing the appropriate frequency transformation for achieving the required effect
and the correct features of the prototype filter is very important and needs careful
consideration. It is not advisable to use a first-order transformation for controlling more
than one feature. The mapping filter will not give enough flexibility. It is also not good
to use higher order transformation just to change the cutoff frequency of the lowpass
filter. The increase of the filter order would be too big, without considering the additional
replica of the prototype filter that may be created in undesired places.
Feature Selection for Real Lowpass to Bandpass Transformation
To illustrate the idea, the second-order real multipoint transformation was applied three
times to the same elliptic halfband filter in order to make it into a bandpass filter. In
each of the three cases, two different features of the prototype filter were selected in
order to obtain a bandpass filter with passband ranging from 0.25 to 0.75. The position of
the DC feature was not important, but it would be advantageous if it were in the middle
between the edges of the passband in the target filter. In the first case the selected
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Filter Analysis, Design, and Implementation
features were the left and the right band edges of the lowpass filter passband, in the
second case they were the left band edge and the DC, in the third case they were DC and
the right band edge.
Magniture responses |H(ω)| in dB
0
−10
Left & right band−edges (solid)
Left band−edge and DC (dashed)
−20
DC and right band−edges (dotted)
−30
−40
−50
−60
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Normalized Frequency (×π rad/sample)
0.8
0.9
1
Result of Choosing Different Features
The results of all three approaches are completely different. For each of them only the
selected features were positioned precisely where they were required. In the first case
the DC is moved toward the left passband edge just like all the other features close to the
left edge being squeezed there. In the second case the right passband edge was pushed
way out of the expected target as the precise position of DC was required. In the third
case the left passband edge was pulled toward the DC in order to position it at the correct
frequency. The conclusion is that if only the DC can be anywhere in the passband, the
edges of the passband should have been selected for the transformation. For most of the
cases requiring the positioning of passbands and stopbands, designers should always
choose the position of the edges of the prototype filter in order to make sure that they get
the edges of the target filter in the correct places. Frequency responses for the three cases
considered are shown in the figure. The prototype filter was a third-order elliptic lowpass
filter with cutoff frequency at 0.5.
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Digital Frequency Transformations
The MATLAB code used to generate the figure is given here.
The prototype filter is a halfband elliptic, real, third-order lowpass filter:
[b, a] = ellip(3, 0.1, 30, 0.409);
In the example the requirements are set to create a real bandpass filter with passband
edges at 0.1 and 0.3 out of the real lowpass filter having the cutoff frequency at 0.5. This
is attempted in three different ways. In the first approach both edges of the passband
are selected, in the second approach the left edge of the passband and the DC are chosen,
while in the third approach the DC and the right edge of the passband are taken:
[num1,den1] = iirlp2xn(b, a, [-0.5, 0.5], [0.1, 0.3]);
[num2,den2] = iirlp2xn(b, a, [-0.5, 0.0], [0.1, 0.2]);
[num3,den3] = iirlp2xn(b, a, [ 0.0, 0.5], [0.2, 0.3]);
Mapping from Prototype Filter to Target Filter
In general the frequency mapping converts the prototype filter, Ho(z), to the target
filter, HT(z), using the NAth-order allpass filter, HA(z). The general form of the allpass
mapping filter is given in “Overview of Transformations” on page 4-77. The frequency
mapping is a mathematical operation that replaces each delayer of the prototype filter
with an allpass filter. There are two ways of performing such mapping. The choice of the
approach is dependent on how prototype and target filters are represented.
When the Nth-order prototype filter is given with pole-zero form
N
H o ( z) =
∑ (z − zi )
i =1
N
∑ (z − pi )
i =1
the mapping will replace each pole, pi, and each zero, zi, with a number of poles and zeros
equal to the order of the allpass mapping filter:
N
H o ( z) =
∑
i =1
N
∑
i =1
N −1
 N −1
k
N−k 
 S ∑ a k z − zi ⋅ ∑ a k z



 k =0
k= 0

N −1
 N −1

 S ∑ a k z k − pi ⋅ ∑ a k z N − k 


 k =0
k= 0

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4
Filter Analysis, Design, and Implementation
The root finding needs to be used on the bracketed expressions in order to find the poles
and zeros of the target filter.
When the prototype filter is described in the numerator-denominator form:
HT ( z) =
b 0 z N + b1 z N −1 + … + b N
a 0 z N + a1 z N −1 + … + a N
z = H A ( z)
Then the mapping process will require a number of convolutions in order to calculate the
numerator and denominator of the target filter:
b N ( z) N + b 2 N A ( z) N −1 DA ( z) + … + b N D A ( z) N
HT ( z) = 1 A
b1 N A ( z) N + b 2 N A ( z) N −1 DA ( z) + … + b N D A ( z) N
For each coefficient αi and βi of the prototype filter the NAth-order polynomials must be
convolved N times. Such approach may cause rounding errors for large prototype filters
and/or high order mapping filters. In such a case the user should consider the alternative
of doing the mapping using via poles and zeros.
Summary of Frequency Transformations
Advantages
• Most frequency transformations are described by closed-form solutions or can be
calculated from the set of linear equations.
• They give predictable and familiar results.
• Ripple heights from the prototype filter are preserved in the target filter.
• They are architecturally appealing for variable and adaptive filters.
Disadvantages
• There are cases when using optimization methods to design the required filter gives
better results.
• High-order transformations increase the dimensionality of the target filter, which
may give expensive final results.
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Digital Frequency Transformations
• Starting from fresh designs helps avoid locked-in compromises.
Frequency Transformations for Real Filters
• “Overview” on page 4-85
• “Real Frequency Shift” on page 4-85
• “Real Lowpass to Real Lowpass” on page 4-87
• “Real Lowpass to Real Highpass” on page 4-89
• “Real Lowpass to Real Bandpass” on page 4-91
• “Real Lowpass to Real Bandstop” on page 4-93
• “Real Lowpass to Real Multiband” on page 4-95
• “Real Lowpass to Real Multipoint” on page 4-97
Overview
This section discusses real frequency transformations that take the real lowpass
prototype filter and convert it into a different real target filter. The target filter has its
frequency response modified in respect to the frequency response of the prototype filter
according to the characteristic of the applied frequency transformation.
Real Frequency Shift
Real frequency shift transformation uses a second-order allpass mapping filter. It
performs an exact mapping of one selected feature of the frequency response into its new
location, additionally moving both the Nyquist and DC features. This effectively moves
the whole response of the lowpass filter by the distance specified by the selection of the
feature from the prototype filter and the target filter. As a real transformation, it works
in a similar way for positive and negative frequencies.
−1
1−a z
H A ( z) = z−1 ⋅
a − z−1
with α given by
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Filter Analysis, Design, and Implementation
p

 cos 2 (wold − 2wnew )
p
for
cos (wold − 2wnew ) < 1

p
2

cos wold

2
a =
 sin p (w − 2w )
new

2 ol d
otherwise

p
w
sin


2 old
where
ωold — Frequency location of the selected feature in the prototype filter
ωnew — Position of the feature originally at ωold in the target filter
The following example shows how this transformation can be used to move the response
of the prototype lowpass filter in either direction. Please note that because the target
filter must also be real, the response of the target filter will inherently be disturbed at
frequencies close to Nyquist and close to DC. Here is the MATLAB code for generating
the example in the figure.
The prototype filter is a halfband elliptic, real, third-order lowpass filter:
[b, a] = ellip(3, 0.1, 30, 0.409);
The example transformation moves the feature originally at 0.5 to 0.9:
[num,den] = iirshift(b, a, 0.5, 0.9);
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Digital Frequency Transformations
Prototype filter
0
|H(ω)|in dB
−10
−20
−30
−40
ωo
−50
−60
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Normalized Frequency (×π rad/sample)
0.8
0.9
1
0.9
1
Target filter
0
|H(ω)| in dB
−10
−20
−30
−40
ωt
−50
−60
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Normalized Frequency (×π rad/sample)
0.8
Example of Real Frequency Shift Mapping
Real Lowpass to Real Lowpass
Real lowpass filter to real lowpass filter transformation uses a first-order allpass
mapping filter. It performs an exact mapping of one feature of the frequency response
into the new location keeping DC and Nyquist features fixed. As a real transformation,
it works in a similar way for positive and negative frequencies. It is important to
mention that using first-order mapping ensures that the order of the filter after the
transformation is the same as it was originally.
 1 − a z −1 
H A ( z) = − 

 a − z −1 


with α given by
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4
Filter Analysis, Design, and Implementation
p
sin (wold − wnew )
2
a =
p
sin (wold − wnew )
2
where
ωold — Frequency location of the selected feature in the prototype filter
ωnew — Frequency location of the same feature in the target filter
The example below shows how to modify the cutoff frequency of the prototype filter. The
MATLAB code for this example is shown in the following figure.
The prototype filter is a halfband elliptic, real, third-order filter:
[b, a] = ellip(3, 0.1, 30, 0.409);
The cutoff frequency moves from 0.5 to 0.75:
[num,den] = iirlp2lp(b, a, 0.5, 0.75);
4-88
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Digital Frequency Transformations
Prototype filter
0
|H(ω)|in dB
−10
−20
−30
−40
ωo
−50
−60
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Normalized Frequency (×π rad/sample)
0.8
0.9
1
0.8
0.9
1
Target filter
0
|H(ω)| in dB
−10
−20
−30
−40
ωt
−50
−60
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Normalized Frequency (×π rad/sample)
Example of Real Lowpass to Real Lowpass Mapping
Real Lowpass to Real Highpass
Real lowpass filter to real highpass filter transformation uses a first-order allpass
mapping filter. It performs an exact mapping of one feature of the frequency response
into the new location additionally swapping DC and Nyquist features. As a real
transformation, it works in a similar way for positive and negative frequencies. Just like
in the previous transformation because of using a first-order mapping, the order of the
filter before and after the transformation is the same.
 1 + a z −1 
H A ( z) = − 

 a + z−1 


with α given by
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4
Filter Analysis, Design, and Implementation
p


 cos 2 (w old + wnew ) 
a = −

p
 cos (wold − wnew ) 

2

where
ωold — Frequency location of the selected feature in the prototype filter
ωnew — Frequency location of the same feature in the target filter
The example below shows how to convert the lowpass filter into a highpass filter with
arbitrarily chosen cutoff frequency. In the MATLAB code below, the lowpass filter is
converted into a highpass with cutoff frequency shifted from 0.5 to 0.75. Results are
shown in the figure.
The prototype filter is a halfband elliptic, real, third-order filter:
[b, a] = ellip(3, 0.1, 30, 0.409);
The example moves the cutoff frequency from 0.5 to 0.75:
[num,den] = iirlp2hp(b, a, 0.5, 0.75);
4-90
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Digital Frequency Transformations
Prototype filter
0
|H(ω)|in dB
−10
−20
−30
−40
ωo
−50
−60
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Normalized Frequency (×π rad/sample)
0.8
0.9
1
0.8
0.9
1
Target filter
0
|H(ω)| in dB
−10
−20
−30
−40
ωt
−50
−60
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Normalized Frequency (×π rad/sample)
Example of Real Lowpass to Real Highpass Mapping
Real Lowpass to Real Bandpass
Real lowpass filter to real bandpass filter transformation uses a second-order allpass
mapping filter. It performs an exact mapping of two features of the frequency response
into their new location additionally moving a DC feature and keeping the Nyquist feature
fixed. As a real transformation, it works in a similar way for positive and negative
frequencies.
 1 − b (1 + a ) z−1 − a z−2
H A ( z) = − 
 a − b (1 + a ) z −1 + z −2





with α and β given by
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4-91
4
Filter Analysis, Design, and Implementation
p
sin ( 2w old − wnew,2 + wnew,1)
4
a =
p
sin ( 2w old + w new,2 − wnew,1)
4
p
b = cos (wnew,1 + wnew,2 )
2
where
ωold — Frequency location of the selected feature in the prototype filter
ωnew,1 — Position of the feature originally at (-ωold) in the target filter
ωnew,2 — Position of the feature originally at (+ωold) in the target filter
The example below shows how to move the response of the prototype lowpass filter in
either direction. Please note that because the target filter must also be real, the response
of the target filter will inherently be disturbed at frequencies close to Nyquist and close
to DC. Here is the MATLAB code for generating the example in the figure.
The prototype filter is a halfband elliptic, real, third-order lowpass filter:
[b, a] = ellip(3, 0.1, 30, 0.409);
The example transformation creates the passband between 0.5 and 0.75:
[num,den] = iirlp2bp(b, a, 0.5, [0.5, 0.75]);
4-92
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Digital Frequency Transformations
Prototype filter
0
|H(ω)|in dB
−10
−20
−30
−40
ωo
−50
−60
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Normalized Frequency (×π rad/sample)
0.8
0.9
1
0.8
0.9
1
Target filter
0
|H(ω)| in dB
−10
−20
−30
−40
ωt1
−50
−60
0
0.1
0.2
ωt2
0.3
0.4
0.5
0.6
0.7
Normalized Frequency (×π rad/sample)
Example of Real Lowpass to Real Bandpass Mapping
Real Lowpass to Real Bandstop
Real lowpass filter to real bandstop filter transformation uses a second-order allpass
mapping filter. It performs an exact mapping of two features of the frequency response
into their new location additionally moving a Nyquist feature and keeping the DC feature
fixed. This effectively creates a stopband between the selected frequency locations in the
target filter. As a real transformation, it works in a similar way for positive and negative
frequencies.
H A ( z) =
1 − b (1 + a ) z−1 + a z −2
a − b (1 + a ) z −1 + z −2
with α and β given by
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Filter Analysis, Design, and Implementation
p
(2wold + wnew,2 − wnew,1 )
4
a =
p
cos (2wold − wnew,2 + wnew,1 )
4
p
b = cos (wnew,1 + wnew,2 )
2
cos
where
ωold — Frequency location of the selected feature in the prototype filter
ωnew,1 — Position of the feature originally at (-ωold) in the target filter
ωnew,2 — Position of the feature originally at (+ωold) in the target filter
The following example shows how this transformation can be used to convert the
prototype lowpass filter with cutoff frequency at 0.5 into a real bandstop filter with the
same passband and stopband ripple structure and stopband positioned between 0.5 and
0.75. Here is the MATLAB code for generating the example in the figure.
The prototype filter is a halfband elliptic, real, third-order lowpass filter:
[b, a] = ellip(3, 0.1, 30, 0.409);
The example transformation creates a stopband from 0.5 to 0.75:
[num,den] = iirlp2bs(b, a, 0.5, [0.5, 0.75]);
4-94
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Digital Frequency Transformations
Prototype filter
0
|H(ω)|in dB
−10
−20
−30
−40
ωo
−50
−60
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Normalized Frequency (×π rad/sample)
0.8
0.9
1
0.9
1
Target filter
0
|H(ω)| in dB
−10
−20
−30
−40
ωt1
−50
−60
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Normalized Frequency (×π rad/sample)
ωt2
0.8
Example of Real Lowpass to Real Bandstop Mapping
Real Lowpass to Real Multiband
This high-order transformation performs an exact mapping of one selected feature of the
prototype filter frequency response into a number of new locations in the target filter. Its
most common use is to convert a real lowpass with predefined passband and stopband
ripples into a real multiband filter with N arbitrary band edges, where N is the order of
the allpass mapping filter.
N
∑ ai z−i
H A ( z) = S Ni = 0
ai z− N +i
∑
a0 = 1
i= 0
The coefficients α are given by
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4-95
4
Filter Analysis, Design, and Implementation
a 0 = 1 k = 1,…, N

p

sin ( Nwnew + ( −1) kwold )

2
a k = − S
p
sin (( N − 2k)wnew + ( −1) kw old )


2
where
ωold,k — Frequency location of the first feature in the prototype filter
ωnew,k — Position of the feature originally at ωold,k in the target filter
The mobility factor, S, specifies the mobility or either DC or Nyquist feature:
 1 Nyquist
S=
DC
 −1
The example below shows how this transformation can be used to convert the prototype
lowpass filter with cutoff frequency at 0.5 into a filter having a number of bands
positioned at arbitrary edge frequencies 1/5, 2/5, 3/5 and 4/5. Parameter S was such that
there is a passband at DC. Here is the MATLAB code for generating the figure.
The prototype filter is a halfband elliptic, real, third-order lowpass filter:
[b, a] = ellip(3, 0.1, 30, 0.409);
The example transformation creates three stopbands, from DC to 0.2, from 0.4 to 0.6 and
from 0.8 to Nyquist:
[num,den] = iirlp2mb(b, a, 0.5, [0.2, 0.4, 0.6, 0.8], `pass');
4-96
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Digital Frequency Transformations
Prototype filter
0
|H(ω)|in dB
−10
−20
−30
−40
ωo
−50
−60
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Normalized Frequency (×π rad/sample)
0.8
0.9
1
0.9
1
Target filter
0
|H(ω)| in dB
−10
−20
−30
−40
ωt1
−50
−60
0
0.1
0.2
ωt2
ωt3
0.3
0.4
0.5
0.6
0.7
Normalized Frequency (×π rad/sample)
ωt4
0.8
Example of Real Lowpass to Real Multiband Mapping
Real Lowpass to Real Multipoint
This high-order frequency transformation performs an exact mapping of a number of
selected features of the prototype filter frequency response to their new locations in
the target filter. The mapping filter is given by the general IIR polynomial form of the
transfer function as given below.
N
∑ ai z −i
H A ( z) = S Ni = 0
ai z − N + i
∑
a0 = 1
i= 0
For the Nth-order multipoint frequency transformation the coefficients α are
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4
Filter Analysis, Design, and Implementation
N
i
N−i
 ∑ a N − i zold ,k ⋅ znew, k − S ⋅ znew,k = − zold ,k − S ⋅ znew, k
 i =1

jpw
 zold ,k = e old, k

j pw
 znew, k = e new,k

 k = 1,…, N
where
ωold,k — Frequency location of the first feature in the prototype filter
ωnew,k — Position of the feature originally at ωold,k in the target filter
The mobility factor, S, specifies the mobility of either DC or Nyquist feature:
 1 Nyquist
S=
DC
 −1
The example below shows how this transformation can be used to move features of the
prototype lowpass filter originally at -0.5 and 0.5 to their new locations at 0.5 and 0.75,
effectively changing a position of the filter passband. Here is the MATLAB code for
generating the figure.
The prototype filter is a halfband elliptic, real, third-order lowpass filter:
[b, a] = ellip(3, 0.1, 30, 0.409);
The example transformation creates a passband from 0.5 to 0.75:
[num,den] = iirlp2xn(b, a, [-0.5, 0.5], [0.5, 0.75], `pass');
4-98
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Digital Frequency Transformations
Prototype filter
0
|H(ω)|in dB
−10
−20
−30
−40
ωo2
−50
−60
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Normalized Frequency (×π rad/sample)
0.8
0.9
1
0.9
1
Target filter
0
|H(ω)| in dB
−10
−20
−30
−40
ωt1
−50
−60
0
0.1
0.2
ωt2
0.3
0.4
0.5
0.6
0.7
Normalized Frequency (×π rad/sample)
0.8
Example of Real Lowpass to Real Multipoint Mapping
Frequency Transformations for Complex Filters
• “Overview” on page 4-99
• “Complex Frequency Shift” on page 4-100
• “Real Lowpass to Complex Bandpass” on page 4-101
• “Real Lowpass to Complex Bandstop” on page 4-103
• “Real Lowpass to Complex Multiband” on page 4-104
• “Real Lowpass to Complex Multipoint” on page 4-106
• “Complex Bandpass to Complex Bandpass” on page 4-108
Overview
This section discusses complex frequency transformation that take the complex prototype
filter and convert it into a different complex target filter. The target filter has its
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4-99
4
Filter Analysis, Design, and Implementation
frequency response modified in respect to the frequency response of the prototype filter
according to the characteristic of the applied frequency transformation from:
Complex Frequency Shift
Complex frequency shift transformation is the simplest first-order transformation that
performs an exact mapping of one selected feature of the frequency response into its new
location. At the same time it rotates the whole response of the prototype lowpass filter
by the distance specified by the selection of the feature from the prototype filter and the
target filter.
H A ( z) = a z−1
with α given by
a = e j 2p (n new −n ol d )
where
ωold — Frequency location of the selected feature in the prototype filter
ωnew — Position of the feature originally at ωold in the target filter
A special case of the complex frequency shift is a, so called, Hilbert Transformer. It can
be designed by setting the parameter to |α|=1, that is
 1 forward
a =
 −1 inverse
The example below shows how to apply this transformation to rotate the response of the
prototype lowpass filter in either direction. Please note that because the transformation
can be achieved by a simple phase shift operator, all features of the prototype filter will
be moved by the same amount. Here is the MATLAB code for generating the example in
the figure.
The prototype filter is a halfband elliptic, real, third-order lowpass filter:
[b, a] = ellip(3, 0.1, 30, 0.409);
The example transformation moves the feature originally at 0.5 to 0.3:
[num,den] = iirshiftc(b, a, 0.5, 0.3);
4-100
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Digital Frequency Transformations
Prototype filter
0
|H(ω)|in dB
−10
−20
−30
−40
ωo
−50
−60
−1
−0.8
−0.6
−0.4
−0.2
0
0.2
0.4
Normalized Frequency (×π rad/sample)
0.6
0.8
1
0.6
0.8
1
Target filter
0
|H(ω)| in dB
−10
−20
−30
−40
ωt
−50
−60
−1
−0.8
−0.6
−0.4
−0.2
0
0.2
0.4
Normalized Frequency (×π rad/sample)
Example of Complex Frequency Shift Mapping
Real Lowpass to Complex Bandpass
This first-order transformation performs an exact mapping of one selected feature of the
prototype filter frequency response into two new locations in the target filter creating a
passband between them. Both Nyquist and DC features can be moved with the rest of the
frequency response.
H A ( z) =
b − a z−1
z−1 − ab
with α and β are given by
p
sin ( 2w old − wnew,2 + wnew,1)
4
a =
sin p (2wold + wnew,2 − wnew,1 )
b = e − jp (wnew −wo ld )
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4-101
4
Filter Analysis, Design, and Implementation
where
ωold — Frequency location of the selected feature in the prototype filter
ωnew,1 — Position of the feature originally at (-ωold) in the target filter
ωnew,2 — Position of the feature originally at (+ωold) in the target filter
The following example shows the use of such a transformation for converting a real
halfband lowpass filter into a complex bandpass filter with band edges at 0.5 and 0.75.
Here is the MATLAB code for generating the example in the figure.
The prototype filter is a half band elliptic, real, third-order lowpass filter:
[b, a] = ellip(3, 0.1, 30, 0.409);
The transformation creates a passband from 0.5 to 0.75:
[num,den] = iirlp2bpc(b, a, 0.5, [0.5 0.75]);
Prototype filter
0
|H(ω)|in dB
−10
−20
−30
−40
ωo
−50
−60
−1
−0.8
−0.6
−0.4
−0.2
0
0.2
0.4
Normalized Frequency (×π rad/sample)
0.6
0.8
1
0.8
1
Target filter
0
|H(ω)| in dB
−10
−20
−30
−40
ωt1
−50
ωt2
−60
−1
−0.8
−0.6
−0.4
−0.2
0
0.2
0.4
Normalized Frequency (×π rad/sample)
0.6
Example of Real Lowpass to Complex Bandpass Mapping
4-102
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Digital Frequency Transformations
Real Lowpass to Complex Bandstop
This first-order transformation performs an exact mapping of one selected feature of the
prototype filter frequency response into two new locations in the target filter creating a
stopband between them. Both Nyquist and DC features can be moved with the rest of the
frequency response.
H A ( z) =
b − a z−1
ab − z−1
with α and β are given by
a =
cos p (2wold + n new,2 − n new,1 )
cos p (2wold − n new,2 + n new,1 )
b = e − jp (wnew −wo ld )
where
ωold — Frequency location of the selected feature in the prototype filter
ωnew,1 — Position of the feature originally at (-ωold) in the target filter
ωnew,2 — Position of the feature originally at (+ωold) in the target filter
The example below shows the use of such a transformation for converting a real halfband
lowpass filter into a complex bandstop filter with band edges at 0.5 and 0.75. Here is the
MATLAB code for generating the example in the figure.
The prototype filter is a halfband elliptic, real, third-order lowpass filter:
[b, a] = ellip(3, 0.1, 30, 0.409);
The transformation creates a stopband from 0.5 to 0.75:
[num,den] = iirlp2bsc(b, a, 0.5, [0.5 0.75]);
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4-103
4
Filter Analysis, Design, and Implementation
Prototype filter
0
|H(ω)|in dB
−10
−20
−30
−40
ωo
−50
−60
−1
−0.8
−0.6
−0.4
−0.2
0
0.2
0.4
Normalized Frequency (×π rad/sample)
0.6
0.8
1
Target filter
0
|H(ω)| in dB
−10
−20
−30
−40
ωt1
−50
−60
−1
−0.8
−0.6
−0.4
−0.2
0
0.2
0.4
Normalized Frequency (×π rad/sample)
ωt2
0.6
0.8
1
Example of Real Lowpass to Complex Bandstop Mapping
Real Lowpass to Complex Multiband
This high-order transformation performs an exact mapping of one selected feature of the
prototype filter frequency response into a number of new locations in the target filter. Its
most common use is to convert a real lowpass with predefined passband and stopband
ripples into a multiband filter with arbitrary band edges. The order of the mapping filter
must be even, which corresponds to an even number of band edges in the target filter.
The Nth-order complex allpass mapping filter is given by the following general transfer
function form:
N
∑ ai z− i
H A ( z) = S N i = 0
ai ± z− N +i
∑
a0 = 1
4-104
i= 0
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Digital Frequency Transformations
The coefficients α are calculated from the system of linear equations:
N
 ℜ(ai ) ⋅ cos b1,k − cos b 2,k  + ℑ(a i ) ⋅ sin b1, k + sin b 2, k  = cos b 3,k
 i =1
N
 ℜ(a ) ⋅ sin b − sin b  − ℑ(a ) ⋅  cos b + cos b  = sin b
3, k
i 
1, k
2, k 
i 
1 ,k
2, k 

 i =1
 b = −p n
⋅ ( −1) k + n new,k ( N − k) 
 1 ,k
 old




 b 2, k = −p ∆ C + n n ew, kk 

k
 b 3, k = −p n old ⋅ ( −1) + n new, k N 

 k = 1… N
∑
∑
where
ωold — Frequency location of the selected feature in the prototype filter
ωnew,i — Position of features originally at ±ωold in the target filter
Parameter S is the additional rotation factor by the frequency distance ΔC, giving the
additional flexibility of achieving the required mapping:
S = e − jp∆C
The example shows the use of such a transformation for converting a prototype real
lowpass filter with the cutoff frequency at 0.5 into a multiband complex filter with band
edges at 0.2, 0.4, 0.6 and 0.8, creating two passbands around the unit circle. Here is the
MATLAB code for generating the figure.
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Filter Analysis, Design, and Implementation
Prototype filter
0
|H(ω)|in dB
−10
−20
−30
−40
ωo
−50
−60
−1
−0.8
−0.6
−0.4
−0.2
0
0.2
0.4
Normalized Frequency (×π rad/sample)
0.6
0.8
1
Target filter
0
|H(ω)| in dB
−10
−20
−30
−40
ωt1
−50
−60
−1
−0.8
−0.6
ωt2
−0.4
−0.2
0
0.2
0.4
Normalized Frequency (×π rad/sample)
ωt3
0.6
ωt4
0.8
1
Example of Real Lowpass to Complex Multiband Mapping
The prototype filter is a halfband elliptic, real, third-order lowpass filter:
[b, a] = ellip(3, 0.1, 30, 0.409);
The example transformation creates two complex passbands:
[num,den] = iirlp2mbc(b, a, 0.5, [0.2, 0.4, 0.6, 0.8]);
Real Lowpass to Complex Multipoint
This high-order transformation performs an exact mapping of a number of selected
features of the prototype filter frequency response to their new locations in the target
filter. The Nth-order complex allpass mapping filter is given by the following general
transfer function form.
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Digital Frequency Transformations
N
∑ ai z− i
H A ( z) = S N i = 0
ai ± z− N +i
∑
a0 = 1
i= 0
The coefficients α can be calculated from the system of linear equations:
N
 ℜ(ai ) ⋅ cos b1,k − cos b 2,k  + ℑ(a i ) ⋅ sin b1, k + sin b 2, k  = cos b 3,k
 i =1
N
 ℜ(a ) ⋅ sin b − sin b  − ℑ(a ) ⋅  cos b + cos b  = sin b
3, k
i 
1, k
2, k 
i 
1 ,k
2, k 

 i =1

p
 b1,k = − w old ,k + wnew,k ( N − k)
2


p
 b 2, k = −  2∆C + wnew,k k
2

 b = − p w
old ,k + wnew,k N 
 3, k
2

 k = 1… N
∑
∑
where
ωold,k — Frequency location of the first feature in the prototype filter
ωnew,k — Position of the feature originally at ωold,k in the target filter
Parameter S is the additional rotation factor by the frequency distance ΔC, giving the
additional flexibility of achieving the required mapping:
S = e − jp∆C
The following example shows how this transformation can be used to move one selected
feature of the prototype lowpass filter originally at -0.5 to two new frequencies -0.5 and
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4
Filter Analysis, Design, and Implementation
0.1, and the second feature of the prototype filter from 0.5 to new locations at -0.25 and
0.3. This creates two nonsymmetric passbands around the unit circle, creating a complex
filter. Here is the MATLAB code for generating the figure.
The prototype filter is a halfband elliptic, real, third-order lowpass filter:
[b, a] = ellip(3, 0.1, 30, 0.409);
The example transformation creates two nonsymmetric passbands:
[num,den] = iirlp2xc(b,a,0.5*[-1,1,-1,1], [-0.5,-0.25,0.1,0.3]);
Prototype filter
0
|H(ω)|in dB
−10
−20
−30
−40
−50
−60
−1
−0.8
−0.6
ωo1
ωo2
ωo3
ωo4
−0.4
−0.2
0
0.2
0.4
Normalized Frequency (×π rad/sample)
0.6
0.8
1
0.6
0.8
1
Target filter
0
|H(ω)| in dB
−10
−20
−30
−40
−50
−60
−1
ωt1
−0.8
−0.6
ωt2
ωt3
ωt4
−0.4
−0.2
0
0.2
0.4
Normalized Frequency (×π rad/sample)
Example of Real Lowpass to Complex Multipoint Mapping
Complex Bandpass to Complex Bandpass
This first-order transformation performs an exact mapping of two selected features of the
prototype filter frequency response into two new locations in the target filter. Its most
common use is to adjust the edges of the complex bandpass filter.
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Digital Frequency Transformations
H A ( z) =
a (g − b z−1 )
z−1 − bg
with α and β are given by
p
((wold,2 − wold,1) − (wnew,2 − wnew,1 ))
4
a =
p
sin ((wold,2 − w old,,1 ) + (wnew,2 − wnew,1 ))
4
sin
a =e
g =e
− jp (w old ,2 −wold,1 )
− jp (wnew,2 −wneew,1 )
where
ωold,1 — Frequency location of the first feature in the prototype filter
ωold,2 — Frequency location of the second feature in the prototype filter
ωnew,1 — Position of the feature originally at ωold,1 in the target filter
ωnew,2 — Position of the feature originally at ωold,2 in the target filter
The following example shows how this transformation can be used to modify the position
of the passband of the prototype filter, either real or complex. In the example below
the prototype filter passband spanned from 0.5 to 0.75. It was converted to having a
passband between -0.5 and 0.1. Here is the MATLAB code for generating the figure.
The prototype filter is a halfband elliptic, real, third-order lowpass filter:
[b, a] = ellip(3, 0.1, 30, 0.409);
The example transformation creates a passband from 0.25 to 0.75:
[num,den] = iirbpc2bpc(b, a, [0.25, 0.75], [-0.5, 0.1]);
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4
Filter Analysis, Design, and Implementation
Prototype filter
0
|H(ω)|in dB
−10
−20
−30
−40
ωo1
−50
−60
−1
−0.8
−0.6
−0.4
−0.2
0
0.2
0.4
Normalized Frequency (×π rad/sample)
ωo2
0.6
0.8
1
0.6
0.8
1
Target filter
0
|H(ω)| in dB
−10
−20
−30
−40
ωt1
−50
−60
−1
−0.8
−0.6
ωt2
−0.4
−0.2
0
0.2
0.4
Normalized Frequency (×π rad/sample)
Example of Complex Bandpass to Complex Bandpass Mapping
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Digital Filter Design Block
Digital Filter Design Block
In this section...
“Overview of the Digital Filter Design Block” on page 4-111
“Select a Filter Design Block” on page 4-112
“Create a Lowpass Filter in Simulink” on page 4-113
“Create a Highpass Filter in Simulink” on page 4-114
“Filter High-Frequency Noise in Simulink” on page 4-116
Overview of the Digital Filter Design Block
You can use the Digital Filter Design block to design and implement a digital filter. The
filter you design can filter single-channel or multichannel signals. The Digital Filter
Design block is ideal for simulating the numerical behavior of your filter on a floatingpoint system, such as a personal computer or DSP chip. You can use the Simulink Coder
product to generate C code from your filter block. For more information on generating C
code from models, see “Understanding C Code Generation” on page 10-2.
Filter Design and Analysis
You perform all filter design and analysis within the Filter Design and Analysis Tool
(FDATool) GUI, which opens when you double-click the Digital Filter Design block.
FDATool provides extensive filter design parameters and analysis tools such as pole-zero
and impulse response plots.
Filter Implementation
Once you have designed your filter using FDATool, the block automatically realizes the
filter using the filter structure you specify. You can then use the block to filter signals
in your model. You can also fine-tune the filter by changing the filter specification
parameters during a simulation. The outputs of the Digital Filter Design block
numerically match the outputs of the DSP System Toolbox filter function and the
MATLAB filter function.
Saving, Exporting, and Importing Filters
The Digital Filter Design block allows you to save the filters you design, export filters (to
the MATLAB workspace, MAT-files, etc.), and import filters designed elsewhere.
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4
Filter Analysis, Design, and Implementation
To learn how to save your filter designs, see “Saving and Opening Filter Design Sessions”
in the Signal Processing Toolbox documentation. To learn how to import and export your
filter designs, see “Import and Export Quantized Filters”.
Note: You can use the Digital Filter Design block to design and implement a filter. To
implement a pre-designed filter, use the Discrete FIR Filter or Biquad Filter blocks.
Both methods implement a filter design in the same manner and have the same behavior
during simulation and code generation.
See the Digital Filter Design block reference page for more information. For information
on choosing between the Digital Filter Design block and the Filter Realization Wizard,
see “Select a Filter Design Block” on page 4-112.
Select a Filter Design Block
This section explains the similarities and differences between the Digital Filter Design
and Filter Realization Wizard blocks.
Similarities
The Digital Filter Design block and Filter Realization Wizard are similar in the following
ways:
• Filter design and analysis options — Both blocks use the Filter Design and Analysis
Tool (FDATool) GUI for filter design and analysis.
• Output values — If the output of both blocks is double-precision floating point, singleprecision floating point, or fixed point, the output values of both blocks numerically
match the output of the filter method of the dfilt object.
Differences
The Digital Filter Design block and Filter Realization Wizard handle the following things
differently:
• Supported filter structures — Both blocks support many of the same basic filter
structures, but the Filter Realization Wizard supports more structures than the
Digital Filter Design block. This is because the block can implement filters using
Sum, Gain, and Delay blocks. See the Filter Realization Wizard and Digital Filter
Design block reference pages for a list of all the structures they support.
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Digital Filter Design Block
• Data type support — The Filter Realization Wizard block supports single- and
double-precision floating-point computation for all filter structures and fixed-point
computation for some filter structures. The Digital Filter Design block only supports
single- and double-precision floating-point computation.
• Block versus Wizard — The Digital Filter Design block is the filter itself, but the
Filter Realization Wizard block just enables you to create new filters and put them in
an existing model. Thus, the Filter Realization Wizard is not a block that processes
data in your model, it is a wizard that generates filter blocks (or subsystems) which
you can then use to process data in your model.
When to Use Each Block
The following are specific situations where only the Digital Filter Design block or the
Filter Realization Wizard is appropriate.
• Digital Filter Design
• Use to simulate single- and double-precision floating-point filters.
• Use to generate highly optimized ANSI® C code that implements floating-point
filters for embedded systems.
• Filter Realization Wizard
• Use to simulate numerical behavior of fixed-point filters in a DSP chip, a fieldprogrammable gate array (FPGA), or an application-specific integrated circuit
(ASIC).
• Use to simulate single- and double-precision floating-point filters with structures
that the Digital Filter Design block does not support.
• Use to visualize the filter structure, as the block can build the filter from Sum,
Gain, and Delay blocks.
• Use to rapidly generate multiple filter blocks.
See “Filter Realization Wizard” on page 4-121 and the Filter Realization Wizard block
reference page for information.
Create a Lowpass Filter in Simulink
You can use the Digital Filter Design block to design and implement a digital FIR or IIR
filter. In this topic, you use it to create an FIR lowpass filter:
1
Open Simulink and create a new model file.
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Filter Analysis, Design, and Implementation
2
From the DSP System Toolbox Filtering library, and then from the Filter
Implementations library, click-and-drag a Digital Filter Design block into your
model.
3
Double-click the Digital Filter Design block.
The Filter Design and Analysis Tool (FDATool) GUI opens.
4
Set the parameters as follows, and then click OK:
• Response Type = Lowpass
• Design Method = FIR, Equiripple
• Filter Order = Minimum order
• Units = Normalized (0 to 1)
• wpass = 0.2
• wstop = 0.5
5
Click Design Filter at the bottom of the GUI to design the filter.
Your Digital Filter Design block now represents a filter with the parameters you
specified.
6
From the Edit menu, select Convert Structure.
The Convert Structure dialog box opens.
7
Select Direct-Form FIR Transposed and click OK.
8
Rename your block Digital Filter Design - Lowpass.
The Digital Filter Design block now represents a lowpass filter with a Direct-Form
FIR Transposed structure. The filter passes all frequencies up to 20% of the Nyquist
frequency (half the sampling frequency), and stops frequencies greater than or equal to
50% of the Nyquist frequency as defined by the wpass and wstop parameters. In the
next topic, “Create a Highpass Filter in Simulink” on page 4-114, you use a Digital
Filter Design block to create a highpass filter. For more information about implementing
a pre-designed filter, see “Digital Filter Implementations” on page 4-133.
Create a Highpass Filter in Simulink
In this topic, you create a highpass filter using the Digital Filter Design block:
1
4-114
If the model you created in “Create a Lowpass Filter in Simulink” on page 4-113 is
not open on your desktop, you can open an equivalent model by typing
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Digital Filter Design Block
ex_filter_ex4
at the MATLAB command prompt.
2
From the DSP System Toolbox Filtering library, and then from the Filter
Implementations library, click-and-drag a second Digital Filter Design block into
your model.
3
Double-click the Digital Filter Design block.
The Filter Design and Analysis Tool (FDATool) GUI opens.
4
Set the parameters as follows:
• Response Type = Highpass
• Design Method = FIR, Equiripple
• Filter Order = Minimum order
• Units = Normalized (0 to 1)
• wstop = 0.2
• wpass = 0.5
5
Click the Design Filter button at the bottom of the GUI to design the filter.
Your Digital Filter Design block now represents a filter with the parameters you
specified.
6
In the Edit menu, select Convert Structure.
The Convert Structure dialog box opens.
7
Select Direct-Form FIR Transposed and click OK.
8
Rename your block Digital Filter Design - Highpass .
The block now implements a highpass filter with a direct form FIR transpose structure.
The filter passes all frequencies greater than or equal to 50% of the Nyquist frequency
(half the sampling frequency), and stops frequencies less than or equal to 20% of the
Nyquist frequency as defined by the wpass and wstop parameters. This highpass filter
is the opposite of the lowpass filter described in “Create a Lowpass Filter in Simulink”
on page 4-113. The highpass filter passes the frequencies stopped by the lowpass
filter, and stops the frequencies passed by the lowpass filter. In the next topic, “Filter
High-Frequency Noise in Simulink” on page 4-116, you use these Digital Filter
Design blocks to create a model capable of removing high frequency noise from a signal.
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Filter Analysis, Design, and Implementation
For more information about implementing a pre-designed filter, see “Digital Filter
Implementations” on page 4-133.
Filter High-Frequency Noise in Simulink
In the previous topics, you used Digital Filter Design blocks to create FIR lowpass and
highpass filters. In this topic, you use these blocks to build a model that removes high
frequency noise from a signal. In this model, you use the highpass filter, which is excited
using a uniform random signal, to create high-frequency noise. After you add this noise
to a sine wave, you use the lowpass filter to filter out the high-frequency noise:
1
If the model you created in “Create a Highpass Filter in Simulink” on page 4-114
is not open on your desktop, you can open an equivalent model by typing
ex_filter_ex5
at the MATLAB command prompt.
2
3
Click-and-drag the following blocks into your model.
Block
Library
Quantity
Add
Simulink Math Operations library
1
Random Source
Sources
1
Sine Wave
Sources
1
Time Scope
Sinks
1
Set the parameters for these blocks as indicated in the following table. Leave the
parameters not listed in the table at their default settings.
Parameter Settings for the Other Blocks
Block
Parameter Setting
Add
• Icon shape = rectangular
• List of signs = ++
Random Source
• Source type = = Uniform
• Minimum = 0
• Maximum = 4
• Sample mode = Discrete
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Digital Filter Design Block
Block
Parameter Setting
• Sample time = 1/1000
• Samples per frame = 50
Sine Wave
• Frequency (Hz) = 75
• Sample time = 1/1000
• Samples per frame = 50
Time Scope
• File > Number of Input Ports > 3
• File > Configuration ...
• Open the Visuals:Time Domain Options dialog and set
Time span = One frame period
4
Connect the blocks as shown in the following figure. You might need to resize some
of the blocks to accomplish this task.
5
From the Simulation menu, select Model Configuration Parameters.
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Filter Analysis, Design, and Implementation
The Configuration Parameters dialog box opens.
6
In the Solver pane, set the parameters as follows, and then click OK:
• Start time = 0
• Stop time = 5
• Type = Fixed-step
• Solver = Discrete (no continuous states)
7
In the model window, from the Simulation menu, choose Run.
The model simulation begins and the scope displays the three input signals.
8
After simulation is complete, select View > Legend from the Time Scope menu. The
legend appears in the Time Scope window. You can click-and-drag it anywhere on
the scope display. To change the channel names, double-click inside the legend and
replace the default channel names with the following:
• Add = Noisy Sine Wave
• Digital Filter Design – Lowpass = Filtered Noisy Sine Wave
• Sine Wave = Original Sine Wave
In the next step, you will set the color, style, and marker of each channel.
9
In the Time Scope window, select View > Line Properties, and set the following:
Line
Style
Marker
Color
Noisy Sine Wave
-
None
Black
Filtered Noisy Sine Wave
diamond
Red
Original Sine Wave None
*
Blue
10 The Time Scope display should now appear as follows:
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Digital Filter Design Block
You can see that the lowpass filter filters out the high-frequency noise in the noisy
sine wave.
You have now used Digital Filter Design blocks to build a model that removes high
frequency noise from a signal. For more information about these blocks, see the Digital
Filter Design block reference page. For information on another block capable of designing
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Filter Analysis, Design, and Implementation
and implementing filters, see “Filter Realization Wizard” on page 4-121. To learn how
to save your filter designs, see “Saving and Opening Filter Design Sessions” in the Signal
Processing Toolbox documentation. To learn how to import and export your filter designs,
see “Import and Export Quantized Filters” in the DSP System Toolbox documentation.
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Filter Realization Wizard
Filter Realization Wizard
In this section...
“Overview of the Filter Realization Wizard” on page 4-121
“Design and Implement a Fixed-Point Filter in Simulink” on page 4-121
“Set the Filter Structure and Number of Filter Sections” on page 4-130
“Optimize the Filter Structure” on page 4-131
Overview of the Filter Realization Wizard
The Filter Realization Wizard is another DSP System Toolbox block that can be used
to design and implement digital filters. You can use this tool to filter single-channel
floating-point or fixed-point signals. Like the Digital Filter Design block, double-clicking
a Filter Realization Wizard block opens FDATool. Unlike the Digital Filter Design block,
the Filter Realization Wizard starts FDATool with the Realize Model panel selected.
This panel is optimized for use with DSP System Toolbox software.
For more information, see the Filter Realization Wizard block reference page. For
information on choosing between the Digital Filter Design block and the Filter
Realization Wizard, see “Select a Filter Design Block” on page 4-112.
Design and Implement a Fixed-Point Filter in Simulink
In this section, a tutorial guides you through creating a fixed-point filter with the Filter
Realization Wizard. You will use the Filter Realization Wizard to remove noise from a
signal. This tutorial has the following parts:
• “Part 1 — Create a Signal with Added Noise” on page 4-121
• “Part 2 — Create a Fixed-Point Filter with the Filter Realization Wizard” on page
4-123
• “Part 3 — Build a Model to Filter a Signal” on page 4-127
• “Part 4 — Examine Filtering Results” on page 4-129
Part 1 — Create a Signal with Added Noise
In this section of the tutorial, you will create a signal with added noise. Later in the
tutorial, you will filter this signal with a fixed-point filter that you design with the Filter
Realization Wizard.
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Filter Analysis, Design, and Implementation
1
Type
load mtlb
soundsc(mtlb,Fs)
at the MATLAB command line. You should hear a voice say “MATLAB.” This is the
signal to which you will add noise.
2
Create a noise signal by typing
noise = cos(2*pi*3*Fs/8*(0:length(mtlb)-1)/Fs)';
at the command line. You can hear the noise signal by typing
soundsc(noise,Fs)
3
Add the noise to the original signal by typing
u = mtlb + noise;
at the command line.
4
Scale the signal with noise by typing
u = u/max(abs(u));
at the command line. You scale the signal to try to avoid overflows later on. You can
hear the scaled signal with noise by typing
soundsc(u,Fs)
5
View the scaled signal with noise by typing
spectrogram(u,256,[],[],Fs);colorbar
at the command line.
The spectrogram appears as follows.
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Filter Realization Wizard
In the spectrogram, you can see the noise signal as a line at about 2800 Hz, which is
equal to 3*Fs/8.
Part 2 — Create a Fixed-Point Filter with the Filter Realization Wizard
Next you will create a fixed-point filter using the Filter Realization Wizard. You will
create a filter that reduces the effects of the noise on the signal.
1
Open a new Simulink model, and drag-and-drop a Filter Realization Wizard block
from the Filtering / Filter Implementations library into the model.
Note: You do not have to place a Filter Realization Wizard block in a model in order
to use it. You can open the GUI from within a library. However, for purposes of this
tutorial, we will keep the Filter Realization Wizard block in the model.
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4
Filter Analysis, Design, and Implementation
2
Double-click the Filter Realization Wizard block in your model. The Realize Model
panel of the Filter Design and Analysis Tool (FDATool) appears.
3
Click the Design Filter button (
) on the bottom left of FDATool. This brings
forward the Design filter panel of the tool.
4
Set the following fields in the Design filter panel:
• Set Design Method to IIR -- Constrained Least Pth-norm
• Set Fs to Fs
• Set Fpass to 0.2*Fs
• Set Fstop to 0.25*Fs
• Set Max pole radius to 0.8
• Click the Design Filter button
The Design filter panel should now appear as follows.
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Filter Realization Wizard
5
Click the Set quantization parameters button on the bottom left of FDATool
(
6
). This brings forward the Set quantization parameters panel of the tool.
Set the following fields in the Set quantization parameters panel:
• Select Fixed-point for the Filter arithmetic parameter.
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4
Filter Analysis, Design, and Implementation
• Make sure the Best precision fraction lengths check box is selected on the
Coefficients pane.
The Set quantization parameters panel should appear as follows.
7
Click the Realize Model button on the left side of FDATool (
forward the Realize Model panel of the tool.
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). This brings
Filter Realization Wizard
8
Select the Build model using basic elements check box, then click the Realize
Model button on the bottom of FDATool. A subsystem block for the new filter
appears in your model.
Note: You do not have to keep the Filter Realization Wizard block in the same model
as the generated Filter block. However, for this tutorial, we will keep the blocks in
the same model.
9
Double-click the Filter subsystem block in your model to view the filter
implementation.
Part 3 — Build a Model to Filter a Signal
In this section of the tutorial, you will filter noise from a signal in your Simulink model.
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Filter Analysis, Design, and Implementation
1
Connect a Signal From Workspace block from the Sources library to the input port of
your filter block.
2
Connect a To Workspace block from the Sinks library to the output port of your filter
block. Your blocks should now be connected as follows.
3
Open the Signal From Workspace block dialog box and set the Signal parameter to
u. Click OK to save your changes and close the dialog box.
4
Open the Model Configuration Parameters dialog box from the Simulation
menu of the model. In the Solver pane of the dialog, set the following fields:
• Stop time = length(u)-1
• Type = Fixed-step
Click OK to save your changes and close the dialog box.
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5
Run the model.
6
From the Display menu of the model, select Signals & Ports > Port Data Types.
You can now see that the input to the Filter block is a signal of type double and the
output of the Filter block has a data type of sfix16_En11.
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Filter Realization Wizard
Part 4 — Examine Filtering Results
Now you can listen to and look at the results of the fixed-point filter you designed and
implemented.
1
Type
soundsc(yout,Fs)
at the command line to hear the output of the filter. You should hear a voice say
“MATLAB.” The noise portion of the signal should be close to inaudible.
2
Type
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Filter Analysis, Design, and Implementation
figure
spectrogram(yout,256,[],[],Fs);colorbar
at the command line.
From the colorbars at the side of the input and output spectrograms, you can see that the
noise has been reduced by about 40 dB.
Set the Filter Structure and Number of Filter Sections
The Current Filter Information region of FDATool shows the structure and the
number of second-order sections in your filter.
Change the filter structure and number of filter sections of your filter as follows:
• Select Convert Structure from the Edit menu to open the Convert Structure
dialog box. For details, see “Converting to a New Structure” in the Signal Processing
Toolbox documentation.
• Select Convert to Second-order Sections from the Edit menu to open the
Convert to SOS dialog box. For details, see “Converting to Second-Order Sections” in
the Signal Processing Toolbox documentation.
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Filter Realization Wizard
Note: You might not be able to directly access some of the supported structures through
the Convert Structure dialog of FDATool. However, you can access all of the structures
by creating a dfilt filter object with the desired structure, and then importing the filter
into FDATool. To learn more about the Import Filter panel, see “Importing a Filter
Design” in the Signal Processing Toolbox documentation.
Optimize the Filter Structure
The Filter Realization Wizard can implement a digital filter using either digital filter
blocks from the DSP System Toolbox library or by creating a “subsystem” block that
implements the filter using Sum, Gain, and Delay blocks. The following procedure shows
you how to optimize the filter implementation:
1
Open the Realize Model pane of FDATool by clicking the Realize Model button
in the lower-left corner of FDATool.
2
Select the desired optimizations in the Optimization region of the Realize Model
pane. See the following descriptions and illustrations of each optimization option.
• Optimize for zero gains — Remove zero-gain paths.
• Optimize for unity gains — Substitute gains equal to one with a wire (short
circuit).
• Optimize for negative gains — Substitute gains equal to -1 with a wire (short
circuit), and change the corresponding sums to subtractions.
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Filter Analysis, Design, and Implementation
• Optimize delay chains — Substitute any delay chain made up of n unit delays with
a single delay by n.
• Optimize for unity scale values — Remove all scale value multiplications by 1
from the filter structure.
The following diagram illustrates the results of each of these optimizations.
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Digital Filter Implementations
Digital Filter Implementations
In this section...
“Using Digital Filter Blocks” on page 4-133
“Implement a Lowpass Filter in Simulink” on page 4-133
“Implement a Highpass Filter in Simulink” on page 4-134
“Filter High-Frequency Noise in Simulink” on page 4-135
“Specify Static Filters” on page 4-140
“Specify Time-Varying Filters” on page 4-140
“Specify the SOS Matrix (Biquadratic Filter Coefficients)” on page 4-141
Using Digital Filter Blocks
DSP System Toolbox provides several blocks implementing digital filters, such as
Discrete FIR Filter and Biquad Filter.
Use these blocks if you have already performed the design and analysis and know
your desired filter coefficients. You can use these blocks to filter single-channel and
multichannel signals, and to simulate floating-point and fixed-point filters. Then, you can
use the Simulink Coder product to generate highly optimized C code from your filters.
To implement a filter, you must provide the following basic information about the filter:
• The desired filter structure
• The filter coefficients
Note: Use the Digital Filter Design block to design and implement a filter. Use the
Discrete FIR Filter and Biquad Filter blocks to implement a pre-designed filter. Both
methods implement a filter in the same manner and have the same behavior during
simulation and code generation.
Implement a Lowpass Filter in Simulink
Use the Discrete FIR Filter block to implement a lowpass filter:
1
Define the lowpass filter coefficients in the MATLAB workspace by typing
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Filter Analysis, Design, and Implementation
lopassNum = [-0.0021 -0.0108 -0.0274 -0.0409 -0.0266 0.0374
0.1435 0.2465 0.2896 0.2465 0.1435 0.0374 -0.0266 -0.0409 -0.0274
-0.0108 -0.0021];
2
Open Simulink and create a new model file.
3
From the DSP System Toolbox Filtering>Filter Implementations library, click-anddrag a Discrete FIR Filter block into your model.
4
Double-click the Discrete FIR Filter block. Set the block parameters as follows, and
then click OK:
• Coefficient source = Dialog parameters
• Filter structure = Direct form transposed
• Coefficients = lopassNum
• Input processing = Columns as channels (frame based)
• Initial states = 0
Note that you can provide the filter coefficients in several ways:
• Type in a variable name from the MATLAB workspace, such as lopassNum.
• Type in filter design commands from Signal Processing Toolbox software or DSP
System Toolbox software, such as fir1(5, 0.2, 'low').
• Type in a vector of the filter coefficient values.
5
Rename your block Digital Filter - Lowpass.
The Discrete FIR Filter block in your model now represents a lowpass filter. In the next
topic, “Implement a Highpass Filter in Simulink” on page 4-134, you use a Discrete
FIR Filter block to implement a highpass filter. For more information about the Discrete
FIR Filter block, see the Discrete FIR Filter block reference page. For more information
about designing and implementing a new filter, see “Digital Filter Design Block” on page
4-111.
Implement a Highpass Filter in Simulink
In this topic, you implement a highpass filter using the Discrete FIR Filter block:
1
4-134
If the model you created in “Implement a Lowpass Filter in Simulink” on page
4-133 is not open on your desktop, you can open an equivalent model by typing
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Digital Filter Implementations
ex_filter_ex1
at the MATLAB command prompt.
2
Define the highpass filter coefficients in the MATLAB workspace by typing
hipassNum = [-0.0051 0.0181 -0.0069 -0.0283 -0.0061 ...
0.0549 0.0579 -0.0826 -0.2992 0.5946 -0.2992 -0.0826 ...
0.0579 0.0549 -0.0061 -0.0283 -0.0069 0.0181 -0.0051];
3
From the DSP System Toolbox Filtering library, and then from the Filter
Implementations library, click-and-drag a Discrete FIR Filter block into your model.
4
Double-click the Discrete FIR Filter block. Set the block parameters as follows, and
then click OK:
• Coefficient source = Dialog parameters
• Filter structure = Direct form transposed
• Coefficients = hipassNum
• Input processing = Columns as channels (frame based)
• Initial states = 0
You can provide the filter coefficients in several ways:
• Type in a variable name from the MATLAB workspace, such as hipassNum.
• Type in filter design commands from Signal Processing Toolbox software or DSP
System Toolbox software, such as fir1(5, 0.2, 'low').
• Type in a vector of the filter coefficient values.
5
Rename your block Digital Filter - Highpass.
You have now successfully implemented a highpass filter. In the next topic, “Filter HighFrequency Noise in Simulink” on page 4-135, you use these Discrete FIR Filter blocks
to create a model capable of removing high frequency noise from a signal. For more
information about designing and implementing a new filter, see “Digital Filter Design
Block” on page 4-111.
Filter High-Frequency Noise in Simulink
In the previous topics, you used Discrete FIR Filter blocks to implement lowpass and
highpass filters. In this topic, you use these blocks to build a model that removes high
frequency noise from a signal. In this model, you use the highpass filter, which is excited
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Filter Analysis, Design, and Implementation
using a uniform random signal, to create high-frequency noise. After you add this noise
to a sine wave, you use the lowpass filter to filter out the high-frequency noise:
1
If the model you created in “Implement a Highpass Filter in Simulink” on page
4-134 is not open on your desktop, you can open an equivalent model by typing
ex_filter_ex2
at the MATLAB command prompt.
2
If you have not already done so, define the lowpass and highpass filter coefficients in
the MATLAB workspace by typing
lopassNum = [-0.0021 -0.0108 -0.0274 -0.0409 -0.0266 ...
0.0374 0.1435 0.2465 0.2896 0.2465 0.1435 0.0374 ...
-0.0266 -0.0409 -0.0274 -0.0108 -0.0021];
hipassNum = [-0.0051 0.0181 -0.0069 -0.0283 -0.0061 ...
0.0549 0.0579 -0.0826 -0.2992 0.5946 -0.2992 -0.0826 ...
0.0579 0.0549 -0.0061 -0.0283 -0.0069 0.0181 -0.0051];
3
4
Click-and-drag the following blocks into your model file.
Block
Library
Quantity
Add
Simulink / Math Operations library
1
Random Source
Sources
1
Sine Wave
Sources
1
Time Scope
Sinks
1
Set the parameters for the rest of the blocks as indicated in the following table. For
any parameters not listed in the table, leave them at their default settings.
Block
Parameter Setting
Add
• Icon shape = rectangular
• List of signs = ++
Random Source
• Source type = Uniform
• Minimum = 0
• Maximum = 4
• Sample mode = Discrete
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• Sample time = 1/1000
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Digital Filter Implementations
Block
Parameter Setting
• Samples per frame = 50
Sine Wave
• Frequency (Hz) = 75
• Sample time = 1/1000
• Samples per frame = 50
Time Scope
• File > Number of Input Ports > 3
• File > Configuration ...
• Open the Visuals:Time Domain Options dialog
and set Time span = One frame period
5
Connect the blocks as shown in the following figure. You may need to resize some of
your blocks to accomplish this task.
6
From the Simulation menu, select Model Configuration Parameters.
The Configuration Parameters dialog box opens.
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Filter Analysis, Design, and Implementation
7
In the Solver pane, set the parameters as follows, and then click OK:
• Start time = 0
• Stop time = 5
• Type = Fixed-step
• Solver = discrete (no continuous states)
8
In the model window, from the Simulation menu, choose Run.
The model simulation begins and the Scope displays the three input signals.
9
After simulation is complete, select View > Legend from the Time Scope menu. The
legend appears in the Time Scope window. You can click-and-drag it anywhere on
the scope display. To change the channel names, double-click inside the legend and
replace the current numbered channel names with the following:
• Add = Noisy Sine Wave
• Digital Filter – Lowpass = Filtered Noisy Sine Wave
• Sine Wave = Original Sine Wave
In the next step, you will set the color, style, and marker of each channel.
10 In the Time Scope window, select View > Line Properties, and set the following:
Line
Style
Marker
Color
Noisy Sine Wave
-
None
Black
Filtered Noisy Sine Wave
diamond
Red
Original Sine Wave None
*
Blue
11 The Time Scope display should now appear as follows:
You can see that the lowpass filter filters out the high-frequency noise in the noisy
sine wave.
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Digital Filter Implementations
You have now used Discrete FIR Filter blocks to build a model that removes high
frequency noise from a signal. For more information about designing and implementing a
new filter, see “Digital Filter Design Block” on page 4-111.
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Filter Analysis, Design, and Implementation
Specify Static Filters
You can specify a static filter using the Discrete FIR Filter or Biquad Filter block. To do
so, set the Coefficient source parameter to Dialog parameters.
For the Discrete FIR Filter, set the Coefficients parameter to a row vector of numerator
coefficients. If you set Filter structure to Lattice MA, the Coefficients parameter
represents reflection coefficients.
For the Biquad Filter, set the SOS matrix (Mx6) to an M-by-6 matrix, where M is
the number of sections in the second-order section filter. Each row of the SOS matrix
contains the numerator and denominator coefficients of the corresponding section in
the filter. Set Scale values to a scalar or vector of M+1 scale values used between SOS
stages.
Tuning the Filter Coefficient Values During Simulation
To change the static filter coefficients during simulation, double-click the block, type
in the new filter coefficients, and click OK. You cannot change the filter order, so you
cannot change the number of elements in the matrix of filter coefficients.
Specify Time-Varying Filters
Time-varying filters are filters whose coefficients change with time. You can specify a
time-varying filter that changes once per frame. You can filter multiple channels with
each filter. However, you cannot apply different filters to each channel; all channels use
the same filter.
To specify a time-varying filter using a Biquad Filter block or a Discrete FIR Filter block:
1
Set the Coefficient source parameter to Input port(s), which enables extra
block input ports for the time-varying filter coefficients.
• The Discrete FIR Filter block has a Num port for the numerator coefficients.
• The Biquad Filter block has Num and Den ports rather than a single port for
the SOS matrix. Separate ports enable you to use different fraction lengths for
numerator and denominator coefficients. The scale values port, g, is optional.
You can disable the g port by setting Scale values mode to Assume all are
unity and optimize.
2
4-140
Provide matrices of filter coefficients to the block input ports.
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Digital Filter Implementations
• For Discrete FIR Filter block, the number of filter taps, N, cannot vary over time.
The input coefficients must be in a 1-by-N vector.
• For Biquad Filter block, the number of filter sections, N, cannot vary over
time. The numerator coefficients input, Num, must be a 3-by-N matrix. The
denominator input coefficients, Den, must be a 2-by-N matrix. The scale values
input, g, must be a 1-by-(N+1) vector.
Specify the SOS Matrix (Biquadratic Filter Coefficients)
Use the Biquad Filter block to specify a static biquadratic IIR filter (also known as a
second-order section or SOS filter). Set the following parameters:
• Filter structure — Direct form I, or Direct form I transposed, or Direct
form II, or Direct form II transposed
• SOS matrix (Mx6) M-by-6 SOS matrix
The SOS matrix is an M-by-6 matrix, where M is the number of sections in the
second-order section filter. Each row of the SOS matrix contains the numerator and
denominator coefficients (bik and aik) of the corresponding section in the filter.
• Scale values Scalar or vector of M+1 scale values to be used between SOS stages
If you enter a scalar, the value is used as the gain value before the first section of the
second-order filter. The rest of the gain values are set to 1.
If you enter a vector of M+1 values, each value is used for a separate section of the
filter. For example, the first element is the first gain value, the second element is the
second gain value, and so on.
You can use the ss2sos and tf2sos functions from Signal Processing Toolbox software
to convert a state-space or transfer function description of your filter into the secondorder section description used by this block.
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4
Filter Analysis, Design, and Implementation
È b01
Íb
Í 02
Í M
Í
Îb0 M
b11
b12
M
b1 M
b21
b22
M
b2M
a01
a02
M
a0 M
a11
a12
M
a1M
a21 ˘
a22 ˙˙
M ˙
˙
a2M ˚
The block normalizes each row by a1i to ensure a value of 1 for the zero-delay
denominator coefficients.
4-142
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Analog Filter Design Block
Analog Filter Design Block
The Analog Filter Design block designs and implements analog IIR filters with standard
band configurations. All of the analog filter designs let you specify a filter order. The
other available parameters depend on the filter type and band configuration, as shown in
the following table.
Configuration
Butterworth
Chebyshev I
Chebyshev II
Elliptic
Lowpass
Ωp
Ωp, Rp
Ωs, Rs
Ωp, Rp, Rs
Highpass
Ωp
Ωp, Rp
Ωs, Rs
Ωp, Rp, Rs
Bandpass
Ωp1, Ωp2
Ωp1, Ωp2, Rp
Ωs1, Ωs2, Rs
Ωp1, Ωp2, Rp, Rs
Bandstop
Ωp1, Ωp2
Ωp1, Ωp2, Rp
Ωs1, Ωs2, Rs
Ωp1, Ωp2, Rp, Rs
The table parameters are
• Ωp — passband edge frequency
• Ωp1 — lower passband edge frequency
• Ωp2 — upper cutoff frequency
• Ωs — stopband edge frequency
• Ωs1 — lower stopband edge frequency
• Ωs2 — upper stopband edge frequency
• Rp — passband ripple in decibels
• Rs — stopband attenuation in decibels
For all of the analog filter designs, frequency parameters are in units of radians per
second.
The Analog Filter Design block uses a state-space filter representation, and applies the
filter using the State-Space block in the Simulink Continuous library. All of the design
methods use Signal Processing Toolbox functions to design the filter:
• The Butterworth design uses the toolbox function butter.
• The Chebyshev type I design uses the toolbox function cheby1.
• The Chebyshev type II design uses the toolbox function cheby2.
• The elliptic design uses the toolbox function ellip.
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4
Filter Analysis, Design, and Implementation
The Analog Filter Design block is built on the filter design capabilities of Signal
Processing Toolbox software.
Note: The Analog Filter Design block does not work with the Simulink discrete solver,
which is enabled when the Solver list is set to Discrete (no continuous states)
in the Solver pane of the Model Configuration Parameters dialog box. Select one of
the continuous solvers (such as ode4) instead.
4-144
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Removing High-Frequency Noise from an ECG Signal
Removing High-Frequency Noise from an ECG Signal
This examples shows you how to filter an ECG signal that has high-freqquency noise,
and remove the noise by low-pass filtering.
% Create one period of ECG signal
x = ecg(500).';
y = sgolayfilt(x,0,5);
Fs = 1000;
[M,N] = size(y);
% Initialize scopes
TS = dsp.TimeScope('SampleRate',Fs,...
'TimeSpan',1.5,...
'YLimits',[-1 1],...
'ShowGrid',true,...
'NumInputPorts',2,...
'LayoutDimensions',[2 1],...
'Title','Noisy and Filtered Signals');
% Design lowpass filter
Fpass = 200;
Fstop = 400;
Dpass = 0.05;
Dstop = 0.0001;
F
= [0 Fpass Fstop Fs/2]/(Fs/2);
A
= [1 1
0
0];
D
= [Dpass Dstop];
b = firgr('minorder', F, A, D);
LP = dsp.FIRFilter('Numerator',b);
% Design Highpass Filter
Fstop = 200;
Fpass = 400;
Dstop = 0.0001;
Dpass = 0.05;
F = [0 Fstop Fpass Fs/2]/(Fs/2); % Frequency vector
A = [0 0
1
1]; % Amplitude vector
D = [Dstop
Dpass];
% Deviation (ripple) vector
b = firgr('minord', F, A, D);
HP = dsp.FIRFilter('Numerator', b);
% Stream
tic;
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4-145
4
Filter Analysis, Design, and Implementation
while toc < 30
x = .1 * randn(M,N);
highFreqNoise = step(HP,x);
noisySignal
= y + highFreqNoise;
filteredSignal = step(LP,noisySignal);
step(TS,noisySignal,filteredSignal);
end
% Finalize
release(TS)
4-146
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Removing High-Frequency Noise from an ECG Signal
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4-147
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‫‪4-148‬‬
5
Adaptive Filters
Learn how to design and implement adaptive filters.
• “Overview of Adaptive Filters and Applications” on page 5-2
• “Adaptive Filters in DSP System Toolbox Software” on page 5-9
• “LMS Adaptive Filters” on page 5-13
• “RLS Adaptive Filters” on page 5-32
• “Signal Enhancement Using LMS and Normalized LMS” on page 5-37
• “Adaptive Filters in Simulink” on page 5-46
• “Selected Bibliography” on page 5-60
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5
Adaptive Filters
Overview of Adaptive Filters and Applications
In this section...
“Introduction to Adaptive Filtering” on page 5-2
“Adaptive Filtering Methodology” on page 5-2
“Choosing an Adaptive Filter” on page 5-4
“System Identification” on page 5-5
“Inverse System Identification” on page 5-6
“Noise or Interference Cancellation” on page 5-7
“Prediction” on page 5-7
Introduction to Adaptive Filtering
Adaptive filtering involves the changing of filter parameters (coefficients) over time,
to adapt to changing signal characteristics. Over the past three decades, digital signal
processors have made great advances in increasing speed and complexity, and reducing
power consumption. As a result, real-time adaptive filtering algorithms are quickly
becoming practical and essential for the future of communications, both wired and
wireless.
For more detailed information about adaptive filters and adaptive filter theory, refer to
the books listed in the “Selected Bibliography” on page 5-60.
Adaptive Filtering Methodology
This section presents a brief description of how adaptive filters work and some of the
applications where they can be useful.
Adaptive filters self learn. As the signal into the filter continues, the adaptive filter
coefficients adjust themselves to achieve the desired result, such as identifying an
unknown filter or canceling noise in the input signal. In the figure below, the shaded box
represents the adaptive filter, comprising the adaptive filter and the adaptive recursive
least squares (RLS) algorithm.
5-2
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Overview of Adaptive Filters and Applications
Desired Signal
d(k)
Input Signal
x(k)
+
Output Signal
y(k)
Adaptive FIR or IIR Digital Filter
_
SUM
Error Signal
e(k)
text
RLS Adaptive Algorithm
Block Diagram That Defines the Inputs and Output of a Generic RLS Adaptive Filter
The next figure provides the general adaptive filter setup with inputs and outputs.
Desired Signal
d(k)
Input Signal
x(k)
+
Output Signal
y(k)
Adaptive FIR or IIR Digital Filter
_
SUM
Error Signal
e(k)
text
Adapting Algorithm
Block Diagram Defining General Adaptive Filter Algorithm Inputs and Outputs
DSP System Toolbox software includes adaptive filters of a broad range of forms, all of
which can be worthwhile for specific needs. Some of the common ones are:
• Adaptive filters based on least mean squares (LMS) techniques, such as
adaptfilt.lms, adaptfilt.filtxlms, and adaptfilt.nlms
• Adaptive filters based on recursive least squares (RLS) techniques. For example,
adaptfilt.rls and adaptfilt.swrls
• Adaptive filters based on sign-data (adaptfilt.sd), sign-error (adaptfilt.se), and
sign-sign (adaptfilt.ss) techniques
• Adaptive filters based on lattice filters. For example, adaptfilt.gal and
adaptfilt.lsl
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5-3
5
Adaptive Filters
• Adaptive filters that operate in the frequency domain, such as adaptfilt.fdaf and
adaptfilt.pbufdaf.
• Adaptive filters that operate in the transform domain. Two of these are the
adaptfilt.tdafdft and adaptfilt.tdafdct filters
An adaptive filter designs itself based on the characteristics of the input signal to the
filter and a signal that represents the desired behavior of the filter on its input.
Designing the filter does not require any other frequency response information or
specification. To define the self-learning process the filter uses, you select the adaptive
algorithm used to reduce the error between the output signal y(k) and the desired signal
d(k).
When the LMS performance criterion for e(k) has achieved its minimum value through
the iterations of the adapting algorithm, the adaptive filter is finished and its coefficients
have converged to a solution. Now the output from the adaptive filter matches closely the
desired signal d(k). When you change the input data characteristics, sometimes called
the filter environment, the filter adapts to the new environment by generating a new set
of coefficients for the new data. Notice that when e(k) goes to zero and remains there you
achieve perfect adaptation, the ideal result but not likely in the real world.
The adaptive filter functions in this toolbox implement the shaded portion of the figures,
replacing the adaptive algorithm with an appropriate technique. To use one of the
functions, you provide the input signal or signals and the initial values for the filter.
“Adaptive Filters in DSP System Toolbox Software” on page 5-9 offers details about
the algorithms available and the inputs required to use them in MATLAB.
Choosing an Adaptive Filter
Selecting the adaptive filter that best meets your needs requires careful consideration.
An exhaustive discussion of the criteria for selecting your approach is beyond the scope of
this User's Guide. However, a few guidelines can help you make your choice.
Two main considerations frame the decision — how you plan to use the filter and the
filter algorithm to use.
When you begin to develop an adaptive filter for your needs, most likely the primary
concern is whether using an adaptive filter is a cost-competitive approach to solving your
filtering needs. Generally many areas determine the suitability of adaptive filters (these
5-4
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Overview of Adaptive Filters and Applications
areas are common to most filtering and signal processing applications). Four such areas
are
• Filter consistency — Does your filter performance degrade when the filter coefficients
change slightly as a result of quantization, or you switch to fixed-point arithmetic?
Will excessive noise in the signal hurt the performance of your filter?
• Filter performance — Does your adaptive filter provide sufficient identification
accuracy or fidelity, or does the filter provide sufficient signal discrimination or noise
cancellation to meet your requirements?
• Tools — Do tools exist that make your filter development process easier? Better tools
can make it practical to use more complex adaptive algorithms.
• DSP requirements — Can your filter perform its job within the constraints of your
application? Does your processor have sufficient memory, throughput, and time to use
your proposed adaptive filtering approach? Can you trade memory for throughput: use
more memory to reduce the throughput requirements or use a faster signal processor?
Of the preceding considerations, characterizing filter consistency or robustness may be
the most difficult.
The simulations in DSP System Toolbox software offers a good first step in
developing and studying these issues. LMS algorithm filters provide both a relatively
straightforward filters to implement and sufficiently powerful tool for evaluating whether
adaptive filtering can be useful for your problem.
Additionally, starting with an LMS approach can form a solid baseline against which
you can study and compare the more complex adaptive filters available in the toolbox.
Finally, your development process should, at some time, test your algorithm and
adaptive filter with real data. For truly testing the value of your work there is no
substitute for actual data.
System Identification
One common adaptive filter application is to use adaptive filters to identify an unknown
system, such as the response of an unknown communications channel or the frequency
response of an auditorium, to pick fairly divergent applications. Other applications
include echo cancellation and channel identification.
In the figure, the unknown system is placed in parallel with the adaptive filter. This
layout represents just one of many possible structures. The shaded area contains the
adaptive filter system.
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5-5
5
Adaptive Filters
Unknown System
d(k)
+
y(k)
x(k)
Adaptive Filter
text
e(k)
_ SUM
Using an Adaptive Filter to Identify an Unknown System
Clearly, when e(k) is very small, the adaptive filter response is close to the response of
the unknown system. In this case the same input feeds both the adaptive filter and the
unknown. If, for example, the unknown system is a modem, the input often represents
white noise, and is a part of the sound you hear from your modem when you log in to your
Internet service provider.
Inverse System Identification
By placing the unknown system in series with your adaptive filter, your filter adapts to
become the inverse of the unknown system as e(k) becomes very small. As shown in the
figure the process requires a delay inserted in the desired signal d(k) path to keep the
data at the summation synchronized. Adding the delay keeps the system causal.
Determining an Inverse Response to an Unknown System
Including the delay to account for the delay caused by the unknown system prevents this
condition.
5-6
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Overview of Adaptive Filters and Applications
Plain old telephone systems (POTS) commonly use inverse system identification to
compensate for the copper transmission medium. When you send data or voice over
telephone lines, the copper wires behave like a filter, having a response that rolls off at
higher frequencies (or data rates) and having other anomalies as well.
Adding an adaptive filter that has a response that is the inverse of the wire response,
and configuring the filter to adapt in real time, lets the filter compensate for the rolloff
and anomalies, increasing the available frequency output range and data rate for the
telephone system.
Noise or Interference Cancellation
In noise cancellation, adaptive filters let you remove noise from a signal in real time.
Here, the desired signal, the one to clean up, combines noise and desired information. To
remove the noise, feed a signal n'(k) to the adaptive filter that represents noise that is
correlated to the noise to remove from the desired signal.
s(k) + n(k)
d(k)
+
n'(k)
y(k)
x(k)
Adaptive Filter
e(k)
_
SUM
Using an Adaptive Filter to Remove Noise from an Unknown System
So long as the input noise to the filter remains correlated to the unwanted noise
accompanying the desired signal, the adaptive filter adjusts its coefficients to reduce the
value of the difference between y(k) and d(k), removing the noise and resulting in a clean
signal in e(k). Notice that in this application, the error signal actually converges to the
input data signal, rather than converging to zero.
Prediction
Predicting signals requires that you make some key assumptions. Assume that the signal
is either steady or slowly varying over time, and periodic over time as well.
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5-7
5
Adaptive Filters
d(k)
+
x(k)
s(k)
Delay
y(k)
Adaptive Filter
e(k)
_
SUM
Predicting Future Values of a Periodic Signal
Accepting these assumptions, the adaptive filter must predict the future values of the
desired signal based on past values. When s(k) is periodic and the filter is long enough to
remember previous values, this structure with the delay in the input signal, can perform
the prediction. You might use this structure to remove a periodic signal from stochastic
noise signals.
Finally, notice that most systems of interest contain elements of more than one of the
four adaptive filter structures. Carefully reviewing the real structure may be required to
determine what the adaptive filter is adapting to.
Also, for clarity in the figures, the analog-to-digital (A/D) and digital-to-analog (D/A)
components do not appear. Since the adaptive filters are assumed to be digital in nature,
and many of the problems produce analog data, converting the input signals to and from
the analog domain is probably necessary.
5-8
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Adaptive Filters in DSP System Toolbox Software
Adaptive Filters in DSP System Toolbox Software
In this section...
“Overview of Adaptive Filtering in DSP System Toolbox Software” on page 5-9
“Algorithms” on page 5-9
“Using Adaptive Filter Objects” on page 5-12
Overview of Adaptive Filtering in DSP System Toolbox Software
DSP System Toolbox software contains many objects for constructing and applying
adaptive filters to data. As you see in the tables in the next section, the objects use
various algorithms to determine the weights for the filter coefficients of the adapting
filter. While the algorithms differ in their detail implementations, the LMS and RLS
share a common operational approach — minimizing the error between the filter output
and the desired signal.
Algorithms
For adaptive filter (adaptfilt) objects, the algorithm string determines which
adaptive filter algorithm your adaptfilt object implements. Each available algorithm
entry appears in one of the tables along with a brief description of the algorithm. Click on
the algorithm in the first column to get more information about the associated adaptive
filter technique.
• LMS based adaptive filters
• RLS based adaptive filters
• Affine projection adaptive filters
• Adaptive filters in the frequency domain
• Lattice based adaptive filters
Least Mean Squares (LMS) Based FIR Adaptive Filters
Adaptive Filter Method
Adapting Algorithm Used to Generate Filter Coefficients During
Adaptation
adaptfilt.adjlms
Adjoint LMS FIR adaptive filter algorithm
adaptfilt.blms
Block LMS FIR adaptive filter algorithm
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5-9
5
Adaptive Filters
Adaptive Filter Method
Adapting Algorithm Used to Generate Filter Coefficients During
Adaptation
adaptfilt.blmsfft
FFT-based Block LMS FIR adaptive filter algorithm
adaptfilt.dlms
Delayed LMS FIR adaptive filter algorithm
adaptfilt.filtxlms
Filtered-x LMS FIR adaptive filter algorithm
adaptfilt.lms
LMS FIR adaptive filter algorithm
adaptfilt.nlms
Normalized LMS FIR adaptive filter algorithm
adaptfilt.sd
Sign-data LMS FIR adaptive filter algorithm
adaptfilt.se
Sign-error LMS FIR adaptive filter algorithm
adaptfilt.ss
Sign-sign LMS FIR adaptive filter algorithm
For further information about an adapting algorithm, refer to the reference page for the
algorithm.
Recursive Least Squares (RLS) Based FIR Adaptive Filters
Adaptive Filter Method
Adapting Algorithm Used to Generate Filter Coefficients During
Adaptation
adaptfilt.ftf
Fast transversal least-squares adaptation algorithm
adaptfilt.qrdrls
QR-decomposition RLS adaptation algorithm
adaptfilt.hrls
Householder RLS adaptation algorithm
adaptfilt.hswrls
Householder SWRLS adaptation algorithm
adaptfilt.rls
Recursive-least squares (RLS) adaptation algorithm
adaptfilt.swrls
Sliding window (SW) RLS adaptation algorithm
adaptfilt.swftf
Sliding window FTF adaptation algorithm
For more complete information about an adapting algorithm, refer to the reference page
for the algorithm.
Affine Projection (AP) FIR Adaptive Filters
5-10
Adaptive Filter Method
Adapting Algorithm Used to Generate Filter Coefficients During
Adaptation
adaptfilt.ap
Affine projection algorithm that uses direct matrix inversion
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Adaptive Filters in DSP System Toolbox Software
Adaptive Filter Method
Adapting Algorithm Used to Generate Filter Coefficients During
Adaptation
adaptfilt.apru
Affine projection algorithm that uses recursive matrix updating
adaptfilt.bap
Block affine projection adaptation algorithm
To find more information about an adapting algorithm, refer to the reference page for the
algorithm.
FIR Adaptive Filters in the Frequency Domain (FD)
Adaptive Filter Method
Description of the Adapting Algorithm Used to Generate Filter
Coefficients During Adaptation
adaptfilt.fdaf
Frequency domain adaptation algorithm
adaptfilt.pbfdaf
Partition block version of the FDAF algorithm
adaptfilt.pbufdaf
Partition block unconstrained version of the FDAF
algorithm
adaptfilt.tdafdct
Transform domain adaptation algorithm using DCT
adaptfilt.tdafdft
Transform domain adaptation algorithm using DFT
adaptfilt.ufdaf
Unconstrained FDAF algorithm for adaptation
For more information about an adapting algorithm, refer to the reference page for the
algorithm.
Lattice-Based (L) FIR Adaptive Filters
Adaptive Filter Method
Description of the Adapting Algorithm Used to Generate Filter
Coefficients During Adaptation
adaptfilt.gal
Gradient adaptive lattice filter adaptation algorithm
adaptfilt.lsl
Least squares lattice adaptation algorithm
adaptfilt.qrdlsl
QR decomposition RLS adaptation algorithm
For more information about an adapting algorithm, refer to the reference page for the
algorithm.
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5-11
5
Adaptive Filters
Presenting a detailed derivation of the Wiener-Hopf equation and determining solutions
to it is beyond the scope of this User's Guide. Full descriptions of the theory appear in the
adaptive filter references provided in the “Selected Bibliography” on page 5-60.
Using Adaptive Filter Objects
After you construct an adaptive filter object, how do you apply it to your data or system?
Like quantizer objects, adaptive filter objects have a filter method that you use to
apply the adaptfilt object to data. In the following sections, various examples of using
LMS and RLS adaptive filters show you how filter works with the objects to apply
them to data.
• “LMS Adaptive Filters” on page 5-13
• “RLS Adaptive Filters” on page 5-32
5-12
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LMS Adaptive Filters
LMS Adaptive Filters
In this section...
“LMS Methods for adaptfilt Objects” on page 5-13
“System Identification Using adaptfilt.lms” on page 5-15
“System Identification Using adaptfilt.nlms” on page 5-18
“Noise Cancellation Using adaptfilt.sd” on page 5-20
“Noise Cancellation Using adaptfilt.se” on page 5-23
“Noise Cancellation Using adaptfilt.ss” on page 5-27
LMS Methods for adaptfilt Objects
This section provides introductory examples using some of the least mean squares (LMS)
adaptive filter functions in the toolbox.
The toolbox provides many adaptive filter design functions that use the LMS algorithms
to search for the optimal solution to the adaptive filter, including
• adaptfilt.lms — Implement the LMS algorithm to solve the Wiener-Hopf equation
and find the filter coefficients for an adaptive filter.
• adaptfilt.nlms — Implement the normalized variation of the LMS algorithm to
solve the Wiener-Hopf equation and determine the filter coefficients of an adaptive
filter.
• adaptfilt.sd — Implement the sign-data variation of the LMS algorithm to solve
the Wiener-Hopf equation and determine the filter coefficients of an adaptive filter.
The correction to the filter weights at each iteration depends on the sign of the input
x(k).
• adaptfilt.se — Implement the sign-error variation of the LMS algorithm to solve
the Wiener-Hopf equation and determine the filter coefficients of an adaptive filter.
The correction applied to the current filter weights for each successive iteration
depends on the sign of the error, e(k).
• adaptfilt.ss — Implement the sign-sign variation of the LMS algorithm to solve
the Wiener-Hopf equation and determine the filter coefficients of an adaptive filter.
The correction applied to the current filter weights for each successive iteration
depends on both the sign of x(k) and the sign of e(k).
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5-13
5
Adaptive Filters
To demonstrate the differences and similarities among the various LMS algorithms
supplied in the toolbox, the LMS and NLMS adaptive filter examples use the same filter
for the unknown system. The unknown filter is the constrained lowpass filter from firgr
and fircband examples.
[b,err,res]=firgr(12,[0 0.4 0.5 1], [1 1 0 0], [1 0.2],...
{'w' 'c'});
From the figure you see that the filter is indeed lowpass and constrained to 0.2 ripple
in the stopband. With this as the baseline, the adaptive LMS filter examples use the
adaptive LMS algorithms and their initialization functions to identify this filter in a
system identification role.
To review the general model for system ID mode, look at “System Identification” on page
5-5 for the layout.
For the sign variations of the LMS algorithm, the examples use noise cancellation as the
demonstration application, as opposed to the system identification application used in
the LMS examples.
5-14
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LMS Adaptive Filters
System Identification Using adaptfilt.lms
To use the adaptive filter functions in the toolbox you need to provide three things:
• The adaptive LMS function to use. This example uses the LMS adaptive filter
function adaptfilt.lms.
• An unknown system or process to adapt to. In this example, the filter designed by
firgr is the unknown system.
• Appropriate input data to exercise the adaptation process. In terms of the generic
LMS model, these are the desired signal d(k) and the input signal x(k).
Start by defining an input signal x.
x = 0.1*randn(1,250);
The input is broadband noise. For the unknown system filter, use firgr to create a
twelfth-order lowpass filter:
[b,err,res] = fircband(12,[0 0.4 0.5 1],[1 1 0 0],[1 0.2],{'w','c'});
Although you do not need them here, include the err and res output arguments.
Now filter the signal through the unknown system to get the desired signal.
d = filter(b,1,x);
With the unknown filter designed and the desired signal in place you construct and apply
the adaptive LMS filter object to identify the unknown.
Preparing the adaptive filter object requires that you provide starting values for
estimates of the filter coefficients and the LMS step size. You could start with estimated
coefficients of some set of nonzero values; this example uses zeros for the 12 initial filter
weights.
For the step size, 0.8 is a reasonable value — a good compromise between being large
enough to converge well within the 250 iterations (250 input sample points) and small
enough to create an accurate estimate of the unknown filter.
mu = 0.8;
ha = adaptfilt.lms(13,mu);
Finally, using the adaptfilt object ha, desired signal, d, and the input to the filter, x,
run the adaptive filter to determine the unknown system and plot the results, comparing
the actual coefficients from firgr to the coefficients found by adaptfilt.lms.
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5-15
5
Adaptive Filters
[y,e] = filter(ha,x,d);
stem([b.' ha.coefficients.'])
title('System Identification by Adaptive LMS Algorithm')
legend('Actual Filter Weights', 'Estimated Filter Weights',...
'Location', 'NorthEast')
In the stem plot the actual and estimated filter weights are the same. As an experiment,
try changing the step size to 0.2. Repeating the example with mu = 0.2 results in the
following stem plot. The estimated weights fail to approximate the actual weights closely.
5-16
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LMS Adaptive Filters
Since this may be because you did not iterate over the LMS algorithm enough times, try
using 1000 samples. With 1000 samples, the stem plot, shown in the next figure, looks
much better, albeit at the expense of much more computation. Clearly you should take
care to select the step size with both the computation required and the fidelity of the
estimated filter in mind.
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5-17
5
Adaptive Filters
System Identification Using adaptfilt.nlms
To improve the convergence performance of the LMS algorithm, the normalized variant
(NLMS) uses an adaptive step size based on the signal power. As the input signal power
changes, the algorithm calculates the input power and adjusts the step size to maintain
an appropriate value. Thus the step size changes with time.
As a result, the normalized algorithm converges more quickly with fewer samples in
many cases. For input signals that change slowly over time, the normalized LMS can
represent a more efficient LMS approach.
In the adaptfilt.nlms example, you used firgr to create the filter that you
would identify. So you can compare the results, you use the same filter, and replace
adaptfilt.lms with adaptfilt.nlms, to use the normalized LMS algorithm
variation. You should see better convergence with similar fidelity.
First, generate the input signal and the unknown filter.
x = 0.1*randn(1,500);
[b,err,res] = fircband(12,[0 0.4 0.5 1], [1 1 0 0], [1 0.2],...
{'w' 'c'});
d = filter(b,1,x);
Again d represents the desired signal d(x) as you defined it earlier and b contains the
filter coefficients for your unknown filter.
mu = 0.8;
ha = adaptfilt.nlms(13,mu);
You use the preceding code to initialize the normalized LMS algorithm. For more
information about the optional input arguments, refer to adaptfilt.nlms in the
reference section of this User's Guide.
Running the system identification process is a matter of using adaptfilt.nlms with
the desired signal, the input signal, and the initial filter coefficients and conditions
specified in s as input arguments. Then plot the results to compare the adapted filter to
the actual filter.
[y,e] = filter(ha,x,d);
stem([b.' ha.coefficients.'])
title('System Identification by Normalized LMS Algorithm')
legend('Actual Filter Weights', 'Estimated Filter Weights',...
5-18
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LMS Adaptive Filters
'Location', 'NorthEast')
As shown in the following stem plot (a convenient way to compare the estimated and
actual filter coefficients), the two are nearly identical.
If you compare the convergence performance of the regular LMS algorithm to the
normalized LMS variant, you see the normalized version adapts in far fewer iterations to
a result almost as good as the nonnormalized version.
plot(e);
title('Comparing the LMS and NLMS Conversion Performance');
legend('NLMS Derived Filter Weights', ...
'LMS Derived Filter Weights', 'Location', 'NorthEast');
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5-19
5
Adaptive Filters
Noise Cancellation Using adaptfilt.sd
When the amount of computation required to derive an adaptive filter drives your
development process, the sign-data variant of the LMS (SDLMS) algorithm may be a
very good choice as demonstrated in this example.
Fortunately, the current state of digital signal processor (DSP) design has relaxed
the need to minimize the operations count by making DSPs whose multiply and shift
operations are as fast as add operations. Thus some of the impetus for the sign-data
algorithm (and the sign-error and sign-sign variations) has been lost to DSP technology
improvements.
In the standard and normalized variations of the LMS adaptive filter, coefficients for
the adapting filter arise from the mean square error between the desired signal and the
output signal from the unknown system. Using the sign-data algorithm changes the
mean square error calculation by using the sign of the input data to change the filter
coefficients.
When the error is positive, the new coefficients are the previous coefficients plus the
error multiplied by the step size µ. If the error is negative, the new coefficients are again
the previous coefficients minus the error multiplied by µ — note the sign change.
When the input is zero, the new coefficients are the same as the previous set.
5-20
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LMS Adaptive Filters
In vector form, the sign-data LMS algorithm is
w( k + 1) = w( k) + m e( k)sgn [ x( k) ] ,
1, x( k) > 0

sgn [ x( k)] =  0, x( k) = 0
 −1, x( k) < 0

with vector w containing the weights applied to the filter coefficients and vector x
containing the input data. e(k) (equal to desired signal - filtered signal) is the error at
time k and is the quantity the SDLMS algorithm seeks to minimize. µ (mu) is the step
size.
As you specify mu smaller, the correction to the filter weights gets smaller for each
sample and the SDLMS error falls more slowly. Larger mu changes the weights more for
each step so the error falls more rapidly, but the resulting error does not approach the
ideal solution as closely. To ensure good convergence rate and stability, select mu within
the following practical bounds
0<m<
1
N { InputSignalPower}
where N is the number of samples in the signal. Also, define mu as a power of two for
efficient computing.
Note How you set the initial conditions of the sign-data algorithm profoundly influences
the effectiveness of the adaptation. Because the algorithm essentially quantizes the input
signal, the algorithm can become unstable easily.
A series of large input values, coupled with the quantization process may result in the
error growing beyond all bounds. You restrain the tendency of the sign-data algorithm to
get out of control by choosing a small step size (µ<< 1) and setting the initial conditions
for the algorithm to nonzero positive and negative values.
In this noise cancellation example, adaptfilt.sd requires two input data sets:
• Data containing a signal corrupted by noise. In Using an Adaptive Filter to
Remove Noise from an Unknown System, this is d(k), the desired signal. The noise
cancellation process removes the noise, leaving the signal.
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5-21
5
Adaptive Filters
• Data containing random noise (x(k) in Using an Adaptive Filter to Remove Noise
from an Unknown System) that is correlated with the noise that corrupts the signal
data. Without the correlation between the noise data, the adapting algorithm cannot
remove the noise from the signal.
For the signal, use a sine wave. Note that signal is a column vector of 1000 elements.
signal = sin(2*pi*0.055*[0:1000-1]');
Now, add correlated white noise to signal. To ensure that the noise is correlated, pass
the noise through a lowpass FIR filter, and then add the filtered noise to the signal.
noise=randn(1,1000);
nfilt=fir1(11,0.4); % Eleventh order lowpass filter
fnoise=filter(nfilt,1,noise); % Correlated noise data
d=signal.'+fnoise;
fnoise is the correlated noise and d is now the desired input to the sign-data algorithm.
To prepare the adaptfilt object for processing, set the input conditions coeffs and
mu for the object. As noted earlier in this section, the values you set for coeffs and mu
determine whether the adaptive filter can remove the noise from the signal path.
In “System Identification Using adaptfilt.lms” on page 5-15, you constructed a
default filter that sets the filter coefficients to zeros. In most cases that approach does
not work for the sign-data algorithm. The closer you set your initial filter coefficients to
the expected values, the more likely it is that the algorithm remains well behaved and
converges to a filter solution that removes the noise effectively.
For this example, start with the coefficients in the filter you used to filter the noise
(nfilt), and modify them slightly so the algorithm has to adapt.
coeffs = nfilt.' -0.01; % Set the filter initial conditions.
mu = 0.05;
% Set the step size for algorithm updating.
With the required input arguments for adaptfilt.sd prepared, construct the
adaptfilt object, run the adaptation, and view the results.
ha = adaptfilt.sd(12,mu)
set(ha,'coefficients',coeffs);
[y,e] = filter(ha,noise,d);
plot(0:199,signal(1:200),0:199,e(1:200));
title('Noise Cancellation by the Sign-Data Algorithm');
5-22
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LMS Adaptive Filters
legend('Actual Signal', 'Result of Noise Cancellation',...
'Location', 'NorthEast');
When adaptfilt.sd runs, it uses far fewer multiply operations than either of the
LMS algorithms. Also, performing the sign-data adaptation requires only bit shifting
multiplies when the step size is a power of two.
Although the performance of the sign-data algorithm as shown in the next figure is quite
good, the sign-data algorithm is much less stable than the standard LMS variations. In
this noise cancellation example, the signal after processing is a very good match to the
input signal, but the algorithm could very easily grow without bound rather than achieve
good performance.
Changing coeffs, mu, or even the lowpass filter you used to create the correlated noise
can cause noise cancellation to fail and the algorithm to become useless.
Noise Cancellation Using adaptfilt.se
In some cases, the sign-error variant of the LMS algorithm (SELMS) may be a very good
choice for an adaptive filter application.
In the standard and normalized variations of the LMS adaptive filter, the coefficients
for the adapting filter arise from calculating the mean square error between the desired
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5-23
5
Adaptive Filters
signal and the output signal from the unknown system, and applying the result to the
current filter coefficients. Using the sign-error algorithm replaces the mean square error
calculation by using the sign of the error to modify the filter coefficients.
When the error is positive, the new coefficients are the previous coefficients plus the
error multiplied by the step size µ. If the error is negative, the new coefficients are again
the previous coefficients minus the error multiplied by µ — note the sign change. When
the input is zero, the new coefficients are the same as the previous set.
In vector form, the sign-error LMS algorithm is
w( k + 1) = w( k) + m sgn [ e( k)][ x(k) ] ,
1, e( k) > 0 


sgn [ e(k) ] =  0, e( k) = 0 
 −1, e(k) < 0 


with vector w containing the weights applied to the filter coefficients and vector x
containing the input data. e(k) (equal to desired signal - filtered signal) is the error at
time k and is the quantity the SELMS algorithm seeks to minimize. µ (mu) is the step
size. As you specify mu smaller, the correction to the filter weights gets smaller for each
sample and the SELMS error falls more slowly.
Larger mu changes the weights more for each step so the error falls more rapidly, but
the resulting error does not approach the ideal solution as closely. To ensure good
convergence rate and stability, select mu within the following practical bounds
0<m<
1
N { InputSignalPower}
where N is the number of samples in the signal. Also, define mu as a power of two for
efficient computation.
Note How you set the initial conditions of the sign-data algorithm profoundly influences
the effectiveness of the adaptation. Because the algorithm essentially quantizes the error
signal, the algorithm can become unstable easily.
A series of large error values, coupled with the quantization process may result in the
error growing beyond all bounds. You restrain the tendency of the sign-error algorithm to
5-24
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LMS Adaptive Filters
get out of control by choosing a small step size (µ<< 1) and setting the initial conditions
for the algorithm to nonzero positive and negative values.
In this noise cancellation example, adaptfilt.se requires two input data sets:
• Data containing a signal corrupted by noise. In Using an Adaptive Filter to
Remove Noise from an Unknown System, this is d(k), the desired signal. The noise
cancellation process removes the noise, leaving the signal.
• Data containing random noise (x(k) in Using an Adaptive Filter to Remove Noise
from an Unknown System) that is correlated with the noise that corrupts the signal
data. Without the correlation between the noise data, the adapting algorithm cannot
remove the noise from the signal.
For the signal, use a sine wave. Note that signal is a column vector of 1000 elements.
signal = sin(2*pi*0.055*[0:1000-1]');
Now, add correlated white noise to signal. To ensure that the noise is correlated, pass
the noise through a lowpass FIR filter, then add the filtered noise to the signal.
noise=randn(1,1000);
nfilt=fir1(11,0.4); % Eleventh order lowpass filter.
fnoise=filter(nfilt,1,noise); % Correlated noise data.
d=signal.'+fnoise;
fnoise is the correlated noise and d is now the desired input to the sign-data algorithm.
To prepare the adaptfilt object for processing, set the input conditions coeffs and
mu for the object. As noted earlier in this section, the values you set for coeffs and mu
determine whether the adaptive filter can remove the noise from the signal path. In
“System Identification Using adaptfilt.lms” on page 5-15, you constructed a default
filter that sets the filter coefficients to zeros.
Setting the coefficients to zero often does not work for the sign-error algorithm. The
closer you set your initial filter coefficients to the expected values, the more likely it is
that the algorithm remains well behaved and converges to a filter solution that removes
the noise effectively.
For this example, you start with the coefficients in the filter you used to filter the noise
(nfilt), and modify them slightly so the algorithm has to adapt.
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5
Adaptive Filters
coeffs = nfilt.' -0.01; % Set the filter initial conditions.
mu = 0.05;
% Set step size for algorithm update.
With the required input arguments for adaptfilt.se prepared, run the adaptation and
view the results.
ha = adaptfilt.se(12,mu)
set(ha,'coefficients',coeffs);
set(ha,'persistentmemory',true); % Prevent filter reset.
[y,e] = filter(ha,noise,d);
plot(0:199,signal(1:200),0:199,e(1:200));
title('Noise Cancellation Performance by the Sign-Error LMS Algorithm');
legend('Actual Signal','Error After Noise Reduction',...
'Location','NorthEast')
Notice that you have to set the property PersistentMemory to true when you
manually change the settings of object ha.
If PersistentMemory is left to false, the default, when you try to apply ha with the
method filter, the filtering process starts by resetting the object properties to their
initial conditions at construction. To preserve the customized coefficients in this example,
you set PersistentMemory to true so the coefficients do not get reset automatically
back to zero.
When adaptfilt.se runs, it uses far fewer multiply operations than either of the
LMS algorithms. Also, performing the sign-error adaptation requires only bit shifting
multiplies when the step size is a power of two.
Although the performance of the sign-data algorithm as shown in the next figure is quite
good, the sign-data algorithm is much less stable than the standard LMS variations. In
this noise cancellation example, the signal after processing is a very good match to the
input signal, but the algorithm could very easily become unstable rather than achieve
good performance.
Changing coeffs, mu, or even the lowpass filter you used to create the correlated noise
can cause noise cancellation to fail and the algorithm to become useless.
5-26
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LMS Adaptive Filters
Noise Cancellation Using adaptfilt.ss
One more example of a variation of the LMS algorithm in the toolbox is the sign-sign
variant (SSLMS). The rationale for this version matches those for the sign-data and
sign-error algorithms presented in preceding sections. For more details, refer to “Noise
Cancellation Using adaptfilt.sd” on page 5-20.
The sign-sign algorithm (SSLMS) replaces the mean square error calculation with using
the sign of the input data to change the filter coefficients. When the error is positive, the
new coefficients are the previous coefficients plus the error multiplied by the step size µ.
If the error is negative, the new coefficients are again the previous coefficients minus the
error multiplied by µ — note the sign change. When the input is zero, the new coefficients
are the same as the previous set.
In essence, the algorithm quantizes both the error and the input by applying the sign
operator to them.
In vector form, the sign-sign LMS algorithm is
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5
Adaptive Filters
w( k + 1) = w( k) + m sgn [ e( k)] sgn [ x( k) ] ,
1, z(k) > 0

sgn [ z( k) ] =  0, z( k) = 0
 − 1, z( k) < 0

where
z( k) = [ e(k) ] sgn [ x( k)]
Vector w contains the weights applied to the filter coefficients and vector x contains
the input data. e(k) ( = desired signal - filtered signal) is the error at time k and is the
quantity the SSLMS algorithm seeks to minimize. µ(mu) is the step size. As you specify
mu smaller, the correction to the filter weights gets smaller for each sample and the
SSLMS error falls more slowly.
Larger mu changes the weights more for each step so the error falls more rapidly, but
the resulting error does not approach the ideal solution as closely. To ensure good
convergence rate and stability, select mu within the following practical bounds
0<m<
1
N { InputSignalPower}
where N is the number of samples in the signal. Also, define mu as a power of two for
efficient computation.
Note How you set the initial conditions of the sign-sign algorithm profoundly influences
the effectiveness of the adaptation. Because the algorithm essentially quantizes the input
signal and the error signal, the algorithm can become unstable easily.
A series of large error values, coupled with the quantization process may result in the
error growing beyond all bounds. You restrain the tendency of the sign-sign algorithm to
get out of control by choosing a small step size (µ<< 1) and setting the initial conditions
for the algorithm to nonzero positive and negative values.
In this noise cancellation example, adaptfilt.ss requires two input data sets:
• Data containing a signal corrupted by noise. In Using an Adaptive Filter to
Remove Noise from an Unknown System, this is d(k), the desired signal. The noise
5-28
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LMS Adaptive Filters
cancellation process removes the noise, leaving the cleaned signal as the content of
the error signal.
• Data containing random noise (x(k) in Using an Adaptive Filter to Remove Noise from
an Unknown System) that is correlated with the noise that corrupts the signal data,
called. Without the correlation between the noise data, the adapting algorithm cannot
remove the noise from the signal.
For the signal, use a sine wave. Note that signal is a column vector of 1000 elements.
signal = sin(2*pi*0.055*[0:1000-1]');
Now, add correlated white noise to signal. To ensure that the noise is correlated, pass
the noise through a lowpass FIR filter, then add the filtered noise to the signal.
noise=randn(1,1000);
nfilt=fir1(11,0.4); % Eleventh order lowpass filter
fnoise=filter(nfilt,1,noise); % Correlated noise data
d=signal.'+fnoise;
fnoise is the correlated noise and d is now the desired input to the sign-data algorithm.
To prepare the adaptfilt object for processing, set the input conditions coeffs and
mu for the object. As noted earlier in this section, the values you set for coeffs and mu
determine whether the adaptive filter can remove the noise from the signal path. In
“System Identification Using adaptfilt.lms” on page 5-15, you constructed a default
filter that sets the filter coefficients to zeros. Usually that approach does not work for the
sign-sign algorithm.
The closer you set your initial filter coefficients to the expected values, the more likely
it is that the algorithm remains well behaved and converges to a filter solution that
removes the noise effectively. For this example, you start with the coefficients in the
filter you used to filter the noise (nfilt), and modify them slightly so the algorithm has
to adapt.
coeffs = nfilt.' -0.01; % Set the filter initial conditions.
mu = 0.05;
% Set the step size for algorithm updating.
With the required input arguments for adaptfilt.ss prepared, run the adaptation and
view the results.
ha = adaptfilt.ss(12,mu)
set(ha,'coefficients',coeffs);
set(ha,'persistentmemory',true); % Prevent filter reset.
[y,e] = filter(ha,noise,d);
plot(0:199,signal(1:200),0:199,e(1:200));
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5-29
5
Adaptive Filters
title('Noise Cancellation Performance of the Sign-Sign LMS Algorithm');
legend('Actual Signal', 'Error After Noise Reduction', ...
'Location', 'NorthEast');
Notice that you have to set the property PersistentMemory to true when you
manually change the settings of object ha.
If PersistentMemory is left to false, when you try to apply ha with the method
filter the filtering process starts by resetting the object properties to their initial
conditions at construction. To preserve the customized coefficients in this example, you
set PersistentMemory to true so the coefficients do not get reset automatically back to
zero.
When adaptfilt.ss runs, it uses far fewer multiply operations than either of the
LMS algorithms. Also, performing the sign-sign adaptation requires only bit shifting
multiplies when the step size is a power of two.
Although the performance of the sign-sign algorithm as shown in the next figure is quite
good, the sign-sign algorithm is much less stable than the standard LMS variations. In
this noise cancellation example, the signal after processing is a very good match to the
input signal, but the algorithm could very easily become unstable rather than achieve
good performance.
Changing coeffs, mu, or even the lowpass filter you used to create the correlated noise
can cause noise cancellation to fail and the algorithm to become useless.
5-30
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LMS Adaptive Filters
As an aside, the sign-sign LMS algorithm is part of the international CCITT standard for
32 Kb/s ADPCM telephony.
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5
Adaptive Filters
RLS Adaptive Filters
In this section...
“Compare RLS and LMS Adaptive Filter Algorithms” on page 5-32
“Inverse System Identification Using adaptfilt.rls” on page 5-33
Compare RLS and LMS Adaptive Filter Algorithms
This section provides an introductory example that uses the RLS adaptive filter function
adaptfilt.rls.
If LMS algorithms represent the simplest and most easily applied adaptive algorithms,
the recursive least squares (RLS) algorithms represents increased complexity,
computational cost, and fidelity. In performance, RLS approaches the Kalman filter in
adaptive filtering applications, at somewhat reduced required throughput in the signal
processor.
Compared to the LMS algorithm, the RLS approach offers faster convergence and
smaller error with respect to the unknown system, at the expense of requiring more
computations.
In contrast to the least mean squares algorithm, from which it can be derived, the RLS
adaptive algorithm minimizes the total squared error between the desired signal and the
output from the unknown system.
Note that the signal paths and identifications are the same whether the filter uses RLS
or LMS. The difference lies in the adapting portion.
Within limits, you can use any of the adaptive filter algorithms to solve an adaptive filter
problem by replacing the adaptive portion of the application with a new algorithm.
Examples of the sign variants of the LMS algorithms demonstrated this feature to
demonstrate the differences between the sign-data, sign-error, and sign-sign variations of
the LMS algorithm.
One interesting input option that applies to RLS algorithms is not present in the LMS
processes — a forgetting factor, λ, that determines how the algorithm treats past data
input to the algorithm.
5-32
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RLS Adaptive Filters
When the LMS algorithm looks at the error to minimize, it considers only the current
error value. In the RLS method, the error considered is the total error from the beginning
to the current data point.
Said another way, the RLS algorithm has infinite memory — all error data is given the
same consideration in the total error. In cases where the error value might come from a
spurious input data point or points, the forgetting factor lets the RLS algorithm reduce
the value of older error data by multiplying the old data by the forgetting factor.
Since 0 ≤λ< 1, applying the factor is equivalent to weighting the older error. When λ = 1,
all previous error is considered of equal weight in the total error.
As λ approaches zero, the past errors play a smaller role in the total. For example, when
λ = 0.9, the RLS algorithm multiplies an error value from 50 samples in the past by an
attenuation factor of 0.950 = 5.15 x 10-3, considerably deemphasizing the influence of the
past error on the current total error.
Inverse System Identification Using adaptfilt.rls
Rather than use a system identification application to demonstrate the RLS adaptive
algorithm, or a noise cancellation model, this example use the inverse system
identification model shown in here.
Unknown System
d(k)
+
y(k)
x(k)
Adaptive Filter
text
e(k)
_ SUM
Cascading the adaptive filter with the unknown filter causes the adaptive filter to
converge to a solution that is the inverse of the unknown system.
If the transfer function of the unknown is H(z) and the adaptive filter transfer function
is G(z), the error measured between the desired signal and the signal from the cascaded
system reaches its minimum when the product of H(z) and G(z) is 1, G(z)*H(z) = 1. For
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5-33
5
Adaptive Filters
this relation to be true, G(z) must equal 1/H(z), the inverse of the transfer function of the
unknown system.
To demonstrate that this is true, create a signal to input to the cascaded filter pair.
x = randn(1,3000);
In the cascaded filters case, the unknown filter results in a delay in the signal arriving at
the summation point after both filters. To prevent the adaptive filter from trying to adapt
to a signal it has not yet seen (equivalent to predicting the future), delay the desired
signal by 32 samples, the order of the unknown system.
Generally, you do not know the order of the system you are trying to identify. In that
case, delay the desired signal by the number of samples equal to half the order of the
adaptive filter. Delaying the input requires prepending 12 zero-values samples to x.
delay = zeros(1,12);
d = [delay x(1:2988)]; % Concatenate the delay and the signal.
You have to keep the desired signal vector d the same length as x, hence adjust the
signal element count to allow for the delay samples.
Although not generally true, for this example you know the order of the unknown filter,
so you add a delay equal to the order of the unknown filter.
For the unknown system, use a lowpass, 12th-order FIR filter.
ufilt = fir1(12,0.55,'low');
Filtering x provides the input data signal for the adaptive algorithm function.
xdata = filter(ufilt,1,x);
To set the input argument values for the adaptfilt.rls object, use the constructor
adaptfilt.rls, providing the needed arguments l, lambda, and invcov.
For more information about the input conditions to prepare the RLS algorithm object,
refer to adaptfilt.rls in the reference section of this user's guide.
p0 = 2*eye(13);
lambda = 0.99;
ha = adaptfilt.rls(13,lambda,p0);
Most of the process to this point is the same as the preceding examples. However, since
this example seeks to develop an inverse solution, you need to be careful about which
signal carries the data and which is the desired signal.
5-34
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RLS Adaptive Filters
Earlier examples of adaptive filters use the filtered noise as the desired signal. In this
case, the filtered noise (xdata) carries the unknown system information. With Gaussian
distribution and variance of 1, the unfiltered noise d is the desired signal. The code to
run this adaptive filter example is
[y,e] = filter(ha,xdata,d);
where y returns the coefficients of the adapted filter and e contains the error signal as
the filter adapts to find the inverse of the unknown system. You can review the returned
elements of the adapted filter in the properties of ha.
The next figure presents the results of the adaptation. In the figure, the magnitude
response curves for the unknown and adapted filters show. As a reminder, the unknown
filter was a lowpass filter with cutoff at 0.55, on the normalized frequency scale from 0 to
1.
Comparing the Inverse Filter to the Unknown System
Magnitude (dB)
50
0
−50
−100
Inverse Filter
Unknown System
−150
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Normalized Frequency (×π rad/sample)
0.8
0.9
1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Normalized Frequency (×π rad/sample)
0.8
0.9
1
0
Phase (degrees)
−200
−400
−600
−800
−1000
−1200
Viewed alone (refer to the following figure), the inverse system looks like a fair
compensator for the unknown lowpass filter — a high pass filter with linear phase.
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5-35
5
Adaptive Filters
Inverse Filter Resulting from RLS Adaptation
40
Magnitude (dB)
30
20
10
0
−10
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Normalized Frequency (×π rad/sample)
0.8
0.9
1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Normalized Frequency (×π rad/sample)
0.8
0.9
1
0
Phase (degrees)
−200
−400
−600
−800
−1000
−1200
5-36
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Signal Enhancement Using LMS and Normalized LMS
Signal Enhancement Using LMS and Normalized LMS
In this section...
“Create the Signals for Adaptation” on page 5-37
“Construct Two Adaptive Filters” on page 5-38
“Choose the Step Size” on page 5-38
“Set the Adapting Filter Step Size” on page 5-39
“Filter with the Adaptive Filters” on page 5-40
“Compute the Optimal Solution” on page 5-40
“Plot the Results” on page 5-40
“Compare the Final Coefficients” on page 5-42
“Reset the Filter Before Filtering” on page 5-43
“Investigate Convergence Through Learning Curves” on page 5-43
“Compute the Learning Curves” on page 5-44
“Compute the Theoretical Learning Curves” on page 5-45
This example illustrates one way to use a few of the adaptive filter algorithms provided
in the toolbox. In this example, a signal enhancement application is used as an
illustration. While there are about 30 different adaptive filtering algorithms included
with the toolbox, this example demonstrates two algorithms — least means square
(LMS), using adaptfilt.lms, and normalized LMS, using adaptfilt.nlms, for
adaptation.
Create the Signals for Adaptation
The goal is to use an adaptive filter to extract a desired signal from a noise-corrupted
signal by filtering out the noise. The desired signal (the output from the process) is a
sinusoid with 1000 samples.
n = (1:1000)';
s = sin(0.075*pi*n);
To perform adaptation requires two signals:
• a reference signal
• a noisy signal that contains both the desired signal and an added noise component.
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5-37
5
Adaptive Filters
Generate the Noise Signal
To create a noise signal, assume that the noise v1 is autoregressive, meaning that
the value of the noise at time t depends only on its previous values and on a random
disturbance.
v = 0.8*randn(1000,1); % Random noise part.
ar = [1,1/2];
% Autoregression coefficients.
v1 = filter(1,ar,v);
% Noise signal. Applies a 1-D digital
% filter.
Corrupt the Desired Signal to Create a Noisy Signal
To generate the noisy signal that contains both the desired signal and the noise, add the
noise signal v1 to the desired signal s. The noise-corrupted sinusoid x is
x = s + v1;
where s is the desired signal and the noise is v1. Adaptive filter processing seeks to
recover s from x by removing v1. To complete the signals needed to perform adaptive
filtering, the adaptation process requires a reference signal.
Create a Reference Signal
Define a moving average signal v2 that is correlated with v1. This v2 is the reference
signal for the examples.
ma = [1, -0.8, 0.4 , -0.2];
v2 = filter(ma,1,v);
Construct Two Adaptive Filters
Two similar adaptive filters — LMS and NLMS — form the basis of this example, both
sixth order. Set the order as a variable in MATLAB and create the filters.
L = 7;
hlms = adaptfilt.lms(7);
hnlms = adaptfilt.nlms(7);
Choose the Step Size
LMS-like algorithms have a step size that determines the amount of correction applied as
the filter adapts from one iteration to the next. Choosing the appropriate step size is not
always easy, usually requiring experience in adaptive filter design.
5-38
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Signal Enhancement Using LMS and Normalized LMS
• A step size that is too small increases the time for the filter to converge on a set of
coefficients. This becomes an issue of speed and accuracy.
• One that is too large may cause the adapting filter to diverge, never reaching
convergence. In this case, the issue is stability — the resulting filter might not be
stable.
As a rule of thumb, smaller step sizes improve the accuracy of the convergence of the
filter to match the characteristics of the unknown, at the expense of the time it takes to
adapt.
The toolbox includes an algorithm — maxstep — to determine the maximum step size
suitable for each LMS adaptive filter algorithm that still ensures that the filter converges
to a solution. Often, the notation for the step size is µ.
>> [mumaxlms,mumaxmselms]
= maxstep(hlms,x)
[mumaxnlms,mumaxmsenlms] = maxstep(hnlms);
Warning: Step size is not in the range 0 < mu < mumaxmse/2:
Erratic behavior might result.
> In adaptfilt.lms.maxstep at 32
mumaxlms =
0.2096
mumaxmselms =
0.1261
Set the Adapting Filter Step Size
The first output of maxstep is the value needed for the mean of the coefficients to
converge while the second is the value needed for the mean squared coefficients to
converge. Choosing a large step size often causes large variations from the convergence
values, so choose smaller step sizes generally.
hlms.StepSize = mumaxmselms/30;
% This can also be set graphically: inspect(hlms)
hnlms.StepSize = mumaxmsenlms/20;
% This can also be set graphically: inspect(hnlms)
If you know the step size to use, you can set the step size value with the step input
argument when you create your filter.
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5-39
5
Adaptive Filters
hlms = adaptfilt.lms(N,step); Adds the step input argument.
Filter with the Adaptive Filters
Now you have set up the parameters of the adaptive filters and you are ready to filter the
noisy signal. The reference signal, v2, is the input to the adaptive filters. x is the desired
signal in this configuration.
Through adaptation, y, the output of the filters, tries to emulate x as closely as possible.
Since v2 is correlated only with the noise component v1 of x, it can only really emulate
v1. The error signal (the desired x), minus the actual output y, constitutes an estimate of
the part of x that is not correlated with v2 — s, the signal to extract from x.
[ylms,elms] = filter(hlms,v2,x);
[ynlms,enlms] = filter(hnlms,v2,x);
Compute the Optimal Solution
For comparison, compute the optimal FIR Wiener filter.
bw = firwiener(L-1,v2,x); % Optimal FIR Wiener filter
yw = filter(bw,1,v2);
% Estimate of x using Wiener filter
ew = x - yw;
% Estimate of actual sinusoid
Plot the Results
Plot the resulting denoised sinusoid for each filter — the Wiener filter, the LMS adaptive
filter, and the NLMS adaptive filter — to compare the performance of the various
techniques.
plot(n(900:end),[ew(900:end), elms(900:end),enlms(900:end)]);
legend('Wiener filter denoised sinusoid',...
'LMS denoised sinusoid', 'NLMS denoised sinusoid');
xlabel('Time index (n)');
ylabel('Amplitude');
5-40
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Signal Enhancement Using LMS and Normalized LMS
As a reference point, include the noisy signal as a dotted line in the plot.
hold on
plot(n(900:end),x(900:end),'k:')
xlabel('Time index (n)');
ylabel('Amplitude');
hold off
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5-41
5
Adaptive Filters
Compare the Final Coefficients
Finally, compare the Wiener filter coefficients with the coefficients of the adaptive filters.
While adapting, the adaptive filters try to converge to the Wiener coefficients.
[bw.' hlms.Coefficients.' hnlms.Coefficients.']
ans =
1.0317
0.3555
0.1500
0.0848
0.1624
0.1079
0.0492
5-42
0.8879
0.1359
0.0036
0.0023
0.0810
0.0184
-0.0001
1.0712
0.4070
0.1539
0.0549
0.1098
0.0521
0.0041
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Signal Enhancement Using LMS and Normalized LMS
Reset the Filter Before Filtering
Adaptive filters have a PersistentMemory property that you can use to reproduce
experiments exactly. By default, the PersistentMemory is false. The states and the
coefficients of the filter are reset before filtering and the filter does not remember the
results from previous times you use the filter.
For instance, the following successive calls produce the same output when
PersistentMemory is false.
[ylms,elms] = filter(hlms,v2,x);
[ylms2,elms2] = filter(hlms,v2,x);
To keep the history of the filter when filtering a new set of data, enable persistent
memory for the filter by setting the PersistentMemory property to true. In this
configuration, the filter uses the final states and coefficients from the previous run as the
initial conditions for the next run and set of data.
[ylms,elms] = filter(hlms,v2,x);
hlms.PersistentMemory = true;
[ylms2,elms2] = filter(hlms,v2,x); % No longer the same
Setting the property value to true is useful when you are filtering large amounts of
data that you partition into smaller sets and then feed into the filter using a for-loop
construction.
Investigate Convergence Through Learning Curves
To analyze the convergence of the adaptive filters, look at the learning curves. The
toolbox provides methods to generate the learning curves, but you need more than one
iteration of the experiment to obtain significant results.
This demonstration uses 25 sample realizations of the noisy sinusoids.
n = (1:5000)';
s = sin(0.075*pi*n);
nr = 25;
v = 0.8*randn(5000,nr);
v1 = filter(1,ar,v);
x = repmat(s,1,nr) + v1;
v2 = filter(ma,1,v);
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Adaptive Filters
Compute the Learning Curves
Now compute the mean-square error. To speed things up, compute the error every 10
samples.
First, reset the adaptive filters to avoid using the coefficients it has already computed
and the states it has stored.
reset(hlms);
reset(hnlms);
M = 10; % Decimation factor
mselms = msesim(hlms,v2,x,M);
msenlms = msesim(hnlms,v2,x,M);
plot(1:M:n(end),[mselms,msenlms])
legend('LMS learning curve','NLMS learning curve')
xlabel('Time index (n)');
ylabel('MSE');
In the next plot you see the calculated learning curves for the LMS and NLMS adaptive
filters.
5-44
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Signal Enhancement Using LMS and Normalized LMS
Compute the Theoretical Learning Curves
For the LMS and NLMS algorithms, functions in the toolbox help you compute the
theoretical learning curves, along with the minimum mean-square error (MMSE) the
excess mean-square error (EMSE) and the mean value of the coefficients.
MATLAB may take some time to calculate the curves. The figure shown after the code
plots the predicted and actual LMS curves.
reset(hlms);
[mmselms,emselms,meanwlms,pmselms] = msepred(hlms,v2,x,M);
plot(1:M:n(end),[mmselms*ones(500,1),emselms*ones(500,1),...
pmselms,mselms])
legend('MMSE','EMSE','predicted LMS learning curve',...
'LMS learning curve')
xlabel('Time index (n)');
ylabel('MSE');
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Adaptive Filters
Adaptive Filters in Simulink
In this section...
“Create an Acoustic Environment in Simulink” on page 5-46
“LMS Filter Configuration for Adaptive Noise Cancellation” on page 5-48
“Modify Adaptive Filter Parameters During Model Simulation” on page 5-54
“Adaptive Filtering Examples” on page 5-59
Create an Acoustic Environment in Simulink
Adaptive filters are filters whose coefficients or weights change over time to adapt to
the statistics of a signal. They are used in a variety of fields including communications,
controls, radar, sonar, seismology, and biomedical engineering.
In this topic, you learn how to create an acoustic environment that simulates both white
noise and colored noise added to an input signal. You later use this environment to build
a model capable of adaptive noise cancellation using adaptive filtering:
1
At the MATLAB command line, type dspanc.
The DSP System Toolbox Acoustic Noise Cancellation example opens.
5-46
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Adaptive Filters in Simulink
2
Copy and paste the subsystem called Acoustic Environment into a new model.
3
Double-click the Acoustic Environment subsystem.
Gaussian noise is used to create the signal sent to the Exterior Mic output port. If
the input to the Filter port changes from 0 to 1, the Digital Filter block changes from
a lowpass filter to a bandpass filter. The filtered noise output from the Digital Filter
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Adaptive Filters
block is added to signal coming from a .wav file to produce the signal sent to the
Pilot's Mic output port.
You have now created an acoustic environment. In the following topics, you use this
acoustic environment to produce a model capable of adaptive noise cancellation.
LMS Filter Configuration for Adaptive Noise Cancellation
In the previous topic, “Create an Acoustic Environment in Simulink” on page 5-46,
you created a system that produced two output signals. The signal output at the Exterior
Mic port is composed of white noise. The signal output at the Pilot's Mic port is composed
of colored noise added to a signal from a .wav file. In this topic, you create an adaptive
filter to remove the noise from the Pilot's Mic signal. This topic assumes that you are
working on a Windows operating system:
1
If the model you created in “Create an Acoustic Environment in Simulink” on page
5-46 is not open on your desktop, you can open an equivalent model by typing
ex_adapt1_audio
at the MATLAB command prompt.
2
From the DSP System Toolbox Filtering library, and then from the Adaptive Filters
library, click-and-drag an LMS Filter block into the model that contains the Acoustic
Environment subsystem.
3
Double-click the LMS Filter block. Set the block parameters as follows, and then
click OK:
• Algorithm = Normalized LMS
• Filter length = 40
• Step size (mu) = 0.002
• Leakage factor (0 to 1) = 1
The block uses the normalized LMS algorithm to calculate the forty filter
coefficients. Setting the Leakage factor (0 to 1) parameter to 1 means that the
current filter coefficient values depend on the filter's initial conditions and all of the
previous input values.
4
5-48
Click-and-drag the following blocks into your model.
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Adaptive Filters in Simulink
5
Block
Library
Quantity
Constant
Simulink/Sources
2
Manual Switch
Simulink/Signal Routing
1
Terminator
Simulink/Sinks
1
Downsample
Signal Operations
1
To Audio Device
Sinks
1
Waterfall Scope
Sinks
1
Connect the blocks so that your model resembles the following figure.
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5-49
5
Adaptive Filters
5-50
6
Double-click the Constant block. Set the Constant value parameter to 0 and then
click OK.
7
Double-click the Downsample block. Set the Downsample factor, K parameter to
32. Click OK.
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Adaptive Filters in Simulink
The filter weights are being updated so often that there is very little change from one
update to the next. To see a more noticeable change, you need to downsample the
output from the Wts port.
8
Double-click the Waterfall Scope block. The Waterfall scope window opens.
9
Click the Scope parameters button.
The Parameters window opens.
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Adaptive Filters
10 Click the Axes tab. Set the parameters as follows:
• Y Min = -0.188
• Y Max = 0.179
11 Click the Data history tab. Set the parameters as follows:
• History traces = 50
• Data logging = All visible
12 Close the Parameters window leaving all other parameters at their default values.
You might need to adjust the axes in the Waterfall scope window in order to view
the plots.
13 Click the Fit to view button in the Waterfall scope window. Then, click-and-drag
the axes until they resemble the following figure.
5-52
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Adaptive Filters in Simulink
14 In the model window, from the Simulation menu, select Model Configuration
Parameters. In the Select pane, click Solver. Set the parameters as follows, and
then click OK:
• Stop time = inf
• Type = Fixed-step
• Solver = Discrete (no continuous states)
15 Run the simulation and view the results in the Waterfall scope window. You can
also listen to the simulation using the speakers attached to your computer.
16 Experiment with changing the Manual Switch so that the input to the Acoustic
Environment subsystem is either 0 or 1.
When the value is 0, the Gaussian noise in the signal is being filtered by a lowpass
filter. When the value is 1, the noise is being filtered by a bandpass filter. The
adaptive filter can remove the noise in both cases.
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5-53
5
Adaptive Filters
You have now created a model capable of adaptive noise cancellation. The adaptive filter
in your model is able to filter out both low frequency noise and noise within a frequency
range. In the next topic, “Modify Adaptive Filter Parameters During Model Simulation”
on page 5-54, you modify the LMS Filter block and change its parameters during
simulation.
Modify Adaptive Filter Parameters During Model Simulation
In the previous topic, “LMS Filter Configuration for Adaptive Noise Cancellation” on
page 5-48, you created an adaptive filter and used it to remove the noise generated
by the Acoustic Environment subsystem. In this topic, you modify the adaptive filter and
adjust its parameters during simulation. This topic assumes that you are working on a
Windows operating system:
1
If the model you created in “Create an Acoustic Environment in Simulink” on page
5-46 is not open on your desktop, you can open an equivalent model by typing
ex_adapt2_audio
at the MATLAB command prompt.
2
Double-click the LMS filter block. Set the block parameters as follows, and then click
OK:
• Specify step size via = Input port
• Initial value of filter weights = 0
• Select the Adapt port check box.
• Reset port = Non-zero sample
The Block Parameters: LMS Filter dialog box should now look similar to the
following figure.
5-54
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Adaptive Filters in Simulink
Step-size, Adapt, and Reset ports appear on the LMS Filter block.
3
Click-and-drag the following blocks into your model.
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5-55
5
Adaptive Filters
4
5-56
Block
Library
Quantity
Constant
Simulink/Sources
6
Manual Switch
Simulink/Signal Routing
3
Connect the blocks as shown in the following figure.
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Adaptive Filters in Simulink
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5-57
5
Adaptive Filters
5
Double-click the Constant2 block. Set the block parameters as follows, and then click
OK:
• Constant value = 0.002
• Select the Interpret vector parameters as 1-D check box.
• Sample time (-1 for inherited) = inf
• Output data type mode = Inherit via back propagation
6
Double-click the Constant3 block. Set the block parameters as follows, and then click
OK:
• Constant value = 0.04
• Select the Interpret vector parameters as 1-D check box.
• Sample time (-1 for inherited) = inf
• Output data type mode = Inherit via back propagation
7
Double-click the Constant4 block. Set the Constant value parameter to 0 and then
click OK.
8
Double-click the Constant6 block. Set the Constant value parameter to 0 and then
click OK.
9
In the model window, from the Display menu, point to Signals & Ports, and select
Wide Nonscalar Lines and Signal Dimensions.
10 Double-click Manual Switch2 so that the input to the Adapt port is 1.
11 Run the simulation and view the results in the Waterfall scope window. You can
also listen to the simulation using the speakers attached to your computer.
12 Double-click the Manual Switch block so that the input to the Acoustic Environment
subsystem is 1. Then, double-click Manual Switch2 so that the input to the Adapt
port to 0.
The filter weights displayed in the Waterfall scope window remain constant. When
the input to the Adapt port is 0, the filter weights are not updated.
13 Double-click Manual Switch2 so that the input to the Adapt port is 1.
The LMS Filter block updates the coefficients.
14 Connect the Manual Switch1 block to the Constant block that represents 0.002.
Then, change the input to the Acoustic Environment subsystem. Repeat this
procedure with the Constant block that represents 0.04.
5-58
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Adaptive Filters in Simulink
You can see that the system reaches steady state faster when the step size is larger.
15 Double-click the Manual Switch3 block so that the input to the Reset port is 1.
The block resets the filter weights to their initial values. In the Block Parameters:
LMS Filter dialog box, from the Reset port list, you chose Non-zero sample. This
means that any nonzero input to the Reset port triggers a reset operation.
You have now experimented with adaptive noise cancellation using the LMS Filter
block. You adjusted the parameters of your adaptive filter and viewed the effects of your
changes while the model was running.
For more information about adaptive filters, see the following block reference pages:
• LMS Filter
• RLS Filter
• Block LMS Filter
• Fast Block LMS Filter
Adaptive Filtering Examples
DSP System Toolbox software provides a collection of adaptive filtering examples that
illustrate typical applications of the adaptive filtering blocks, listed in the following table.
Adaptive Filtering Examples
Commands for Opening Examples in MATLAB
LMS Adaptive Equalization
lmsadeq
LMS Adaptive Time-Delay
Estimation
lmsadtde
Nonstationary Channel Estimation dspchanest
RLS Adaptive Noise Cancellation
rlsdemo
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5
Adaptive Filters
Selected Bibliography
[1] Hayes, Monson H., Statistical Digital Signal Processing and Modeling, John Wiley &
Sons, 1996, 493–552.
[2] Haykin, Simon, Adaptive Filter Theory, Prentice-Hall, Inc., 1996
5-60
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6
Multirate and Multistage Filters
Learn how to analyze, design, and implement multirate and multistage filters in
MATLAB and Simulink.
• “Multirate Filters” on page 6-2
• “Multistage Filters” on page 6-6
• “Example Case for Multirate/Multistage Filters” on page 6-7
• “Filter Banks” on page 6-11
• “Multirate Filtering in Simulink” on page 6-19
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6
Multirate and Multistage Filters
Multirate Filters
In this section...
“Why Are Multirate Filters Needed?” on page 6-2
“Overview of Multirate Filters” on page 6-2
Why Are Multirate Filters Needed?
Multirate filters can bring efficiency to a particular filter implementation. In general,
multirate filters are filters in which different parts of the filter operate at different rates.
The most obvious application of such a filter is when the input sample rate and output
sample rate need to differ (decimation or interpolation) — however, multirate filters are
also often used in designs where this is not the case. For example you may have a system
where the input sample rate and output sample rate are the same, but internally there is
decimation and interpolation occurring in a series of filters, such that the final output of
the system has the same sample rate as the input. Such a design may exhibit lower cost
than could be achieved with a single-rate filter for various reasons. For more information
about the relative cost benefit of using multirate filters, refer to [2] Harris, Fredric J.,
Multirate Signal Processing for Communication Systems, Prentice Hall PTR, 2004.
Overview of Multirate Filters
A filter that reduces the input rate is called a decimator. A filter that increases the input
rate is called an interpolator. To visualize this process, examine the following figure,
which illustrates the processes of interpolation and decimation in the time domain.
6-2
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Multirate Filters
If you start with the top signal, sampled at a frequency Fs, then the bottom signal is
sampled at Fs/2 frequency. In this case, the decimation factor, or M, is 2.
The following figure illustrates effect of decimation in the frequency domain.
In the first graphic in the figure you can see a signal that is critically sampled, i.e.
the sample rate is equal to two times the highest frequency component of the sampled
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6-3
6
Multirate and Multistage Filters
signal. As such the period of the signal in the frequency domain is no greater than
the bandwidth of the sampling frequency. When reduce the sampling frequency
(decimation), aliasing can occur, where the magnitudes at the frequencies near the
edges of the original period become indistinguishable, and the information about these
values becomes lost. To work around this problem, the signal can be filtered before the
decimation process, avoiding overlap of the signal spectra at Fs/2.
An analogous approach must be taken to avoid imaging when performing interpolation
on a sampled signal. For more information about the effects of decimation and
interpolation on a sampled signal, refer to any one of the references in the “Bibliography”
section of the DSP System Toolbox User Guide.
The following list summarizes some guidelines and general requirements regarding
decimation and interpolation:
• By the Nyquist Theorem, for band-limited signals, the sampling frequency must be at
least twice the bandwidth of the signal. For example, if you have a lowpass filter with
the highest frequency of 10 MHz, and a sampling frequency of 60 MHz, the highest
frequency that can be handled by the system without aliasing is 60/2=30, which is
greater than 10. You could safely set M=2 in this case, since (60/2)/2=15, which is still
greater than 10.
• If you wish to decimate a signal which does not meet the frequency criteria, you can
either:
• Interpolate first, and then decimate
6-4
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Multirate Filters
• When decimating, you should apply the filter first, then perform the decimation.
When interpolating a signal, you should interpolate first, then filter the signal.
• Typically in decimation of a signal a filter is applied first, thereby allowing decimation
without aliasing, as shown in the following figure:
• Conversely, a filter is typically applied after interpolation to avoid imaging:
• M must be an integer. Although, if you wish to obtain an M of 4/5, you could
interpolate by 4, and then decimate by 5, provided that frequency restrictions are
met. This type of multirate filter will be referred to as a sample rate converter in the
documentation that follows.
Multirate filters are most often used in stages. This technique is introduced in the
following section.
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6-5
6
Multirate and Multistage Filters
Multistage Filters
In this section...
“Why Are Multistage Filters Needed?” on page 6-6
“Optimal Multistage Filters in DSP System Toolbox” on page 6-6
Why Are Multistage Filters Needed?
Typically used with multirate filters, multistage filters can bring efficiency to a particular
filter implementation. Multistage filters are composed of several filters. These different
parts of the mulitstage filter, called stages, are connected in a cascade or in parallel.
However such a design can conserve resources in many cases. There are many different
uses for a multistage filter. One of these is a filter requirement that includes a very
narrow transition width. For example, you need to design a lowpass filter where the
difference between the pass frequency and the stop frequency is .01 (normalized).
For such a requirement it is possible to design a single filter, but it will be very long
(containing many coefficients) and very costly (having many multiplications and
additions per input sample). Thus, this single filter may be so costly and require so much
memory, that it may be impractical to implement in certain applications where there
are strict hardware requirements. In such cases, a multistage filter is a great solution.
Another application of a multistage filter is for a mulitrate system, where there is a
decimator or an interpolator with a large factor. In these cases, it is usually wise to
break up the filter into several multirate stages, each comprising a multiple of the total
decimation/interpolation factor.
Optimal Multistage Filters in DSP System Toolbox
As described in the previous section, within a multirate filter each interconnected filter
is called a stage. While it is possible to design a multistage filter manually, it is also
possible to perform automatic optimization of a multistage filter automatically. When
designing a filter manually it can be difficult to guess how many stages would provide
an optimal design, optimize each stage, and then optimize all the stages together. DSP
System Toolbox software enables you to create a Specifications Object, and then design a
filter using multistage as an option. The rest of the work is done automatically. Not only
does DSP System Toolbox software determine the optimal number of stages, but it also
optimizes the total filter solution.
6-6
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Example Case for Multirate/Multistage Filters
Example Case for Multirate/Multistage Filters
In this section...
“Example Overview” on page 6-7
“Single-Rate/Single-Stage Equiripple Design” on page 6-7
“Reduce Computational Cost Using Mulitrate/Multistage Design” on page 6-8
“Compare the Responses” on page 6-8
“Further Performance Comparison” on page 6-9
Example Overview
This example shows the efficiency gains that are possible when using multirate and
multistage filters for certain applications. In this case a distinct advantage is achieved
over regular linear-phase equiripple design when a narrow transition-band width is
required. A more detailed treatment of the key points made here can be found in the
example entitled Efficient Narrow Transition-Band FIR Filter Design.
Single-Rate/Single-Stage Equiripple Design
Consider the following design specifications for a lowpass filter (where the ripples are
given in linear units):
Fpass
Fstop
Rpass
Rstop
=
=
=
=
0.13;
0.14;
0.001;
0.0005;
%
%
%
%
Passband
Stopband
Passband
Stopband
edge
edge
ripple, 0.0174 dB peak to peak
ripple, 66.0206 dB minimum attenuation
Hf = fdesign.lowpass(Fpass,Fstop,Rpass,Rstop,'linear');
A regular linear-phase equiripple design using these specifications can be designed by
evaluating the following:
Hd = design(Hf,'equiripple');
When you determine the cost of this design, you can see that 695 multipliers are
required.
cost(Hd)
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6-7
6
Multirate and Multistage Filters
Reduce Computational Cost Using Mulitrate/Multistage Design
The number of multipliers required by a filter using a single state, single rate equiripple
design is 694. This number can be reduced using multirate/multistage techniques. In
any single-rate design, the number of multiplications required by each input sample is
equal to the number of non-zero multipliers in the implementation. However, by using a
multirate/multistage design, decimation and interpolation can be combined to lessen the
computation required. For decimators, the average number of multiplications required
per input sample is given by the number of multipliers divided by the decimation factor.
Hd_multi = design(Hf,'multistage');
You can then view the cost of the filter created using this design step, and you can see
that a significant cost advantage has been achieved.
cost(Hd_multi)
Compare the Responses
You can compare the responses of the equiripple design and this multirate/multistage
design using fvtool:
hfvt = fvtool(Hd,Hd_multi);
legend(hfvt,'Equiripple design', 'Multirate/multistage design')
6-8
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Example Case for Multirate/Multistage Filters
Notice that the stopband attenuation for the multistage design is about twice that of the
other designs. This is because the decimators must attenuate out-of-band components
by 66 dB in order to avoid aliasing that would violate the specifications. Similarly, the
interpolators must attenuate images by 66 dB. You can also see that the passband gain
for this design is no longer 0 dB, because each interpolator has a nominal gain (in linear
units) equal to its interpolation factor, and the total interpolation factor for the three
interpolators is 6.
Further Performance Comparison
You can check the performance of the multirate/multistage design by plotting the power
spectral densities of the input and the various outputs, and you can see that the sinusoid
at 0 .4 p is attenuated comparably by both the equiripple design and the multirate/
multistage design.
n
x
y
y_multi
=
=
=
=
0:1799;
sin(0.1*pi*n') + 2*sin(0.15*pi*n');
filter(Hd,x);
filter(Hd_multi,x);
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6-9
6
Multirate and Multistage Filters
[Pxx,w]
= periodogram(x);
Pyy
= periodogram(y);
Pyy_multi = periodogram(y_multi);
plot(w/pi,10*log10([Pxx,Pyy,Pyy_multi]));
xlabel('Normalized Frequency (x\pi rad/sample)');
ylabel('Power density (dB/rad/sample)');
legend('Input signal PSD','Equiripple output PSD',...
'Multirate/multistage output PSD')
axis([0 1 -50 30])
grid on
6-10
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Filter Banks
Filter Banks
Multirate filters alter the sample rate of the input signal during the filtering process.
Such filters are useful in both rate conversion and filter bank applications.
The Dyadic Analysis Filter Bank block decomposes a broadband signal into a collection of
subbands with smaller bandwidths and slower sample rates. The Dyadic Synthesis Filter
Bank block reconstructs a signal decomposed by the Dyadic Analysis Filter Bank block.
To use a dyadic synthesis filter bank to perfectly reconstruct the output of a dyadic
analysis filter bank, the number of levels and tree structures of both filter banks must
be the same. In addition, the filters in the synthesis filter bank must be designed
to perfectly reconstruct the outputs of the analysis filter bank. Otherwise, the
reconstruction will not be perfect.
Dyadic Analysis Filter Banks
Dyadic analysis filter banks are constructed from the following basic unit. The unit
can be cascaded to construct dyadic analysis filter banks with either a symmetric or
asymmetric tree structure.
Each unit consists of a lowpass (LP) and highpass (HP) FIR filter pair, followed by a
decimation by a factor of 2. The filters are halfband filters with a cutoff frequency of
Fs / 4, a quarter of the input sampling frequency. Each filter passes the frequency band
that the other filter stops.
The unit decomposes its input into adjacent high-frequency and low-frequency subbands.
Compared to the input, each subband has half the bandwidth (due to the half-band
filters) and half the sample rate (due to the decimation by 2).
Note The following figures illustrate the concept of a filter bank, but not how the block
implements a filter bank; the block uses a more efficient polyphase implementation.
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6-11
6
Multirate and Multistage Filters
n-Level Asymmetric Dyadic Analysis Filter Bank
Use the above figure and the following figure to compare the two tree structures of the
dyadic analysis filter bank. Note that the asymmetric structure decomposes only the lowfrequency output from each level, while the symmetric structure decomposes the highand low-frequency subbands output from each level.
6-12
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Filter Banks
n-Level Symmetric Dyadic Analysis Filter Bank
The following table summarizes the key characteristics of the symmetric and asymmetric
dyadic analysis filter bank.
Notable Characteristics of Asymmetric and Symmetric Dyadic Analysis Filter Banks
Characteristic
N-Level Symmetric
Low- and HighAll the low-frequency
Frequency Subband and high-frequency
subbands in a level are
Decomposition
decomposed in the next
level.
N-Level Asymmetric
Each level's low-frequency subband is
decomposed in the next level, and each level's
high-frequency band is an output of the filter
bank.
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6-13
6
Multirate and Multistage Filters
Characteristic
Number of Output
Subbands
N-Level Symmetric
n
2
N-Level Asymmetric
n+1
Bandwidth and
For an input with
For an input with bandwidth BW and N samples,
yk has the bandwidth BWk, and Nk samples,
Number of Samples bandwidth BW
in Output Subbands and N samples,
where
all outputs have
bandwidth BW / 2n and
ÏÔ BW / 2k (1 £ k £ n)
n
BW
=
Ì
k
N / 2 samples.
n
(k = n + 1)
ÓÔ BW / 2
k
ÔÏ N / 2 (1 £ k £ n)
Nk = Ì
n
( k = n + 1)
ÓÔ N / 2
The bandwidth of, and number of samples in
each subband (except the last) is half those of the
previous subband. The last two subbands have
the same bandwidth and number of samples since
they originate from the same level in the filter
bank.
Output Sample
Period
All output subbands
Sample period of kth output
have a sample period of
2n(Tsi)
ÏÔ 2k ( T ) (1 £ k £ n)
si
=Ì
n
ÔÓ2 (Tsi ) (k = n + 1)
Due to the decimations by 2, the sample period of
each subband (except the last) is twice that of the
previous subband. The last two subbands have
the same sample period since they originate from
the same level in the filter bank.
Total Number of
Output Samples
6-14
The total number of samples in all of the output subbands is equal to the
number of samples in the input (due to the of decimations by 2 at each
level).
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Filter Banks
Characteristic
N-Level Symmetric
N-Level Asymmetric
Wavelet
Applications
In wavelet applications, the highpass and lowpass wavelet-based filters
are designed so that the aliasing introduced by the decimations are exactly
canceled in reconstruction.
Dyadic Synthesis Filter Banks
Dyadic synthesis filter banks are constructed from the following basic unit. The unit
can be cascaded to construct dyadic synthesis filter banks with either a asymmetric or
symmetric tree structure as illustrated in the figures entitled n-Level Asymmetric Dyadic
Synthesis Filter Bank and n-Level Symmetric Dyadic Synthesis Filter Bank.
Each unit consists of a lowpass (LP) and highpass (HP) FIR filter pair, preceded by an
interpolation by a factor of 2. The filters are halfband filters with a cutoff frequency of
Fs / 4, a quarter of the input sampling frequency. Each filter passes the frequency band
that the other filter stops.
The unit takes in adjacent high-frequency and low-frequency subbands, and reconstructs
them into a wide-band signal. Compared to each subband input, the output has twice the
bandwidth and twice the sample rate.
Note The following figures illustrate the concept of a filter bank, but not how the block
implements a filter bank; the block uses a more efficient polyphase implementation.
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6-15
6
Multirate and Multistage Filters
n-Level Asymmetric Dyadic Synthesis Filter Bank
Use the above figure and the following figure to compare the two tree structures of the
dyadic synthesis filter bank. Note that in the asymmetric structure, the low-frequency
subband input to each level is the output of the previous level, while the high-frequency
subband input to each level is an input to the filter bank. In the symmetric structure,
both the low- and high-frequency subband inputs to each level are outputs from the
previous level.
6-16
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Filter Banks
n-Level Symmetric Dyadic Synthesis Filter Bank
The following table summarizes the key characteristics of symmetric and asymmetric
dyadic synthesis filter banks.
Notable Characteristics of Asymmetric and Symmetric Dyadic Synthesis Filter Banks
Characteristic
N-Level Symmetric
N-Level Asymmetric
Input Paths
Through the
Filter Bank
Both the high-frequency and lowfrequency input subbands to each
level (except the first) are the
outputs of the previous level. The
inputs to the first level are the
inputs to the filter bank.
The low-frequency subband input
to each level (except the first) is the
output of the previous level. The lowfrequency subband input to the first
level, and the high-frequency subband
input to each level, are inputs to the
filter bank.
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6-17
6
Multirate and Multistage Filters
Characteristic
N-Level Symmetric
N-Level Asymmetric
Number of Input
Subbands
2
n+1
Bandwidth
and Number of
Samples in Input
Subbands
All inputs subbands have
bandwidth BW / 2n and N / 2n
samples, where the output has
bandwidth BW and N samples.
For an output with bandwidth BW and
N samples, the kth input subband has
the following bandwidth and number of
samples.
n
ÏÔ BW / 2k
BWk = Ì
n
ÓÔ BW / 2
(1 £ k £ n)
(k = n + 1)
ÏÔ N / 2 k (1 £ k £ n)
Nk = Ì
n
( k = n + 1)
ÓÔ N / 2
Input Sample
Periods
All input subbands have a sample
period of 2n(Tso), where the output
sample period is Tso.
Sample period of kth input subband
ÏÔ 2k ( T ) (1 £ k £ n)
so
=Ì
n
ÓÔ2 (Tso ) ( k = n + 1 )
where the output sample period is Tso.
Total Number of
Input Samples
The number of samples in the output is always equal to the total number of
samples in all of the input subbands.
Wavelet
Applications
In wavelet applications, the highpass and lowpass wavelet-based filters are
carefully selected so that the aliasing introduced by the decimation in the
dyadic analysis filter bank is exactly canceled in the reconstruction of the
signal in the dyadic synthesis filter bank.
For more information, see “Dyadic Synthesis Filter Bank”.
6-18
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Multirate Filtering in Simulink
Multirate Filtering in Simulink
DSP System Toolbox software provides a collection of multirate filtering examples that
illustrate typical applications of the multirate filtering blocks.
Multirate Filtering
Examples
Description
Command for Opening
Examples in MATLAB
Audio Sample
Rate Conversion
Illustrates sample rate conversion of an audio signal dspaudiosrc
from 22.050 kHz to 8 kHz using a multirate FIR rate
conversion approach
Sigma-Delta A/D
Converter
Illustrates analog-to-digital conversion using a sigma- dspsdadc
delta algorithm implementation
Wavelet
Reconstruction
and Noise
Reduction
Uses the Dyadic Analysis Filter Bank and Dyadic
Synthesis Filter Bank blocks to show both the
perfect reconstruction property of wavelets and an
application for noise reduction
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dspwavelet
6-19
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‫‪6-20‬‬
7
Transforms, Estimation, and Spectral
Analysis
Learn about transforms, estimation and spectral analysis.
• “Transform Time-Domain Data into Frequency Domain” on page 7-2
• “Transform Frequency-Domain Data into Time Domain” on page 7-7
• “Linear and Bit-Reversed Output Order” on page 7-12
• “Calculate Channel Latencies Required for Wavelet Reconstruction” on page 7-14
• “Spectral Analysis” on page 7-23
• “Power Spectrum Estimates” on page 7-24
• “Spectrograms” on page 7-35
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7
Transforms, Estimation, and Spectral Analysis
Transform Time-Domain Data into Frequency Domain
When you want to transform time-domain data into the frequency domain, use the FFT
block.
In this example, you use the Sine Wave block to generate two sinusoids, one at 15 Hz
and the other at 40 Hz. You sum the sinusoids point-by-point to generate the compound
sinusoid
u = sin ( 30p t ) + sin ( 80p t)
Then, you transform this sinusoid into the frequency domain using an FFT block:
1
At the MATLAB command prompt, type ex_fft_tut.
The FFT Example opens.
7-2
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Transform Time-Domain Data into Frequency Domain
2
Double-click the Sine Wave block. The Block Parameters: Sine Wave dialog box
opens.
3
Set the block parameters as follows:
• Amplitude = 1
• Frequency = [15 40]
• Phase offset = 0
• Sample time = 0.001
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7-3
7
Transforms, Estimation, and Spectral Analysis
• Samples per frame = 128
Based on these parameters, the Sine Wave block outputs two sinusoidal signals with
identical amplitudes, phases, and sample times. One sinusoid oscillates at 15 Hz and
the other at 40 Hz.
4
Save these parameters and close the dialog box by clicking OK.
5
Double-click the Matrix Sum block. The Block Parameters: Matrix Sum dialog
box opens.
6
Set the Sum over parameter to Specified dimension and the Dimension
parameter to 2. Click OK to save your changes.
Because each column represents a different signal, you need to sum along the
individual rows in order to add the values of the sinusoids at each time step.
7
Double-click the Complex to Magnitude-Angle block. The Block Parameters:
Complex to Magnitude-Angle dialog box opens.
8
Set the Output parameter to Magnitude, and then click OK.
This block takes the complex output of the FFT block and converts this output to
magnitude.
9
Double-click the Vector Scope block.
10 Set the block parameters as follows, and then click OK:
• Click the Scope Properties tab.
• Input domain = Frequency
• Click the Axis Properties tab.
• Frequency units = Hertz (This corresponds to the units of the input signals.)
• Frequency range = [0...Fs/2]
• Select the Inherit sample time from input check box.
• Amplitude scaling = Magnitude
11 Run the model.
The scope shows the two peaks at 15 and 40 Hz, as expected.
7-4
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Transform Time-Domain Data into Frequency Domain
You have now transformed two sinusoidal signals from the time domain to the
frequency domain.
Note that the sequence of FFT, Complex to Magnitude-Angle, and Vector Scope blocks
could be replaced by a single Spectrum Analyzer block, which computes the magnitude
FFT internally. Other blocks that compute the FFT internally are the blocks in the
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7-5
7
Transforms, Estimation, and Spectral Analysis
Power Spectrum Estimation library. See “Spectral Analysis” on page 7-23 for more
information about these blocks.
7-6
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Transform Frequency-Domain Data into Time Domain
Transform Frequency-Domain Data into Time Domain
When you want to transform frequency-domain data into the time domain, use the IFFT
block.
In this example, you use the Sine Wave block to generate two sinusoids, one at 15 Hz
and the other at 40 Hz. You sum the sinusoids point-by-point to generate the compound
sinusoid, u = sin ( 30p t ) + sin(80p t) . You transform this sinusoid into the frequency
domain using an FFT block, and then immediately transform the frequency-domain
signal back to the time domain using the IFFT block. Lastly, you plot the difference
between the original time-domain signal and transformed time-domain signal using a
scope:
1
At the MATLAB command prompt, type ex_ifft_tut.
The IFFT Example opens.
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7-7
7
Transforms, Estimation, and Spectral Analysis
2
Double-click the Sine Wave block. The Block Parameters: Sine Wave dialog box
opens.
3
Set the block parameters as follows:
• Amplitude = 1
• Frequency = [15 40]
• Phase offset = 0
• Sample time = 0.001
• Samples per frame = 128
7-8
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Transform Frequency-Domain Data into Time Domain
Based on these parameters, the Sine Wave block outputs two sinusoidal signals with
identical amplitudes, phases, and sample times. One sinusoid oscillates at 15 Hz and
the other at 40 Hz.
4
Save these parameters and close the dialog box by clicking OK.
5
Double-click the Matrix Sum block. The Block Parameters: Matrix Sum dialog
box opens.
6
Set the Sum over parameter to Specified dimension and the Dimension
parameter to 2. Click OK to save your changes.
Because each column represents a different signal, you need to sum along the
individual rows in order to add the values of the sinusoids at each time step.
7
Double-click the FFT block. The Block Parameters: FFT dialog box opens.
8
Select the Output in bit-reversed order check box., and then click OK.
9
Double-click the IFFT block. The Block Parameters: IFFT dialog box opens.
10 Set the block parameters as follows, and then click OK:
• Select the Input is in bit-reversed order check box.
• Select the Input is conjugate symmetric check box.
Because the original sinusoidal signal is real valued, the output of the FFT block is
conjugate symmetric. By conveying this information to the IFFT block, you optimize
its operation.
Note that the Sum block subtracts the original signal from the output of the IFFT
block, which is the estimation of the original signal.
11 Double-click the Vector Scope block.
12 Set the block parameters as follows, and then click OK:
• Click the Scope Properties tab.
• Input domain = Time
13 Run the model.
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7-9
7
Transforms, Estimation, and Spectral Analysis
The flat line on the scope suggests that there is no difference between the original
signal and the estimate of the original signal. Therefore, the IFFT block has
accurately reconstructed the original time-domain signal from the frequency-domain
input.
14 Right-click in the Vector Scope window, and select Autoscale.
7-10
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Transform Frequency-Domain Data into Time Domain
In actuality, the two signals are identical to within round-off error. The previous
figure shows the enlarged trace. The differences between the two signals is on the
order of 10-15.
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7-11
7
Transforms, Estimation, and Spectral Analysis
Linear and Bit-Reversed Output Order
In this section...
“FFT and IFFT Blocks Data Order” on page 7-12
“Find the Bit-Reversed Order of Your Frequency Indices” on page 7-12
FFT and IFFT Blocks Data Order
The FFT block enables you to output the frequency indices in linear or bit-reversed order.
Because linear ordering of the frequency indices requires a bit-reversal operation, the
FFT block may run more quickly when the output frequencies are in bit-reversed order.
The input to the IFFT block can be in linear or bit-reversed order. Therefore, you do
not have to alter the ordering of your data before transforming it back into the time
domain. However, the IFFT block may run more quickly when the input is provided in
bit-reversed order.
Find the Bit-Reversed Order of Your Frequency Indices
Two numbers are bit-reversed values of each other when the binary representation of one
is the mirror image of the binary representation of the other. For example, in a threebit system, one and four are bit-reversed values of each other, since the three-bit binary
representation of one, 001, is the mirror image of the three-bit binary representation of
four, 100. In the diagram below, the frequency indices are in linear order. To put them in
bit-reversed order
1
Translate the indices into their binary representation with the minimum number
of bits. In this example, the minimum number of bits is three because the binary
representation of 7 is 111.
2
Find the mirror image of each binary entry, and write it beside the original binary
representation.
3
Translate the indices back to their decimal representation.
The frequency indices are now in bit-reversed order.
7-12
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Linear and Bit-Reversed Output Order
The next diagram illustrates the linear and bit-reversed outputs of the FFT block. The
output values are the same, but they appear in different order.
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7-13
7
Transforms, Estimation, and Spectral Analysis
Calculate Channel Latencies Required for Wavelet Reconstruction
In this section...
“Analyze Your Model” on page 7-14
“Calculate the Group Delay of Your Filters” on page 7-16
“Reconstruct the Filter Bank System” on page 7-18
“Equalize the Delay on Each Filter Path” on page 7-18
“Update and Run the Model” on page 7-21
“References” on page 7-22
Analyze Your Model
The following sections guide you through the process of calculating the channel latencies
required for perfect wavelet reconstruction. This example uses the ex_wavelets model,
but you can apply the process to perform perfect wavelet reconstruction in any model. To
open the example model, type ex_wavelets at the MATLAB command line.
Note: You must have a Wavelet Toolbox™ product license to run the ex_wavelets
model.
7-14
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Calculate Channel Latencies Required for Wavelet Reconstruction
Before you can begin calculating the latencies required for perfect wavelet reconstruction,
you must know the types of filters being used in your model.
The Dyadic Analysis Filter Bank and the Dyadic Synthesis Filter Bank blocks in the
ex_wavelets model have the following settings:
• Filter = Biorthogonal
• Filter order [synthesis/analysis] = [3/5]
• Number of levels = 3
• Tree structure = Asymmetric
• Input = Multiple ports
Based on these settings, the “Dyadic Analysis Filter Bank” and the “Dyadic Synthesis
Filter Bank” blocks construct biorthogonal filters using the Wavelet Toolbox wfilters
function.
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7
Transforms, Estimation, and Spectral Analysis
Calculate the Group Delay of Your Filters
Once you know the types of filters being used by the Dyadic Analysis and Dyadic
Synthesis Filter Bank blocks, you need to calculate the group delay of those filters. To do
so, you can use the Signal Processing Toolbox fvtool.
Before you can use fvtool, you must first reconstruct the filters in the MATLAB
workspace. To do so, type the following code at the MATLAB command line:
[Lo_D, Hi_D, Lo_R, Hi_R] = wfilters('bior3.5')
Where Lo_D and Hi_D represent the low- and high-pass filters used by the Dyadic
Analysis Filter Bank block, and Lo_R and Hi_R represent the low- and high-pass filters
used by the Dyadic Synthesis Filter Bank block.
After you construct the filters in the MATLAB workspace, you can use fvtool to
determine the group delay of the filters. To analyze the low-pass biorthogonal filter used
by the Dyadic Analysis Filter Bank block, you must do the following:
• Type fvtool(Lo_D) at the MATLAB command line to launch the Filter
Visualization Tool.
• When the Filter Visualization Tool opens, click the Group delay response button (
on the toolbar, or select Group Delay Response from the Analysis menu.
Based on the Filter Visualization Tool's analysis, you can see that the group delay of the
Dyadic Analysis Filter Bank block's low-pass biorthogonal filter is 5.5.
7-16
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)
Calculate Channel Latencies Required for Wavelet Reconstruction
Note: Repeat this procedure to analyze the group delay of each of the filters in your
model. This section does not show the results for each filter in the ex_wavelets model
because all wavelet filters in this particular example have the same group delay.
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7
Transforms, Estimation, and Spectral Analysis
Reconstruct the Filter Bank System
To determine the delay introduced by the analysis and synthesis filter bank system, you
must reconstruct the tree structures of the Dyadic Analysis Filter Bank and the Dyadic
Synthesis Filter Bank blocks. To learn more about constructing tree structures for the
Dyadic Analysis Filter Bank and Dyadic Synthesis Filter Bank blocks, see the following
sections of the DSP System Toolbox User's Guide:
• “Dyadic Analysis Filter Banks”
• “Dyadic Synthesis Filter Banks”
Because the filter blocks in the ex_wavelets model use biorthogonal filters with three
levels and an asymmetric tree structure, the filter bank system appears as shown in the
following figure.
Delay N
F1
2
F0
2
F1
2
F0
2
F0
2
F1
2
2
F0
2
F0
2
F0
2
2
2
G1
Path 4
2
G1
2
G0
Path 3
G1
2
G0
2
G0
Path 2
G0
2
G0
2
G0
Path 1
Delay M
F0 = Delay due to low-pass filter of Dyadic Analysis Filter Bank
F1 = Delay due to high-pass filter of Dyadic Analysis Filter Bank
G0 = Delay due to low-pass filter of Dyadic Synthesis Filter Bank
G1 = Delay due to high-pass filter of Dyadic Synthesis Filter Bank
The extra delay values of M and N on paths 3 and 4 in the previous figure ensure that
the total delay on each of the four filter paths is identical.
Equalize the Delay on Each Filter Path
Now that you have reconstructed the filter bank system, you can calculate the delay on
each filter path. To do so, use the following Noble identities:
7-18
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Calculate Channel Latencies Required for Wavelet Reconstruction
First Noble Identity
z-2
2
Equivalent to
2
z-1
z-1
2
Second Noble Identity
2
z-2
Equivalent to
You can apply the Noble identities by summing the delay on each signal path from right
to left. The first Noble identity indicates that moving a delay of 1 before a downsample of
2 is equivalent to multiplying that delay value by 2. Similarly, the second Noble identity
indicates that moving a delay of 2 before an upsample of 2 is equivalent to dividing that
delay value by 2.
The fvtool analysis in step 1 found that both the low- and high-pass filters of the
analysis filter bank have the same group delay (F0 = F1 = 5.5). Thus, you can use F to
represent the group delay of the analysis filter bank. Similarly, the group delay of the
low- and high-pass filters of the synthesis filter bank is the same (G0=G1=5.5), so you can
use G to represent the group delay of the synthesis filter bank.
The following figure shows the filter bank system with the intermediate delay sums
displayed below each path.
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7
Transforms, Estimation, and Spectral Analysis
F
2N+(F+G)
Delay N
2
2N+G
F
N+0.5G
2
F
7(F+G)
2
6F+7G
F
7(F+G)
3F+3.5G
2
6F+7G
F
3F+3.5G
0.5G
Delay M
2
4M+3(F+G) 4M+2F+3G 2M+F+1.5G 2M+1.5G
F
2
2
F
2F+3.5G F+1.75G 1.75G
F
2
F
2F+3.5G F+1.75G 1.75G
0.75G
2
0.875G
2
0.875G
2
G
1.75G
2
1.75G
1.5G
G
0.75G
0.5G
1.5G
G
Path 3
G
Path 2
G
Path 1
1.5G
G
2
0.5G
G
2
0.75G
2
G
2
G
Path 4
G
2
M+0.75G
G
G
2
0.5G
G
F = Delay due to Dyadic Analysis Filter Bank
G = Delay due to Dyadic Synthesis Filter Bank
You can see from the previous figure that the signal delays on paths 1 and 2 are
identical: 7(F+G). Because each path of the filter bank system has identical delay, you
can equate the delay equations for paths 3 and 4 with the delay equation for paths 1 and
2. After constructing these equations, you can solve for M and N, respectively:
Path 3 = Path 1 fi 4 M + 3 ( F + G) = 7( F + G)
fi M = F + G
Path 4 = Path 1 fi 2 N + ( F + G) = 7( F + G )
fi N = 3( F + G)
The fvtool analysis in step 1 found the group delay of each biorthogonal wavelet filter
in this model to be 5.5 samples. Therefore, F = 5.5 and G = 5.5. By inserting these values
into the two previous equations, you get M = 11 and N = 33. Because the total delay on
each filter path must be the same, you can find the overall delay of the filter bank system
by inserting F = 5.5 and G = 5.5 into the delay equation for any of the four filter paths.
Inserting the values of F and G into 7(F+G) yields an overall delay of 77 samples for the
filter bank system of the ex_wavelets model.
7-20
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Calculate Channel Latencies Required for Wavelet Reconstruction
Update and Run the Model
Now that you know the latencies required for perfect wavelet reconstruction, you can
incorporate those delay values into the model. The ex_wavelets model has already been
updated with the correct delay values (M = 11, N = 33, Overall = 77), so it is ready to run.
After you run the model, examine the reconstruction error in the Difference scope. To
further examine any particular areas of interest, use the zoom tools available on the
toolbar of the scope window or from the View menu.
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7
Transforms, Estimation, and Spectral Analysis
References
[1] Strang, G. and Nguyen, T. Wavelets and Filter Banks. Wellesley, MA: WellesleyCambridge Press, 1996.
7-22
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Spectral Analysis
Spectral Analysis
The Power Spectrum Estimation library provides a number of blocks for spectral
analysis. Many of them have correlates in Signal Processing Toolbox software, which are
shown in parentheses:
• Burg Method (pburg)
• Covariance Method (pcov)
• Magnitude FFT (periodogram)
• Modified Covariance Method (pmcov)
• Short-Time FFT
• Yule-Walker Method (pyulear)
See “Spectral Analysis” in the Signal Processing Toolbox documentation for an overview
of spectral analysis theory and a discussion of the above methods.
DSP System Toolbox software provides two examples that illustrate the spectral analysis
blocks:
• A Comparison of Spectral Analysis Techniques (dspsacomp)
• Spectral Analysis: Short-Time FFT (dspstfft)
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7
Transforms, Estimation, and Spectral Analysis
Power Spectrum Estimates
In this section...
“Create the Block Diagram” on page 7-24
“Set the Model Parameters” on page 7-25
“View the Power Spectrum Estimates” on page 7-32
Create the Block Diagram
Up until now, you have been dealing with signals in the time domain. The DSP System
Toolbox product is also capable of working with signals in the frequency domain. You can
use the software to perform fast Fourier transforms (FFTs), power spectrum analysis,
short-time FFTs, and many other frequency-domain applications.
The power spectrum of a signal represents the contribution of every frequency of
the spectrum to the power of the overall signal. It is useful because many signal
processing applications, such as noise cancellation and system identification, are based
on frequency-specific modifications of signals.
First, assemble and connect the blocks needed to calculate the power spectrum of your
speech signal:
1
Open a new Simulink model.
2
Add the following blocks to your model. Subsequent topics describe how to use these
blocks.
3
7-24
Block
Library
Signal From Workspace
Sources
Buffer
Signal Management / Buffers
Periodogram
Estimation / Power Spectrum Estimation
Vector Scope
Sinks
Connect the blocks as shown in the next figure.
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Power Spectrum Estimates
Once you have assembled the blocks needed to calculate the power spectrum of your
speech signal, you can set the block parameters.
Set the Model Parameters
Now that you have assembled the blocks needed to calculate the power spectrum of your
speech signal, you need to set the block parameters. These parameter values ensure that
the model calculates the power spectrum of your signal accurately:
1
If the model you created in “Create the Block Diagram” on page 7-24 is not open
on your desktop, you can open an equivalent model by typing
ex_gstut9
at the MATLAB command prompt.
2
Load the speech signal into the MATLAB workspace by typing load mtlb at
the MATLAB command prompt. This speech signal is a woman's voice saying
“MATLAB.”
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7-25
7
Transforms, Estimation, and Spectral Analysis
3
Use the Signal From Workspace block to import the speech signal from the MATLAB
workspace into your Simulink model. Open the Signal From Workspace dialog box by
double-clicking the block. Set the block parameters as follows:
• Signal = mtlb
• Sample time = 1/8000
• Samples per frame = 80
• Form output after final data value by = Setting to zero
Once you are done setting these parameters, the Signal From Workspace dialog box
should look similar to the figure below. Click OK to apply your changes.
7-26
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Power Spectrum Estimates
The DSP System Toolbox product is capable of frame-based processing. In other
words, DSP System Toolbox blocks can process multiple samples of data at one time.
This improves the computational speed of your model. In this case, by setting the
Samples per frame parameter to 80, you are telling the Signal From Workspace
block to output a frame that contains 80 signal samples at each simulation time step.
Note that the sample period of the input signal is 1/8000 seconds. Also, after the
block outputs the final signal value, all other outputs are zero.
4
Use the Buffer block to buffer the input signal into frames that contain 128 samples.
Open the Buffer dialog box by double-clicking the block. Set the block parameters as
follows:
• Output buffer size (per channel) = 128
• Buffer overlap = 48
• Initial conditions = 0
• Treat Mx1 and unoriented sample-based signals as = One channel
Once you are done setting these parameters, the Buffer dialog box should look
similar to the figure below. Click OK to apply your changes.
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7-27
7
Transforms, Estimation, and Spectral Analysis
Based on these parameters, the first output frame contains 48 initial condition
values followed by the first 80 samples from the first input frame. The second output
frame contains the last 48 values from the previous frame followed by the second 80
samples from the second input frame, and so on. You are buffering your input signal
into an output signal with 128 samples per frame to minimize the estimation noise
added to your signal. Because 128 is a power of 2, this operation also enables the
Periodogram block to perform an FFT on the signal.
5
Use the Periodogram block to compute a nonparametric estimate of the power
spectrum of the speech signal. Open the Periodogram dialog box by double-clicking
the block and set the block parameters as follows:
• Measurement = Power spectral density
• Window = Hamming
• Window sampling = Periodic
• Select the Inherit FFT length from input dimensions check box.
• Number of spectral averages = 2
Once you are done setting these parameters, the Periodogram dialog box should look
similar to the figure below. Click OK to apply your changes.
7-28
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Power Spectrum Estimates
Based on these parameters, the block applies a Hamming window periodically to the
input speech signal and averages two spectra at one time. The length of the FFT is
assumed to be 128, which is the number of samples per frame being output from the
Buffer block.
6
Use the Vector Scope block to view the power spectrum of the speech signal. Open
the Vector Scope dialog box by double-clicking the block. Set the block parameters as
follows:
• Input domain = Frequency
• Click the Axis Properties tab.
• Clear the Inherit sample time from input check box.
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7-29
7
Transforms, Estimation, and Spectral Analysis
• Sample time of original time series = 1/8000
• Y-axis label = Magnitude-squared, dB
Once you are done setting these parameters, the Axis Properties pane of the Vector
Scope dialog box should look similar to the figure below. As you can see by the Yaxis scaling parameter, the decibel amplitude is plotted in a vector scope window.
7-30
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‫‪Power Spectrum Estimates‬‬
‫‪7-31‬‬
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7
Transforms, Estimation, and Spectral Analysis
Because you are buffering the input with a nonzero overlap, you have altered the
sample time of the signal. As a result, you need to specify the sample time of the
original time series. Otherwise, the overlapping buffer samples lead the block to
believe that the sample time is shorter than it actually is.
After you have set the block parameter values, you can calculate and view the power
spectrum of the speech signal.
View the Power Spectrum Estimates
In the previous topics, you created a power spectrum model and set its parameters. In
this topic, you simulate the model and view the power spectrum of your speech signal:
1
If the model you created in “Set the Model Parameters” on page 7-25 is not open
on your desktop, you can open an equivalent model by typing
ex_gstut10
at the MATLAB command prompt.
2
Set the configuration parameters. Open the Configuration Parameters dialog box by
selecting Model Configuration Parameters from the Simulation menu. Select
Solver from the menu on the left side of the dialog box, and set the parameters as
follows:
• Stop time = 0.5
• Type = Fixed-step
• Solver = Discrete (no continuous states)
7-32
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Power Spectrum Estimates
3
Apply these parameters and close the Configuration Parameters dialog box by
clicking OK. These parameters are saved only when you save your model.
4
If you have not already done so, load the speech signal into the MATLAB workspace
by typing load mtlb.
5
Run the model to open the Vector Scope window. The data is not immediately visible
at the end of the simulation. To autoscale the y-axis to fit the data, in the Vector
Scope window, right-click and choose Autoscale. The following figure shows the
data displayed in the Vector Scope window.
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7-33
7
Transforms, Estimation, and Spectral Analysis
During the simulation, the Vector Scope window displays a series of frames output from
the Periodogram block. Each of these frames corresponds to a window of the original
speech signal. The data in each frame represents the power spectrum, or contribution of
every frequency to the power of the original speech signal, for a given window.
In the next section, “Spectrograms” on page 7-35, you use these power spectra to
create a spectrogram of the speech signal.
7-34
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Spectrograms
Spectrograms
In this section...
“Modify the Block Diagram” on page 7-35
“Set the Model Parameters” on page 7-37
“View the Spectrogram of the Speech Signal” on page 7-41
Modify the Block Diagram
Spectrograms are color-based visualizations of the evolution of the power spectrum of a
speech signal as this signal is swept through time. Spectrograms use the periodogram
power spectrum estimation method and are widely used by speech and audio engineers.
You can use them to develop a visual understanding of the frequency content of your
speech signal while a particular sound is being vocalized.
In the previous section, you built a model capable of calculating the power spectrum of a
speech signal that represents a woman saying “MATLAB.” In this topic, you modify this
model to view the spectrogram of your signal:
1
If the model you created in “View the Power Spectrum Estimates” on page 7-32 is not
open on your desktop, you can open an equivalent model by typing
ex_gstut11
at the MATLAB command prompt.
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7-35
7
Transforms, Estimation, and Spectral Analysis
2
3
7-36
Add the following blocks to your model. Subsequent topics describe how to use these
blocks.
Block
Library
Selector
Simulink / Signal Routing
dB Conversion
Math Functions / Math Operations
Buffer
Signal Management / Buffers
Reshape
Simulink / Math Operations
Matrix Viewer
Sinks
Connect the blocks as shown in the figure below. These blocks extract the positive
frequencies of each power spectrum and concatenate them into a matrix that
represents the spectrogram of the speech signal.
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Spectrograms
Once you have assembled the blocks needed to view the spectrogram of your speech
signal, you can set the block parameters.
Set the Model Parameters
In the previous topic, you assembled the blocks you need to view the spectrogram of your
speech signal. Now you must set the block parameters:
1
If the model you created in “Modify the Block Diagram” on page 7-35 is not open
on your desktop, you can open an equivalent model by typing
ex_gstut12
at the MATLAB command prompt.
2
Use the Selector block to extract the first 64 elements, or the positive frequencies, of
each power spectrum. Open the Selector dialog box by double-clicking the block. Set
the block parameters as follows:
• Number of input dimensions = 1
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7-37
7
Transforms, Estimation, and Spectral Analysis
• Index mode = One-based
• Index option = Index vector (dialog)
• Index = 1:64
• Input port size = 128
At each time instance, the input to the Selector block is a vector of 128 elements. The
block assigns one-based indices to these elements and extracts the first 64. Once you
are done setting these parameters, the Selector dialog box should look similar to the
figure below. To apply your changes, click OK.
3
The dB Conversion block converts the magnitude of the input FFT signal to decibels.
Leave this block at its default parameters.
4
Use the Buffer1 block to buffer up the individual power spectrums. Open the Buffer1
dialog box by double-clicking the block. Set the block parameters as follows:
• Output buffer size (per channel) = 64*48
• Buffer overlap = 64*46
7-38
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Spectrograms
• Initial conditions = -70
• Treat Mx1 and unoriented sample-based signals as = One channel
Once you are done setting these parameters, the Buffer1 dialog box should look
similar to the following figure. To apply your changes, click OK.
Setting the value of the Buffer overlap parameter slightly less than the value of
the Output buffer size (per channel) parameter ensures that your spectrogram
represents smooth movement through time. The Initial conditions parameter
represents the initial values in the buffer; -70 represents silence.
5
Use the Reshape block to reshape the input signal into a 64-by-48 matrix. To do so,
set the Output dimensionality to Customize and the Output dimensions to [64
48].
6
The Matrix Viewer enables you to view the spectrogram of the speech signal. Open
the Matrix Viewer dialog box by double-clicking the block. Set the block parameters
as follows:
• Click the Image Properties tab.
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7-39
7
Transforms, Estimation, and Spectral Analysis
• Colormap matrix = jet(256)
• Minimum input value = -150
• Maximum input value = -65
• Select the Display colorbar check box.
Once you are done setting these parameters, the Image Properties pane should
look similar to the figure below.
• Click the Axis Properties tab.
• Axis origin = Lower left corner
• X-axis title = Time Index
• Y-axis title = Frequency Index
• Colorbar title = dB Magnitude
7-40
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Spectrograms
In this case, you are assuming that the power spectrum values do not exceed -65 dB.
Once you are done setting these parameters, the Axis Properties pane should look
similar to the figure below. To apply your changes, click OK.
After you have set the parameter values, you can calculate and view the spectrogram of
the speech signal.
View the Spectrogram of the Speech Signal
In the topic “View the Power Spectrum Estimates” on page 7-32, you used a Vector
Scope block to display the power spectrum of your speech signal. In this topic, you view
the spectrogram of your speech signal using a Matrix Viewer block. The speech signal
represents a woman's voice saying “MATLAB”:
1
If the model you created in “Set the Model Parameters” on page 7-37 is not open
on your desktop, you can open an equivalent model by typing
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7-41
7
Transforms, Estimation, and Spectral Analysis
ex_gstut13
at the MATLAB command prompt.
2
7-42
Run the model. During the simulation, the Vector Scope window displays a sequence
of power spectrums, one for each window of the original speech signal. The power
spectrum is the contribution of every frequency to the power of the speech signal.
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Spectrograms
The Matrix Viewer window, shown below, displays the spectrogram of the speech
signal. This spectrogram is calculated using the Periodogram power spectrum
estimation method. Note the harmonics that are visible in the signal when the
vowels are spoken. Most of the signal's energy is concentrated in these harmonics;
therefore, two distinct peaks are visible in the spectrogram.
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7-43
7
Transforms, Estimation, and Spectral Analysis
In this example, you viewed the spectrogram of your speech signal using a Matrix
Viewer block. You can find additional DSP System Toolbox product examples in the Help
browser. To access these examples, click the Contents tab, double-click DSP System
Toolbox, and then click Examples. A list of the examples in the DSP System Toolbox
documentation appears in the right pane of the Help browser.
7-44
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8
Mathematics
Learn about statistics and linear algebra.
• “Statistics” on page 8-2
• “Linear Algebra and Least Squares” on page 8-5
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8
Mathematics
Statistics
In this section...
“Statistics Blocks” on page 8-2
“Basic Operations” on page 8-2
“Running Operations” on page 8-3
Statistics Blocks
The Statistics library provides fundamental statistical operations such as minimum,
maximum, mean, variance, and standard deviation. Most blocks in the Statistics library
support two types of operations; basic and running.
The blocks listed below toggle between basic and running modes using the Running
check box in the parameter dialog box:
• Histogram
• Mean
• RMS
• Standard Deviation
• Variance
An unselected Running check box means that the block is operating in basic mode,
while a selected Running box means that the block is operating in running mode.
The Maximum and Minimum blocks are slightly different from the blocks above, and
provide a Mode parameter in the block dialog box to select the type of operation. The
Value and Index, Value, and Index options in the Mode menu all specify basic
operation, in each case enabling a different set of output ports on the block. The Running
option in the Mode menu selects running operation.
Basic Operations
A basic operation is one that processes each input independently of previous and
subsequent inputs. For example, in basic mode (with Value and Index selected, for
example) the Maximum block finds the maximum value in each column of the current
input, and returns this result at the top output (Val). Each consecutive Val output
8-2
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Statistics
therefore has the same number of columns as the input, but only one row. Furthermore,
the values in a given output only depend on the values in the corresponding input. The
block repeats this operation for each successive input.
This type of operation is exactly equivalent to the MATLAB command
val = max(u)
% Equivalent MATLAB code
which computes the maximum of each column in input u.
The next section is an example of a basic statistical operation.
Create a Sliding Window
You can use the basic statistics operations in conjunction with the Buffer block to
implement basic sliding window statistics operations. A sliding window is like a stencil
that you move along a data stream, exposing only a set number of data points at one
time.
For example, you may want to process data in 128-sample frames, moving the window
along by one sample point for each operation. One way to implement such a sliding
window is shown in the following ex_mean_tut model.
The Buffer block's Buffer size (Mo) parameter determines the size of the window. The
Buffer overlap (L) parameter defines the “slide factor” for the window. At each sample
instant, the window slides by Mo-L points. The Buffer overlap is often Mo-1, so that a
new statistic is computed for every new signal sample.
Running Operations
A running operation is one that processes successive inputs, and computes a result that
reflects both current and past inputs. In this mode, you must use the Input processing
parameter to specify whether the block performs sample- or frame-based processing on
the inputs. A reset port enables you to restart this tracking at any time. The running
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8-3
8
Mathematics
statistic is computed for each input channel independently, so the block's output is the
same size as the input.
For example, in running mode (Running selected from the Mode parameter) the
Maximum block outputs a record of the input's maximum value over time.
The following figure illustrates how a Maximum block in running mode operates on a
3-by-2 matrix input, u, when the Input processing parameter is set to Columns as
channels (frame based). The running maximum is reset at t=2 by an impulse to the
block's optional Rst port.
8-4
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Linear Algebra and Least Squares
Linear Algebra and Least Squares
In this section...
“Linear Algebra Blocks” on page 8-5
“Linear System Solvers” on page 8-5
“Matrix Factorizations” on page 8-7
“Matrix Inverses” on page 8-8
Linear Algebra Blocks
The Matrices and Linear Algebra library provides three large sublibraries containing
blocks for linear algebra; Linear System Solvers, Matrix Factorizations, and Matrix
Inverses. A fourth library, Matrix Operations, provides other essential blocks for working
with matrices.
Linear System Solvers
The Linear System Solvers library provides the following blocks for solving the system of
linear equations AX = B:
• Autocorrelation LPC
• Cholesky Solver
• Forward Substitution
• LDL Solver
• Levinson-Durbin
• LU Solver
• QR Solver
• SVD Solver
Some of the blocks offer particular strengths for certain classes of problems. For example,
the Cholesky Solver block is particularly adapted for a square Hermitian positive definite
matrix A, whereas the Backward Substitution block is particularly suited for an upper
triangular matrix A.
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8-5
8
Mathematics
Solve AX=B Using the LU Solver Block
In the following ex_lusolver_tut model, the LU Solver block solves the equation Ax = b,
where
È1 -2 3˘
A = ÍÍ4 0 6 ˙˙ b =
ÎÍ 2 -1 3˙˚
È1˘
Í- 2˙
Í ˙
ÎÍ- 1˚˙
and finds x to be the vector [-2 0 1]'.
You can verify the solution by using the Matrix Multiply block to perform the
multiplication Ax, as shown in the following ex_matrixmultiply_tut1 model.
8-6
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Linear Algebra and Least Squares
Matrix Factorizations
The Matrix Factorizations library provides the following blocks for factoring various
kinds of matrices:
• Cholesky Factorization
• LDL Factorization
• LU Factorization
• QR Factorization
• Singular Value Decomposition
Some of the blocks offer particular strengths for certain classes of problems. For example,
the Cholesky Factorization block is particularly suited to factoring a Hermitian positive
definite matrix into triangular components, whereas the QR Factorization is particularly
suited to factoring a rectangular matrix into unitary and upper triangular components.
Factor a Matrix into Upper and Lower Submatrices Using the LU Factorization Block
In the following ex_lufactorization_tut model, the LU Factorization block factors a matrix
Ap into upper and lower triangular submatrices U and L, where Ap is row equivalent to
input matrix A, where
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8-7
8
Mathematics
The lower output of the LU Factorization, P, is the permutation index vector, which
indicates that the factored matrix Ap is generated from A by interchanging the first and
second rows.
È4 0 6 ˘
A p = ÍÍ1 -2 3˙˙
ÍÎ 2 -1 3˙˚
The upper output of the LU Factorization, LU, is a composite matrix containing the two
submatrix factors, U and L, whose product LU is equal to Ap.
6 ˘
0 0˘
È4 0
È 1
U = ÍÍ 0 -2 1.5 ˙˙ L = ÍÍ0 .25 1 0 ˙˙
ÍÎ 0 0 -0 .75 ˙˚
ÍÎ 0 .5 0.5 1 ˙˚
You can check that LU = Ap with the Matrix Multiply block, as shown in the following
ex_matrixmultiply_tut2 model.
Matrix Inverses
The Matrix Inverses library provides the following blocks for inverting various kinds of
matrices:
• Cholesky Inverse
• LDL Inverse
8-8
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Linear Algebra and Least Squares
• LU Inverse
• Pseudoinverse
Find the Inverse of a Matrix Using the LU Inverse Block
In the following ex_luinverse_tut model, the LU Inverse block computes the inverse of
input matrix A, where
È1 -2 3˘
A = ÍÍ4 0 6 ˙˙
ÍÎ 2 -1 3˙˚
and then forms the product A-1A, which yields the identity matrix of order 3, as expected.
As shown above, the computed inverse is
A
-1
-0 .5
2 ˘
È -1
Í
=Í 0
0.5
-1 ˙˙
ÍÎ 0.6667 0.5 - 1.333 ˙˚
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8-9
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‫‪8-10‬‬
9
Fixed-Point Design
Learn about fixed-point data types and how to convert floating-point models to fixedpoint.
• “Fixed-Point Signal Processing” on page 9-2
• “Fixed-Point Concepts and Terminology” on page 9-4
• “Arithmetic Operations” on page 9-9
• “Fixed-Point Support for MATLAB System Objects” on page 9-19
• “Specify Fixed-Point Attributes for Blocks” on page 9-25
• “Quantizers” on page 9-47
• “Fixed-Point Filter Design” on page 9-61
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9
Fixed-Point Design
Fixed-Point Signal Processing
In this section...
“Fixed-Point Features” on page 9-2
“Benefits of Fixed-Point Hardware” on page 9-2
“Benefits of Fixed-Point Design with System Toolboxes Software” on page 9-3
Note: To take full advantage of fixed-point support in System Toolbox software, you must
install Fixed-Point Designer software.
Fixed-Point Features
Many of the blocks in this product have fixed-point support, so you can design signal
processing systems that use fixed-point arithmetic. Fixed-point support in DSP System
Toolbox software includes
• Signed two's complement and unsigned fixed-point data types
• Word lengths from 2 to 128 bits in simulation
• Word lengths from 2 to the size of a long on the Simulink Coder C code-generation
target
• Overflow handling and rounding methods
• C code generation for deployment on a fixed-point embedded processor, with Simulink
Coder code generation software. The generated code uses all allowed data types
supported by the embedded target, and automatically includes all necessary shift and
scaling operations
Benefits of Fixed-Point Hardware
There are both benefits and trade-offs to using fixed-point hardware rather than floatingpoint hardware for signal processing development. Many signal processing applications
require low-power and cost-effective circuitry, which makes fixed-point hardware a
natural choice. Fixed-point hardware tends to be simpler and smaller. As a result, these
units require less power and cost less to produce than floating-point circuitry.
Floating-point hardware is usually larger because it demands functionality and ease of
development. Floating-point hardware can accurately represent real-world numbers, and
9-2
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Fixed-Point Signal Processing
its large dynamic range reduces the risk of overflow, quantization errors, and the need
for scaling. In contrast, the smaller dynamic range of fixed-point hardware that allows
for low-power, inexpensive units brings the possibility of these problems. Therefore,
fixed-point development must minimize the negative effects of these factors, while
exploiting the benefits of fixed-point hardware; cost- and size-effective units, less power
and memory usage, and fast real-time processing.
Benefits of Fixed-Point Design with System Toolboxes Software
Simulating your fixed-point development choices before implementing them in hardware
saves time and money. The built-in fixed-point operations provided by the System
Toolboxes software save time in simulation and allow you to generate code automatically.
This software allows you to easily run multiple simulations with different word length,
scaling, overflow handling, and rounding method choices to see the consequences of
various fixed-point designs before committing to hardware. The traditional risks of fixedpoint development, such as quantization errors and overflow, can be simulated and
mitigated in software before going to hardware.
Fixed-point C code generation with System Toolbox software and Simulink Coder code
generation software produces code ready for execution on a fixed-point processor. All
the choices you make in simulation in terms of scaling, overflow handling, and rounding
methods are automatically optimized in the generated code, without necessitating timeconsuming and costly hand-optimized code.
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9-3
9
Fixed-Point Design
Fixed-Point Concepts and Terminology
In this section...
“Fixed-Point Data Types” on page 9-4
“Scaling” on page 9-5
“Precision and Range” on page 9-6
Note: The “Glossary” defines much of the vocabulary used in these sections. For more
information on these subjects, see the “Fixed-Point Designer” documentation.
Fixed-Point Data Types
In digital hardware, numbers are stored in binary words. A binary word is a fixed-length
sequence of bits (1's and 0's). How hardware components or software functions interpret
this sequence of 1's and 0's is defined by the data type.
Binary numbers are represented as either fixed-point or floating-point data types. In this
section, we discuss many terms and concepts relating to fixed-point numbers, data types,
and mathematics.
A fixed-point data type is characterized by the word length in bits, the position of the
binary point, and whether it is signed or unsigned. The position of the binary point is the
means by which fixed-point values are scaled and interpreted.
For example, a binary representation of a generalized fixed-point number (either signed
or unsigned) is shown below:
where
• bi is the ith binary digit.
9-4
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Fixed-Point Concepts and Terminology
• wl is the word length in bits.
• bwl–1 is the location of the most significant, or highest, bit (MSB).
• b0 is the location of the least significant, or lowest, bit (LSB).
• The binary point is shown four places to the left of the LSB. In this example,
therefore, the number is said to have four fractional bits, or a fraction length of four.
Fixed-point data types can be either signed or unsigned. Signed binary fixed-point
numbers are typically represented in one of three ways:
• Sign/magnitude
• One's complement
• Two's complement
Two's complement is the most common representation of signed fixed-point numbers and
is used by System Toolbox software. See “Two's Complement” on page 9-10 for more
information.
Scaling
Fixed-point numbers can be encoded according to the scheme
real- world value = ( slope ¥ integer) + bias
where the slope can be expressed as
slope = slope adjustment ¥ 2exponent
The integer is sometimes called the stored integer. This is the raw binary number, in
which the binary point assumed to be at the far right of the word. In System Toolboxes,
the negative of the exponent is often referred to as the fraction length.
The slope and bias together represent the scaling of the fixed-point number. In a number
with zero bias, only the slope affects the scaling. A fixed-point number that is only scaled
by binary point position is equivalent to a number in the Fixed-Point Designer [Slope
Bias] representation that has a bias equal to zero and a slope adjustment equal to one.
This is referred to as binary point-only scaling or power-of-two scaling:
real- world value = 2 exponent ¥ integer
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9
Fixed-Point Design
or
real- world value = 2- fraction length ¥ integer
In System Toolbox software, you can define a fixed-point data type and scaling for the
output or the parameters of many blocks by specifying the word length and fraction
length of the quantity. The word length and fraction length define the whole of the data
type and scaling information for binary-point only signals.
All System Toolbox blocks that support fixed-point data types support signals with
binary-point only scaling. Many fixed-point blocks that do not perform arithmetic
operations but merely rearrange data, such as Delay and Matrix Transpose, also support
signals with [Slope Bias] scaling.
Precision and Range
You must pay attention to the precision and range of the fixed-point data types and
scalings you choose for the blocks in your simulations, in order to know whether rounding
methods will be invoked or if overflows will occur.
Range
The range is the span of numbers that a fixed-point data type and scaling can represent.
The range of representable numbers for a two's complement fixed-point number of word
length wl, scaling S, and bias B is illustrated below:
For both signed and unsigned fixed-point numbers of any data type, the number of
different bit patterns is 2wl.
For example, in two's complement, negative numbers must be represented as well as
zero, so the maximum value is 2wl–1. Because there is only one representation for zero,
there are an unequal number of positive and negative numbers. This means there is a
representation for -2wl–1 but not for 2wl –1:
9-6
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Fixed-Point Concepts and Terminology
Overflow Handling
Because a fixed-point data type represents numbers within a finite range, overflows can
occur if the result of an operation is larger or smaller than the numbers in that range.
System Toolbox software does not allow you to add guard bits to a data type on-the-fly
in order to avoid overflows. Any guard bits must be allocated upon model initialization.
However, the software does allow you to either saturate or wrap overflows. Saturation
represents positive overflows as the largest positive number in the range being used, and
negative overflows as the largest negative number in the range being used. Wrapping
uses modulo arithmetic to cast an overflow back into the representable range of the data
type. See “Modulo Arithmetic” on page 9-9 for more information.
Precision
The precision of a fixed-point number is the difference between successive values
representable by its data type and scaling, which is equal to the value of its least
significant bit. The value of the least significant bit, and therefore the precision of the
number, is determined by the number of fractional bits. A fixed-point value can be
represented to within half of the precision of its data type and scaling.
For example, a fixed-point representation with four bits to the right of the binary point
has a precision of 2-4 or 0.0625, which is the value of its least significant bit. Any number
within the range of this data type and scaling can be represented to within (2-4)/2 or
0.03125, which is half the precision. This is an example of representing a number with
finite precision.
Rounding Modes
When you represent numbers with finite precision, not every number in the available
range can be represented exactly. If a number cannot be represented exactly by the
specified data type and scaling, it is rounded to a representable number. Although
precision is always lost in the rounding operation, the cost of the operation and the
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Fixed-Point Design
amount of bias that is introduced depends on the rounding mode itself. To provide you
with greater flexibility in the trade-off between cost and bias, DSP System Toolbox
software currently supports the following rounding modes:
• Ceiling rounds the result of a calculation to the closest representable number in the
direction of positive infinity.
• Convergent rounds the result of a calculation to the closest representable number.
In the case of a tie, Convergent rounds to the nearest even number. This is the least
biased rounding mode provided by the toolbox.
• Floor, which is equivalent to truncation, rounds the result of a calculation to the
closest representable number in the direction of negative infinity.
• Nearest rounds the result of a calculation to the closest representable number. In the
case of a tie, Nearest rounds to the closest representable number in the direction of
positive infinity.
• Round rounds the result of a calculation to the closest representable number. In the
case of a tie, Round rounds positive numbers to the closest representable number
in the direction of positive infinity, and rounds negative numbers to the closest
representable number in the direction of negative infinity.
• Simplest rounds the result of a calculation using the rounding mode (Floor or
Zero) that adds the least amount of extra rounding code to your generated code.
For more information, see “Rounding Mode: Simplest” in the Fixed-Point Designer
documentation.
• Zero rounds the result of a calculation to the closest representable number in the
direction of zero.
To learn more about each of these rounding modes, see “Rounding” in the Fixed-Point
Designer documentation.
For a direct comparison of the rounding modes, see “Choosing a Rounding Method” in the
Fixed-Point Designer documentation.
9-8
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Arithmetic Operations
Arithmetic Operations
In this section...
“Modulo Arithmetic” on page 9-9
“Two's Complement” on page 9-10
“Addition and Subtraction” on page 9-11
“Multiplication” on page 9-12
“Casts” on page 9-14
Note: These sections will help you understand what data type and scaling choices result
in overflows or a loss of precision.
Modulo Arithmetic
Binary math is based on modulo arithmetic. Modulo arithmetic uses only a finite set of
numbers, wrapping the results of any calculations that fall outside the given set back
into the set.
For example, the common everyday clock uses modulo 12 arithmetic. Numbers in this
system can only be 1 through 12. Therefore, in the “clock” system, 9 plus 9 equals 6. This
can be more easily visualized as a number circle:
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Fixed-Point Design
Similarly, binary math can only use the numbers 0 and 1, and any arithmetic results
that fall outside this range are wrapped “around the circle” to either 0 or 1.
Two's Complement
Two's complement is a way to interpret a binary number. In two's complement, positive
numbers always start with a 0 and negative numbers always start with a 1. If the
leading bit of a two's complement number is 0, the value is obtained by calculating the
standard binary value of the number. If the leading bit of a two's complement number
is 1, the value is obtained by assuming that the leftmost bit is negative, and then
calculating the binary value of the number. For example,
01 = (0 + 20 ) = 1
11 = ((- 21 ) + ( 20 )) = (-2 + 1) = -1
To compute the negative of a binary number using two's complement,
9-10
1
Take the one's complement, or “flip the bits.”
2
Add a 1 using binary math.
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Arithmetic Operations
3
Discard any bits carried beyond the original word length.
For example, consider taking the negative of 11010 (-6). First, take the one's complement
of the number, or flip the bits:
11010 Æ 00101
Next, add a 1, wrapping all numbers to 0 or 1:
00101
+1
00110 (6)
Addition and Subtraction
The addition of fixed-point numbers requires that the binary points of the addends be
aligned. The addition is then performed using binary arithmetic so that no number other
than 0 or 1 is used.
For example, consider the addition of 010010.1 (18.5) with 0110.110 (6.75):
010010.1
(18.5)
+0110.110 (6.75)
011001.010 (25.25)
Fixed-point subtraction is equivalent to adding while using the two's complement value
for any negative values. In subtraction, the addends must be sign extended to match each
other's length. For example, consider subtracting 0110.110 (6.75) from 010010.1 (18.5):
Most fixed-point DSP System Toolbox blocks that perform addition cast the adder inputs
to an accumulator data type before performing the addition. Therefore, no further
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9
Fixed-Point Design
shifting is necessary during the addition to line up the binary points. See “Casts” on page
9-14 for more information.
Multiplication
The multiplication of two's complement fixed-point numbers is directly analogous to
regular decimal multiplication, with the exception that the intermediate results must be
sign extended so that their left sides align before you add them together.
For example, consider the multiplication of 10.11 (-1.25) with 011 (3):
Multiplication Data Types
The following diagrams show the data types used for fixed-point multiplication in the
System Toolbox software. The diagrams illustrate the differences between the data types
used for real-real, complex-real, and complex-complex multiplication. See individual
reference pages to determine whether a particular block accepts complex fixed-point
inputs.
In most cases, you can set the data types used during multiplication in the block mask.
See Accumulator Parameters, Intermediate Product Parameters, Product Output
Parameters, and Output Parameters. These data types are defined in “Casts” on page
9-14.
Note: The following diagrams show the use of fixed-point data types in multiplication in
System Toolbox software. They do not represent actual subsystems used by the software
to perform multiplication.
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Arithmetic Operations
Real-Real Multiplication
The following diagram shows the data types used in the multiplication of two real
numbers in System Toolbox software. The software returns the output of this operation
in the product output data type, as the next figure shows.
Real-Complex Multiplication
The following diagram shows the data types used in the multiplication of a real and a
complex fixed-point number in System Toolbox software. Real-complex and complex-real
multiplication are equivalent. The software returns the output of this operation in the
product output data type, as the next figure shows.
Complex-Complex Multiplication
The following diagram shows the multiplication of two complex fixed-point numbers in
System Toolbox software. Note that the software returns the output of this operation in
the accumulator output data type, as the next figure shows.
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9-13
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Fixed-Point Design
System Toolbox blocks cast to the accumulator data type before performing addition or
subtraction operations. In the preceding diagram, this is equivalent to the C code
acc=ac;
acc-=bd;
for the subtractor, and
acc=ad;
acc+=bc;
for the adder, where acc is the accumulator.
Casts
Many fixed-point System Toolbox blocks that perform arithmetic operations allow you
to specify the accumulator, intermediate product, and product output data types, as
9-14
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Arithmetic Operations
applicable, as well as the output data type of the block. This section gives an overview of
the casts to these data types, so that you can tell if the data types you select will invoke
sign extension, padding with zeros, rounding, and/or overflow.
Casts to the Accumulator Data Type
For most fixed-point System Toolbox blocks that perform addition or subtraction, the
operands are first cast to an accumulator data type. Most of the time, you can specify
the accumulator data type on the block mask. See Accumulator Parameters. Since the
addends are both cast to the same accumulator data type before they are added together,
no extra shift is necessary to insure that their binary points align. The result of the
addition remains in the accumulator data type, with the possibility of overflow.
Casts to the Intermediate Product or Product Output Data Type
For System Toolbox blocks that perform multiplication, the output of the multiplier is
placed into a product output data type. Blocks that then feed the product output back
into the multiplier might first cast it to an intermediate product data type. Most of the
time, you can specify these data types on the block mask. See Intermediate Product
Parameters and Product Output Parameters.
Casts to the Output Data Type
Many fixed-point System Toolbox blocks allow you to specify the data type and scaling of
the block output on the mask. Remember that the software does not allow mixed types
on the input and output ports of its blocks. Therefore, if you would like to specify a fixedpoint output data type and scaling for a System Toolbox block that supports fixed-point
data types, you must feed the input port of that block with a fixed-point signal. The final
cast made by a fixed-point System Toolbox block is to the output data type of the block.
Note that although you can not mix fixed-point and floating-point signals on the input
and output ports of blocks, you can have fixed-point signals with different word and
fraction lengths on the ports of blocks that support fixed-point signals.
Casting Examples
It is important to keep in mind the ramifications of each cast when selecting these
intermediate data types, as well as any other intermediate fixed-point data types that
are allowed by a particular block. Depending upon the data types you select, overflow
and/or rounding might occur. The following two examples demonstrate cases where
overflow and rounding can occur.
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9-15
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Fixed-Point Design
Cast from a Shorter Data Type to a Longer Data Type
Consider the cast of a nonzero number, represented by a four-bit data type with two
fractional bits, to an eight-bit data type with seven fractional bits:
As the diagram shows, the source bits are shifted up so that the binary point matches
the destination binary point position. The highest source bit does not fit, so overflow
might occur and the result can saturate or wrap. The empty bits at the low end of the
destination data type are padded with either 0's or 1's:
• If overflow does not occur, the empty bits are padded with 0's.
• If wrapping occurs, the empty bits are padded with 0's.
• If saturation occurs,
• The empty bits of a positive number are padded with 1's.
• The empty bits of a negative number are padded with 0's.
You can see that even with a cast from a shorter data type to a longer data type, overflow
might still occur. This can happen when the integer length of the source data type (in
this case two) is longer than the integer length of the destination data type (in this case
9-16
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Arithmetic Operations
one). Similarly, rounding might be necessary even when casting from a shorter data type
to a longer data type, if the destination data type and scaling has fewer fractional bits
than the source.
Cast from a Longer Data Type to a Shorter Data Type
Consider the cast of a nonzero number, represented by an eight-bit data type with seven
fractional bits, to a four-bit data type with two fractional bits:
As the diagram shows, the source bits are shifted down so that the binary point matches
the destination binary point position. There is no value for the highest bit from the
source, so the result is sign extended to fill the integer portion of the destination
data type. The bottom five bits of the source do not fit into the fraction length of the
destination. Therefore, precision can be lost as the result is rounded.
In this case, even though the cast is from a longer data type to a shorter data type, all
the integer bits are maintained. Conversely, full precision can be maintained even if you
cast to a shorter data type, as long as the fraction length of the destination data type is
the same length or longer than the fraction length of the source data type. In that case,
however, bits are lost from the high end of the result and overflow might occur.
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Fixed-Point Design
The worst case occurs when both the integer length and the fraction length of the
destination data type are shorter than those of the source data type and scaling. In that
case, both overflow and a loss of precision can occur.
9-18
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Fixed-Point Support for MATLAB System Objects
Fixed-Point Support for MATLAB System Objects
In this section...
“Get Information About Fixed-Point System Objects” on page 9-19
“Display Fixed-Point Properties for System Objects” on page 9-22
“Set System Object Fixed-Point Properties” on page 9-23
“Full Precision for Fixed-Point System Objects” on page 9-24
Get Information About Fixed-Point System Objects
System objects that support fixed-point data processing have fixedpoint properties, which you can display for a particular object by typing
dsp.<ObjectName>.helpFixedPoint at the command line. See “ Display Fixed-Point
Properties for System Objects” to set the display of System object fixed-point properties.
The following signal processing System objects support fixed-point data processing.
DSP System Toolbox System Objects that Support Fixed
Point
Object
Description
Estimation
dsp.LevinsonSolver
Solve linear system of equations using LevinsonDurbin recursion
Filters
dsp.AllpoleFilter
IIR Filter with no zeros
dsp.BiquadFilter
Model biquadratic IIR (SOS) filters
dsp.CICDecimator
Decimate inputs using a Cascaded Integrator-Comb
(CIC) filter
dsp.CICInterpolator
Interpolate inputs using a Cascaded IntegratorComb (CIC) filter
dsp.DigitalFilter
Filter each channel of input over time using
discrete-time filter implementations
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Fixed-Point Design
Object
Description
dsp.FIRDecimator
Filter and downsample input signals
dsp.FIRFilter
Static or time-varying FIR filter
dsp.FIRInterpolator
Upsample and filter input signals
dsp.FIRRateConverter
Upsample, filter and downsample input signals
dsp.IIRFilter
Infinite Impulse Response (IIR) filter
dsp.LMSFilter
Compute output, error, and weights using LMS
adaptive algorithm
dsp.SubbandAnalysisFilter
Decompose signal into high-frequency and lowfrequency subbands
dsp.SubbandSynthesisFilter
Reconstruct a signal from high-frequency and lowfrequency subbands
Math Functions
9-20
dsp.ArrayVectorAdder
Add vector to array along specified dimension
dsp.ArrayVectorDivider
Divide array by vector along specified dimension
dsp.ArrayVectorMultiplier
Multiply array by vector along specified dimension
dsp.ArrayVectorSubtractor
Subtract vector from array along specified
dimension
dsp.CumulativeProduct
Compute cumulative product of channel, column, or
row elements
dsp.CumulativeSum
Compute cumulative sum of channel, column, or
row elements
dsp.LDLFactor
Factor square Hermitian positive definite matrices
into lower, upper, and diagonal components
dsp.LevinsonSolver
Solve linear system of equations using LevinsonDurbin recursion
dsp.LowerTriangularSolver
Solve LX = B for X when L is lower triangular
matrix
dsp.LUFactor
Factor square matrix into lower and upper
triangular matrices
dsp.Normalizer
Normalize input
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DSP System Toolbox System Objects that Support Fixed Point
Object
Description
dsp.UpperTriangularSolver
Solve UX = B for X when U is upper triangular
matrix
Quantizers
dsp.ScalarQuantizerDecoder
Convert each index value into quantized output
value
dsp.ScalarQuantizerEncoder
Perform scalar quantization encoding
dsp.VectorQuantizerDecoder
Find vector quantizer codeword for given index
value
dsp.VectorQuantizerEncoder
Perform vector quantization encoding
Signal Management
dsp.Buffer
Buffer an input signal
dsp.Counter
Count up or down through specified range of
numbers
Signal Operations
dsp.Convolver
Compute convolution of two inputs
dsp.DigitalDownConverter
Digitally down convert the input signal
dsp.DigitalUpConverter
Digitally up convert the input signal
dsp.NCO
Generate real or complex sinusoidal signals
dsp.PeakFinder
Determine extrema (maxima or minima) in input
signal
dsp.VariableFractionalDelay Delay input by time-varying fractional number of
sample periods
dsp.Window
Window object
Sinks
dsp.SignalSink
Log MATLAB simulation data
dsp.TimeScope
Display time-domain signals
Sources
dsp.SignalSource
Import a variable from the MATLAB workspace
dsp.SineWave
Generate discrete sine wave
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Fixed-Point Design
Object
Description
Statistics
dsp.Autocorrelator
Compute autocorrelation of vector inputs
dsp.Crosscorrelator
Compute cross-correlation of two inputs
dsp.Histogram
Output histogram of an input or sequence of inputs
dsp.Maximum
Compute maximum value in input
dsp.Mean
Compute average or mean value in input
dsp.Median
Compute median value in input
dsp.Minimum
Compute minimum value in input
dsp.Variance
Compute variance of input or sequence of inputs
Transforms
dsp.DCT
Compute discrete cosine transform (DCT) of input
dsp.FFT
Compute fast Fourier transform (FFT) of input
dsp.IDCT
Compute inverse discrete cosine transform (IDCT)
of input
dsp.IFFT
Compute inverse fast Fourier transform (IFFT) of
input
Display Fixed-Point Properties for System Objects
You can control whether the software displays fixed-point properties with either of the
following commands:
• matlab.system.showFixedPointProperties
• matlab.system.hideFixedPointProperties
at the MATLAB command line. These commands set the Show fixed-point properties
display option. You can also set the display option directly via the MATLAB preferences
dialog box. Click Preferences on the MATLAB Toolstrip. The Preferences dialog box
opens. Scroll down and select System Objects. Finally, select or deselect Show fixedpoint properties.
9-22
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DSP System Toolbox System Objects that Support Fixed Point
If an object supports fixed-point data processing, its fixed-point properties are active
regardless of whether they are displayed or not.
Set System Object Fixed-Point Properties
A number of properties affect the fixed-point data processing used by a System object.
Objects perform fixed-point processing and use the current fixed-point property settings
when they receive fixed-point input.
You change the values of fixed-point properties in the same way as you change any
System object property value. See “Configure Components for Your System”. You also use
the Fixed-Point Designer numerictype object to specify the desired data type as fixed-
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Fixed-Point Design
point, the signedness, and the word- and fraction-lengths. System objects support these
values of DataTypeMode: Boolean, Double, Single, and Fixed-point: binary
point scaling.
In the same way as for blocks, the data type properties of many System objects can set
the appropriate word lengths and scalings automatically by using full precision. System
objects assume that the target specified on the Configuration Parameters Hardware
Implementation target is ASIC/FPGA.
If you have not set the property that activates a dependent property and you attempt
to change that dependent property, a warning message displays. For example, for the
dsp.FFT object, before you set CustomOutputDataType to numerictype(1,32,30)
you must set OutputDataType to 'Custom'.
Note: System objects do not support fixed-point word lengths greater than 128 bits.
For any System object provided in the Toolbox, the fimath settings for any fimath
attached to a fi input or a fi property are ignored. Outputs from a System object never
have an attached fimath.
Full Precision for Fixed-Point System Objects
FullPrecisionOverride is a convenience property that, when you set to true,
automatically sets the appropriate properties for an object to use full-precision to process
fixed-point input. For System objects, full precision, fixed-point operation refers to
growing just enough additional bits to compute the ideal full precision result. This
operation has no minimum or maximum range overflow nor any precision loss due to
rounding or underflow. It is also independent of any hardware-specific settings. The
data types chosen are based only on known data type ranges and not on actual numeric
values. Unlike full precision for dfilt objects, full precision for System objects does not
optimize coefficient values.
When you set the FullPrecisionOverride property to true, the other fixed-point
properties it controls no longer apply and any of their non-default values are ignored.
These properties are also hidden. To specify individual fixed-point properties, you must
first set FullPrecisionOverride to false.
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Specify Fixed-Point Attributes for Blocks
Specify Fixed-Point Attributes for Blocks
In this section...
“Fixed-Point Block Parameters” on page 9-25
“Specify System-Level Settings” on page 9-28
“Inherit via Internal Rule” on page 9-29
“Specify Data Types for Fixed-Point Blocks” on page 9-39
Fixed-Point Block Parameters
System Toolbox blocks that have fixed-point support usually allow you to specify fixedpoint characteristics through block parameters. By specifying data type and scaling
information for these fixed-point parameters, you can simulate your target hardware
more closely.
Note: Floating-point inheritance takes precedence over the settings discussed in this
section. When the block has floating-point input, all block data types match the input.
You can find most fixed-point parameters on the Data Types pane of System Toolbox
blocks. The following figure shows a typical Data Types pane.
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Fixed-Point Design
All System Toolbox blocks with fixed-point capabilities share a set of common
parameters, but each block can have a different subset of these fixed-point parameters.
The following table provides an overview of the most common fixed-point block
parameters.
Fixed-Point Data Type
Parameter
Description
Rounding Mode
Specifies the rounding mode for the block to use when the
specified data type and scaling cannot exactly represent the
result of a fixed-point calculation.
See “Rounding Modes” on page 9-7 for more information on the
available options.
Overflow Mode
Specifies the overflow mode to use when the result of a fixedpoint calculation does not fit into the representable range of
the specified data type.
See “Overflow Handling” on page 9-7 for more information on
the available options.
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Specify Fixed-Point Attributes for Blocks
Fixed-Point Data Type
Parameter
Description
Intermediate Product
Specifies the data type and scaling of the intermediate product
for fixed-point blocks. Blocks that feed multiplication results
back to the input of the multiplier use the intermediate
product data type.
See the reference page of a specific block to learn about the
intermediate product data type for that block.
Product Output
Specifies the data type and scaling of the product output for
fixed-point blocks that must compute multiplication results.
See the reference page of a specific block to learn about the
product output data type for that block. For or complexcomplex multiplication, the multiplication result is in the
accumulator data type. See “Multiplication Data Types”
on page 9-12 for more information on complex fixed-point
multiplication in System toolbox software.
Accumulator
Specifies the data type and scaling of the accumulator (sum)
for fixed-point blocks that must hold summation results for
further calculation. Most such blocks cast to the accumulator
data type before performing the add operations (summation).
See the reference page of a specific block for details on the
accumulator data type of that block.
Output
Specifies the output data type and scaling for blocks.
Using the Data Type Assistant
The Data Type Assistant is an interactive graphical tool available on the Data Types
pane of some fixed-point System Toolbox blocks.
To learn more about using the Data Type Assistant to help you specify block data type
parameters, see the following section of the Simulink documentation:
“Specify Data Types Using Data Type Assistant”
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Fixed-Point Design
Checking Signal Ranges
Some fixed-point System Toolbox blocks have Minimum and Maximum parameters on
the Data Types pane. When a fixed-point data type has these parameters, you can use
them to specify appropriate minimum and maximum values for range checking purposes.
To learn how to specify signal ranges and enable signal range checking, see “Signal
Ranges” in the Simulink documentation.
Specify System-Level Settings
You can monitor and control fixed-point settings for System Toolbox blocks at a system or
subsystem level with the Fixed-Point Tool. For additional information on these subjects,
see
• The fxptdlg reference page — A reference page on the Fixed-Point Tool in the
Simulink documentation
• “Fixed-Point Tool” — A tutorial that highlights the use of the Fixed-Point Tool in the
Fixed-Point Designer software documentation
Logging
The Fixed-Point Tool logs overflows, saturations, and simulation minimums and
maximums for fixed-point System Toolbox blocks. The Fixed-Point Tool does not log
overflows and saturations when the Data overflow line in the Diagnostics > Data
Integrity pane of the Configuration Parameters dialog box is set to None.
Autoscaling
You can use the Fixed-Point Tool autoscaling feature to set the scaling for System
Toolbox fixed-point data types.
Data type override
System Toolbox blocks obey the Use local settings, Double, Single, and
Off modes of the Data type override parameter in the Fixed-Point Tool. The
Scaled double mode is also supported for System Toolboxes source and byte-shuffling
blocks, and for some arithmetic blocks such as Difference and Normalization.
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Specify Fixed-Point Attributes for Blocks
Inherit via Internal Rule
Selecting appropriate word lengths and scalings for the fixed-point parameters in your
model can be challenging. To aid you, an Inherit via internal rule choice is often
available for fixed-point block data type parameters, such as the Accumulator and
Product output signals. The following sections describe how the word and fraction
lengths are selected for you when you choose Inherit via internal rule for a fixedpoint block data type parameter in System Toolbox software:
• “Internal Rule for Accumulator Data Types” on page 9-29
• “Internal Rule for Product Data Types” on page 9-30
• “Internal Rule for Output Data Types” on page 9-30
• “The Effect of the Hardware Implementation Pane on the Internal Rule” on page
9-30
• “Internal Rule Examples” on page 9-32
Note: In the equations in the following sections, WL = word length and FL = fraction
length.
Internal Rule for Accumulator Data Types
The internal rule for accumulator data types first calculates the ideal, full-precision
result. Where N is the number of addends:
WLideal accumulator = WLinput to accumulator + floor(log 2 ( N - 1)) + 1
FLideal accumulator = FLinput to accumulator
For example, consider summing all the elements of a vector of length 6 and data type
sfix10_En8. The ideal, full-precision result has a word length of 13 and a fraction length
of 8.
The accumulator can be real or complex. The preceding equations are used for both the
real and imaginary parts of the accumulator. For any calculation, after the full-precision
result is calculated, the final word and fraction lengths set by the internal rule are
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Fixed-Point Design
affected by your particular hardware. See “The Effect of the Hardware Implementation
Pane on the Internal Rule” on page 9-30 for more information.
Internal Rule for Product Data Types
The internal rule for product data types first calculates the ideal, full-precision result:
WLideal product = WLinput 1 + WLinput 2
FLideal product = FLinput 1 + FLinput 2
For example, multiplying together the elements of a real vector of length 2 and data type
sfix10_En8. The ideal, full-precision result has a word length of 20 and a fraction length
of 16.
For real-complex multiplication, the ideal word length and fraction length is used for
both the complex and real portion of the result. For complex-complex multiplication, the
ideal word length and fraction length is used for the partial products, and the internal
rule for accumulator data types described above is used for the final sums. For any
calculation, after the full-precision result is calculated, the final word and fraction
lengths set by the internal rule are affected by your particular hardware. See “The Effect
of the Hardware Implementation Pane on the Internal Rule” on page 9-30 for more
information.
Internal Rule for Output Data Types
A few System Toolbox blocks have an Inherit via internal rule choice available
for the block output. The internal rule used in these cases is block-specific, and the
equations are listed in the block reference page.
As with accumulator and product data types, the final output word and fraction lengths
set by the internal rule are affected by your particular hardware, as described in “The
Effect of the Hardware Implementation Pane on the Internal Rule” on page 9-30.
The Effect of the Hardware Implementation Pane on the Internal Rule
The internal rule selects word lengths and fraction lengths that are appropriate for your
hardware. To get the best results using the internal rule, you must specify the type of
hardware you are using on the Hardware Implementation pane of the Configuration
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Specify Fixed-Point Attributes for Blocks
Parameters dialog box. You can open this dialog box from the Simulation menu in your
model.
ASIC/FPGA
On an ASIC/FPGA target, the ideal, full-precision word length and fraction length
calculated by the internal rule are used. If the calculated ideal word length is larger than
the largest allowed word length, you receive an error. The largest word length allowed for
Simulink and System Toolbox software is 128 bits.
Other targets
For all targets other than ASIC/FPGA, the ideal, full-precision word length calculated
by the internal rule is rounded up to the next available word length of the target. The
calculated ideal fraction length is used, keeping the least-significant bits.
If the calculated ideal word length for a product data type is larger than the largest
word length on the target, you receive an error. If the calculated ideal word length for an
accumulator or output data type is larger than the largest word length on the target, the
largest target word length is used.
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Fixed-Point Design
Internal Rule Examples
The following sections show examples of how the internal rule interacts with the
Hardware Implementation pane to calculate accumulator data types and product data
types.
Accumulator Data Types
Consider the following model ex_internalRule_accumExp.
In the Difference blocks, the Accumulator parameter is set to Inherit: Inherit
via internal rule, and the Output parameter is set to Inherit: Same as
accumulator. Therefore, you can see the accumulator data type calculated by the
internal rule on the output signal in the model.
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Specify Fixed-Point Attributes for Blocks
In the preceding model, the Device type parameter in the Hardware Implementation
pane of the Configuration Parameters dialog box is set to ASIC/FPGA. Therefore, the
accumulator data type used by the internal rule is the ideal, full-precision result.
Calculate the full-precision word length for each of the Difference blocks in the model:
WLideal accumulator = WLinput to accumulator + floor(log 2 (numb er of accumulations)) + 1
WLideal accumulator = 9 + floor(log 2 (1))) + 1
WLideal accumulator = 9 + 0 + 1 = 10
WLideal accumulator1 = WLinpput to accumulator1 + floor(log 2 ( number of accumulations)) + 1
WLideal accumulator1 = 16 + floor(log 2 (1)) + 1
WLideal accumulator1 = 16 + 0 + 1 = 17
WLideal accumulator 2 = WLinput to accumulator2 + floor(log 2 (number of accumulations)) + 1
WLideal accumulatoor 2 = 127 + floor(log 2 (1)) + 1
WLideal accumulator 2 = 127 + 0 + 1 = 128
Calculate the full-precision fraction length, which is the same for each Matrix Sum block
in this example:
FLideal accumulator = FLinput to accumulator
FLideal accumulator = 4
Now change the Device type parameter in the Hardware Implementation pane
of the Configuration Parameters dialog box to 32–bit Embedded Processor, by
changing the parameters as shown in the following figure.
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Fixed-Point Design
As you can see in the dialog box, this device has 8-, 16-, and 32-bit word lengths
available. Therefore, the ideal word lengths of 10, 17, and 128 bits calculated by the
internal rule cannot be used. Instead, the internal rule uses the next largest available
word length in each case You can see this if you rerun the model, as shown in the
following figure.
9-34
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Specify Fixed-Point Attributes for Blocks
Product Data Types
Consider the following model ex_internalRule_prodExp.
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Fixed-Point Design
In the Array-Vector Multiply blocks, the Product Output parameter is set to Inherit:
Inherit via internal rule, and the Output parameter is set to Inherit: Same
as product output. Therefore, you can see the product output data type calculated
by the internal rule on the output signal in the model. The setting of the Accumulator
parameter does not matter because this example uses real values.
For the preceding model, the Device type parameter in the Hardware
Implementation pane of the Configuration Parameters dialog box is set to ASIC/FPGA.
Therefore, the product data type used by the internal rule is the ideal, full-precision
result.
Calculate the full-precision word length for each of the Array-Vector Multiply blocks in
the model:
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Specify Fixed-Point Attributes for Blocks
WLideal product = WLinput a + WLinput b
WLideal product = 7 + 5 = 12
WLideal product1 = WLinput a + WLinput b
WLideal product1 = 16 + 15 = 31
Calculate the full-precision fraction length, which is the same for each Array-Vector
Multiply block in this example:
FLideal accumulator = FLinput to accumulator
FLideal accumulator = 4
Now change the Device type parameter in the Hardware Implementation pane of
the Configuration Parameters dialog box to 32–bit Embedded Processor, as shown in
the following figure.
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Fixed-Point Design
As you can see in the dialog box, this device has 8-, 16-, and 32-bit word lengths
available. Therefore, the ideal word lengths of 12 and 31 bits calculated by the internal
rule cannot be used. Instead, the internal rule uses the next largest available word
length in each case. You can see this if you rerun the model, as shown in the following
figure.
9-38
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Specify Fixed-Point Attributes for Blocks
Specify Data Types for Fixed-Point Blocks
The following sections show you how to use the Fixed-Point Tool to select appropriate
data types for fixed-point blocks in the ex_fixedpoint_tut model:
• “Prepare the Model” on page 9-39
• “Use Data Type Override to Find a Floating-Point Benchmark” on page 9-44
• “Use the Fixed-Point Tool to Propose Fraction Lengths” on page 9-45
• “Examine the Results and Accept the Proposed Scaling” on page 9-45
Prepare the Model
1
Open the model by typing ex_fixedpoint_tut at the MATLAB command line.
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9
Fixed-Point Design
This model uses the Cumulative Sum block to sum the input coming from the FixedPoint Sources subsystem. The Fixed-Point Sources subsystem outputs two signals
with different data types:
• The Signed source has a word length of 16 bits and a fraction length of 15 bits.
2
• The Unsigned source has a word length of 16 bits and a fraction length of 16 bits.
Run the model to check for overflow. MATLAB displays the following warnings at
the command line:
Warning: Overflow occurred. This originated from
'ex_fixedpoint_tut/Signed Cumulative Sum'.
Warning: Overflow occurred. This originated from
'ex_fixedpoint_tut/Unsigned Cumulative Sum'.
3
9-40
According to these warnings, overflow occurs in both Cumulative Sum blocks.
To investigate the overflows in this model, use the Fixed-Point Tool. You can
open the Fixed-Point Tool by selecting Tools > Fixed-Point > Fixed-Point Tool
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Specify Fixed-Point Attributes for Blocks
4
from the model menu. Turn on logging for all blocks in your model by setting the
Fixed-point instrumentation mode parameter to Minimums, maximums and
overflows.
Now that you have turned on logging, rerun the model by clicking the Simulation
button.
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Fixed-Point Design
5
The results of the simulation appear in a table in the central Contents pane of the
Fixed-Point Tool. Review the following columns:
• Name — Provides the name of each signal in the following format: Subsystem
Name/Block Name: Signal Name.
• SimDT — The simulation data type of each logged signal.
• SpecifiedDT — The data type specified on the block dialog for each signal.
• SimMin — The smallest representable value achieved during simulation for each
logged signal.
• SimMax — The largest representable value achieved during simulation for each
logged signal.
• OverflowWraps — The number of overflows that wrap during simulation.
For more information on each of the columns in this table, see the “Contents Pane”
section of the Simulink fxptdlg function reference page.
You can also see that the SimMin and SimMax values for the Accumulator data
types range from 0 to .9997. The logged results indicate that 8,192 overflows
wrapped during simulation in the Accumulator data type of the Signed Cumulative
Sum block. Similarly, the Accumulator data type of the Unsigned Cumulative Sum
block had 16,383 overflows wrap during simulation.
To get more information about each of these data types, highlight them in the
6
Contents pane, and click the Show details for selected result button (
)
Assume a target hardware that supports 32-bit integers, and set the Accumulator
word length in both Cumulative Sum blocks to 32. To do so, perform the following
steps:
1
Right-click the Signed Cumulative Sum: Accumulator row in the FixedPoint Tool pane, and select Highlight Block In Model.
2
Double-click the block in the model, and select the Data Types pane of the
dialog box.
3
Open the Data Type Assistant for Accumulator by clicking the Assistant
button (
4
9-42
) in the Accumulator data type row.
Set the Mode to Fixed Point. To see the representable range of the current
specified data type, click the Fixed-point details link. The tool displays the
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Specify Fixed-Point Attributes for Blocks
representable maximum and representable minimum values for the current data
type.
5
Change the Word length to 32, and click the Refresh details button in the
Fixed-point details section to see the updated representable range. When you
change the value of the Word length parameter, the data type string in the
Data Type edit box automatically updates.
6
Click OK on the block dialog box to save your changes and close the window.
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Fixed-Point Design
7
Set the word length of the Accumulator data type of the Unsigned Cumulative
Sum block to 32 bits. You can do so in one of two ways:
• Type the data type string fixdt([],32,0) directly into Data Type edit box
for the Accumulator data type parameter.
7
• Perform the same steps you used to set the word length of the Accumulator
data type of the Signed Cumulative Sum block to 32 bits.
To verify your changes in word length and check for overflow, rerun your model. To
do so, click the Simulate button in the Fixed-Point Tool.
The Contents pane of the Fixed-Point Tool updates, and you can see that no
overflows occurred in the most recent simulation. However, you can also see that the
SimMin and SimMax values range from 0 to 0. This underflow happens because
the fraction length of the Accumulator data type is too small. The SpecifiedDT
cannot represent the precision of the data values. The following sections discuss how
to find a floating-point benchmark and use the Fixed-Point Tool to propose fraction
lengths.
Use Data Type Override to Find a Floating-Point Benchmark
The Data type override feature of the Fixed-Point tool allows you to override the data
types specified in your model with floating-point types. Running your model in Double
override mode gives you a reference range to help you select appropriate fraction lengths
for your fixed-point data types. To do so, perform the following steps:
1
2
3
4
9-44
Open the Fixed-Point Tool and set Data type override to Double.
Run your model by clicking the Run simulation and store active results button.
Examine the results in the Contents pane of the Fixed-Point Tool. Because you ran
the model in Double override mode, you get an accurate, idealized representation of
the simulation minimums and maximums. These values appear in the SimMin and
SimMax parameters.
Now that you have an accurate reference representation of the simulation minimum
and maximum values, you can more easily choose appropriate fraction lengths.
Before making these choices, save your active results to reference so you can use
them as your floating-point benchmark. To do so, select Results > Move Active
Results To Reference from the Fixed-Point Tool menu. The status displayed in the
Run column changes from Active to Reference for all signals in your model.
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Specify Fixed-Point Attributes for Blocks
Use the Fixed-Point Tool to Propose Fraction Lengths
Now that you have your Double override results saved as a floating-point reference, you
are ready to propose fraction lengths.
1
2
3
To propose fraction lengths for your data types, you must have a set of Active
results available in the Fixed-Point Tool. To produce an active set of results,
simply rerun your model. The tool now displays both the Active results and the
Reference results for each signal.
Select the Use simulation min/max if design min/max is not available check
box. You did not specify any design minimums or maximums for the data types
in this model. Thus, the tool uses the logged information to compute and propose
fraction lengths. For information on specifying design minimums and maximums,
see “Signal Ranges” in the Simulink documentation.
). The tool populates the proposed
Click the Propose fraction lengths button (
data types in the ProposedDT column of the Contents pane. The corresponding
proposed minimums and maximums are displayed in the ProposedMin and
ProposedMax columns.
Examine the Results and Accept the Proposed Scaling
Before accepting the fraction lengths proposed by the Fixed-Point Tool, it is important
to look at the details of that data type. Doing so allows you to see how much of your data
the suggested data type can represent. To examine the suggested data types and accept
the proposed scaling, perform the following steps:
1
In the Contents pane of the Fixed-Point Tool, you can see the proposed fraction
lengths for the data types in your model.
• The proposed fraction length for the Accumulator data type of both the Signed
and Unsigned Cumulative Sum blocks is 17 bits.
• To get more details about the proposed scaling for a particular data type,
highlight the data type in the Contents pane of the Fixed-Point Tool.
• Open the Autoscale Information window for the highlighted data type by clicking
2
the Show autoscale information for the selected result button (
).
When the Autoscale Information window opens, check the Value and Percent
Proposed Representable columns for the Simulation Minimum and
Simulation Maximum parameters. You can see that the proposed data type can
represent 100% of the range of simulation data.
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Fixed-Point Design
3
To accept the proposed data types, select the check box in the Accept column for
each data type whose proposed scaling you want to keep. Then, click the Apply
accepted fraction lengths button (
4
). The tool updates the specified data types
on the block dialog boxes and the SpecifiedDT column in the Contents pane.
To verify the newly accepted scaling, set the Data type override parameter back
to Use local settings, and run the model. Looking at Contents pane of the FixedPoint Tool, you can see the following details:
• The SimMin and SimMax values of the Active run match the SimMin and
SimMax values from the floating-point Reference run.
• There are no longer any overflows.
• The SimDT does not match the SpecifiedDT for the Accumulator data type of
either Cumulative Sum block. This difference occurs because the Cumulative
Sum block always inherits its Signedness from the input signal and only allows
you to specify a Signedness of Auto. Therefore, the SpecifiedDT for both
Accumulator data types is fixdt([],32,17). However, because the Signed
Cumulative Sum block has a signed input signal, the SimDT for the Accumulator
parameter of that block is also signed (fixdt(1,32,17)). Similarly, the SimDT
for the Accumulator parameter of the Unsigned Cumulative Sum block inherits
its Signedness from its input signal and thus is unsigned (fixdt(0,32,17)).
9-46
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Quantizers
Quantizers
In this section...
“Scalar Quantizers” on page 9-47
“Vector Quantizers” on page 9-54
Scalar Quantizers
• “Analysis and Synthesis of Speech” on page 9-47
• “Identify Your Residual Signal and Reflection Coefficients” on page 9-49
• “Create a Scalar Quantizer” on page 9-50
Analysis and Synthesis of Speech
You can use blocks from the DSP System Toolbox Quantizers library to design scalar
quantizer encoders and decoders. A speech signal is usually represented in digital
format, which is a sequence of binary bits. For storage and transmission applications,
it is desirable to compress a signal by representing it with as few bits as possible,
while maintaining its perceptual quality. Quantization is the process of representing
a signal with a reduced level of precision. If you decrease the number of bits allocated
for the quantization of your speech signal, the signal is distorted and the speech quality
degrades.
In narrowband digital speech compression, speech signals are sampled at a rate of 8000
samples per second. Each sample is typically represented by 8 bits. This corresponds to
a bit rate of 64 kbits per second. Further compression is possible at the cost of quality.
Most of the current low bit rate speech coders are based on the principle of linear
predictive speech coding. This topic shows you how to use the Scalar Quantizer Encoder
and Scalar Quantizer Decoder blocks to implement a simple speech coder.
1
Type ex_sq_example1 at the MATLAB command line to open the example model.
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Fixed-Point Design
This model preemphasizes the input speech signal by applying an FIR filter. Then,
it calculates the reflection coefficients of each frame using the Levinson-Durbin
algorithm. The model uses these reflection coefficients to create the linear prediction
analysis filter (lattice-structure). Next, the model calculates the residual signal
by filtering each frame of the preemphasized speech samples using the reflection
coefficients. The residual signal, which is the output of the analysis stage, usually
has a lower energy than the input signal. The blocks in the synthesis stage of the
model filter the residual signal using the reflection coefficients and apply an all-pole
deemphasis filter. Note that the deemphasis filter is the inverse of the preemphasis
filter. The result is the full recovery of the original signal.
2
9-48
Run this model.
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Quantizers
3
Double-click the Original Signal and Processed Signal blocks and listen to both the
original and the processed signal.
There is no significant difference between the two because no quantization was
performed.
To better approximate a real-world speech analysis and synthesis system, you need to
quantize the residual signal and reflection coefficients before they are transmitted. The
following topics show you how to design scalar quantizers to accomplish this task.
Identify Your Residual Signal and Reflection Coefficients
In the previous topic, “Analysis and Synthesis of Speech” on page 9-47, you learned
the theory behind the LPC Analysis and Synthesis of Speech example model. In this
topic, you define the residual signal and the reflection coefficients in your MATLAB
workspace as the variables E and K, respectively. Later, you use these values to create
your scalar quantizers:
1
Open the example model by typing ex_sq_example2 at the MATLAB command
line.
2
Save the model file as ex_sq_example2 in your working folder.
3
From the Simulink Sinks library, click-and-drag two To Workspace blocks into your
model.
4
Connect the output of the Levinson-Durbin block to one of the To Workspace blocks.
5
Double-click this To Workspace block and set the Variable name parameter to K.
Click OK.
6
Connect the output of the Time-Varying Analysis Filter block to the other To
Workspace block.
7
Double-click this To Workspace block and set the Variable name parameter to E.
Click OK.
You model should now look similar to this figure.
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Fixed-Point Design
8
Run your model.
The residual signal, E, and your reflection coefficients, K, are defined in the
MATLAB workspace. In the next topic, you use these variables to design your scalar
quantizers.
Create a Scalar Quantizer
In this topic, you create scalar quantizer encoders and decoders to quantize the residual
signal, E, and the reflection coefficients, K:
1
9-50
If the model you created in “Identify Your Residual Signal and Reflection
Coefficients” on page 9-49 is not open on your desktop, you can open an
equivalent model by typing ex_sq_example2 at the MATLAB command prompt.
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Quantizers
2
Run this model to define the variables E and K in the MATLAB workspace.
3
From the Quantizers library, click-and-drag a Scalar Quantizer Design block into
your model. Double-click this block to open the SQ Design Tool GUI.
4
For the Training Set parameter, enter K.
The variable K represents the reflection coefficients you want to quantize. By
definition, they range from -1 to 1.
Note: Theoretically, the signal that is used as the Training Set parameter should
contain a representative set of values for the parameter to be quantized. However,
this example provides an approximation to this global training process.
5
For the Number of levels parameter, enter 128.
Assume that your compression system has 7 bits to represent each reflection
coefficient. This means it is capable of representing 27 or 128 values. The Number of
levels parameter is equal to the total number of codewords in the codebook.
6
Set the Block type parameter to Both.
7
For the Encoder block name parameter, enter SQ Encoder - Reflection
Coefficients.
8
For the Decoder block name parameter, enter SQ Decoder - Reflection
Coefficients.
9
Make sure that your desired destination model, ex_sq_example2, is the current
model. You can type gcs in the MATLAB Command Window to display the name of
your current model.
10 In the SQ Design Tool GUI, click the Design and Plot button to apply the changes
you made to the parameters.
The GUI should look similar to the following figure.
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9
Fixed-Point Design
11 Click the Generate Model button.
Two new blocks, SQ Encoder - Reflection Coefficients and SQ Decoder - Reflection
Coefficients, appear in your model file.
12 Click the SQ Design Tool GUI and, for the Training Set parameter, enter E.
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Quantizers
13 Repeat steps 5 to 11 for the variable E, which represents the residual signal you
want to quantize. In steps 6 and 7, name your blocks SQ Encoder - Residual and SQ
Decoder - Residual.
Once you have completed these steps, two new blocks, SQ Encoder - Residual and SQ
Decoder - Residual, appear in your model file.
14 Close the SQ Design Tool GUI. You do not need to save the SQ Design Tool session.
You have now created a scalar quantizer encoder and a scalar quantizer decoder for
each signal you want to quantize. You are ready to quantize the residual signal, E,
and the reflection coefficients, K.
15 Save the model as ex_sq_example3. Your model should look similar to the
following figure.
16 Run your model.
17 Double-click the Original Signal and Processed Signal blocks, and listen to both
signals.
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9
Fixed-Point Design
Again, there is no perceptible difference between the two. You can therefore conclude
that quantizing your residual and reflection coefficients did not affect the ability of
your system to accurately reproduce the input signal.
You have now quantized the residual and reflection coefficients. The bit rate of a
quantization system is calculated as (bits per frame)*(frame rate).
In this example, the bit rate is [(80 residual samples/frame)*(7 bits/sample) + (12
reflection coefficient samples/frame)*(7 bits/sample)]*(100 frames/second), or 64.4 kbits
per second. This is higher than most modern speech coders, which typically have a bit
rate of 8 to 24 kbits per second. If you decrease the number of bits allocated for the
quantization of the reflection coefficients or the residual signal, the overall bit rate would
decrease. However, the speech quality would also degrade.
For information about decreasing the bit rate without affecting speech quality, see
“Vector Quantizers” on page 9-54.
Vector Quantizers
• “Build Your Vector Quantizer Model” on page 9-54
• “Configure and Run Your Model” on page 9-56
Build Your Vector Quantizer Model
In the previous section, you created scalar quantizer encoders and decoders and used
them to quantize your residual signal and reflection coefficients. The bit rate of your
scalar quantization system was 64.4 kbits per second. This bit rate is higher than most
modern speech coders. To accommodate a greater number of users in each channel, you
need to lower this bit rate while maintaining the quality of your speech signal. You can
use vector quantizers, which exploit the correlations between each sample of a signal, to
accomplish this task.
In this topic, you modify your scalar quantization model so that you are using a split
vector quantizer to quantize your reflection coefficients:
1
9-54
Open a model similar to the one you created in “Create a Scalar Quantizer” on
page 9-50 by typing ex_vq_example1 at the MATLAB command prompt. The
example model ex_vq_example1 adds a new LSF Vector Quantization subsystem
to the ex_sq_example3 model. This subsystem is preconfigured to work as a
vector quantizer. You can use this subsystem to encode and decode your reflection
coefficients using the split vector quantization method.
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Quantizers
2
Delete the SQ Encoder – Reflection Coefficients and SQ Decoder – Reflection
Coefficients blocks.
3
From the Simulink Sinks library, click-and-drag a Terminator block into your model.
4
From the DSP System Toolbox Estimation > Linear Prediction library, click-anddrag a LSF/LSP to LPC Conversion block and two LPC to/from RC blocks into your
model.
5
Connect the blocks as shown in the following figure. You do not need to connect
Terminator blocks to the P ports of the LPC to/from RC blocks. These ports
disappear once you set block parameters.
You have modified your model to include a subsystem capable of vector quantization. In
the next topic, you reset your model parameters to quantize your reflection coefficients
using the split vector quantization method.
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Fixed-Point Design
Configure and Run Your Model
In the previous topic, you configured your scalar quantization model for vector
quantization by adding the LSF Vector Quantization subsystem. In this topic, you set
your block parameters and quantize your reflection coefficients using the split vector
quantization method.
1
If the model you created in “Build Your Vector Quantizer Model” on page
9-54 is not open on your desktop, you can open an equivalent model by typing
ex_vq_example2 at the MATLAB command prompt.
2
Double-click the LSF Vector Quantization subsystem, and then double-click the LSF
Split VQ subsystem.
The subsystem opens, and you see the three Vector Quantizer Encoder blocks used to
implement the split vector quantization method.
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Quantizers
This subsystem divides each vector of 10 line spectral frequencies (LSFs), which
represent your reflection coefficients, into three LSF subvectors. Each of these
subvectors is sent to a separate vector quantizer. This method is called split vector
quantization.
3
Double-click the VQ of LSF: 1st subvector block.
The Block Parameters: VQ of LSF: 1st subvector dialog box opens.
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Fixed-Point Design
The variable CB_lsf1to3_10bit is the codebook for the subvector that contains
the first three elements of the LSF vector. It is a 3-by-1024 matrix, where 3 is the
number of elements in each codeword and 1024 is the number of codewords in the
codebook. Because 210 = 1024 , it takes 10 bits to quantize this first subvector.
Similarly, a 10-bit vector quantizer is applied to the second and third subvectors,
9-58
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Quantizers
which contain elements 4 to 6 and 7 to 10 of the LSF vector, respectively. Therefore,
it takes 30 bits to quantize all three subvectors.
Note: If you used the vector quantization method to quantize your reflection
coefficients, you would need 230 or 1.0737e9 codebook values to achieve the same
degree of accuracy as the split vector quantization method.
4
In your model file, double-click the Autocorrelation block and set the Maximum
non-negative lag (less than input length) parameter to 10. Click OK.
This parameter controls the number of linear polynomial coefficients (LPCs) that are
input to the split vector quantization method.
5
Double-click the LPC to/from RC block that is connected to the input of the LSF
Vector Quantization subsystem. Clear the Output normalized prediction error
power check box. Click OK.
6
Double-click the LSF/LSP to LPC Conversion block and set the Input parameter to
LSF in range (0 to pi). Click OK.
7
Double-click the LPC to/from RC block that is connected to the output of the LSF/
LSP to LPC Conversion block. Set the Type of conversion parameter to LPC to
RC, and clear the Output normalized prediction error power check box. Click
OK.
8
Run your model.
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Fixed-Point Design
9
Double-click the Original Signal and Processed Signal blocks to listen to both the
original and the processed signal.
There is no perceptible difference between the two. Quantizing your reflection
coefficients using a split vector quantization method produced good quality speech
without much distortion.
You have now used the split vector quantization method to quantize your reflection
coefficients. The vector quantizers in the LSF Vector Quantization subsystem use 30 bits
to quantize a frame containing 80 reflection coefficients. The bit rate of a quantization
system is calculated as (bits per frame)*(frame rate).
In this example, the bit rate is [(80 residual samples/frame)*(7 bits/sample) + (30 bits/
frame)]*(100 frames/second), or 59 kbits per second. This is less than 64.4 kbits per
second, the bit rate of the scalar quantization system. However, the quality of the speech
signal did not degrade. If you want to further reduce the bit rate of your system, you can
use the vector quantization method to quantize the residual signal.
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Fixed-Point Filter Design
Fixed-Point Filter Design
In this section...
“Overview of Fixed-Point Filters” on page 9-61
“Data Types for Filter Functions” on page 9-61
“Floating-Point to Fixed-Point Filter Conversion” on page 9-62
“Create an FIR Filter Using Integer Coefficients” on page 9-71
“Fixed-Point Filtering in Simulink” on page 9-87
Overview of Fixed-Point Filters
The most common use of fixed-point filters is in the DSP chips, where the data storage
capabilities are limited, or embedded systems and devices where low-power consumption
is necessary. For example, the data input may come from a 12 bit ADC, the data bus
may be 16 bit, and the multiplier may have 24 bits. Within these space constraints, DSP
System Toolbox software enables you to design the best possible fixed-point filter.
What Is a Fixed-Point Filter?
A fixed-point filter uses fixed-point arithmetic and is represented by an equation
with fixed-point coefficients. To learn about fixed-point arithmetic, see “Arithmetic
Operations”.
Data Types for Filter Functions
• “Data Type Support” on page 9-61
• “Fixed Data Type Support” on page 9-62
• “Single Data Type Support” on page 9-62
Data Type Support
There are three different data types supported in DSP System Toolbox software:
• Fixed — Requires Fixed-Point Designer and is supported by packages listed in “Fixed
Data Type Support” on page 9-62.
• Double — Double precision, floating point and is the default data type for DSP System
Toolbox software; accepted by all functions
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Fixed-Point Design
• Single — Single precision, floating point and is supported by specific packages
outlined in “Single Data Type Support” on page 9-62.
Fixed Data Type Support
To use fixed data type, you must have Fixed-Point Designer. Type ver at the MATLAB
command prompt to get a listing of all installed products.
The fixed data type is reserved for any filter whose property arithmetic is set to
fixed. Furthermore all functions that work with this filter, whether in analysis or
design, also accept and support the fixed data types.
To set the filter's arithmetic property:
f = fdesign.bandpass(.35,.45,.55,.65,60,1,60);
Hf = design(f, 'equiripple');
Hf.Arithmetic = 'fixed';
Single Data Type Support
The support of the single data types comes in two varieties. First, input data of type
single can be fed into a double filter, where it is immediately converted to double. Thus,
while the filter still operates in the double mode, the single data type input does not
break it. The second variety is where the filter itself is set to single precision. In this
case, it accepts only single data type input, performs all calculations, and outputs data
in single precision. Furthermore, such analyses as noisepsd and freqrespest also
operate in single precision.
To set the filter to single precision:
>> f = fdesign.bandpass(.35,.45,.55,.65,60,1,60);
>> Hf = design(f, 'equiripple');
>> Hf.Arithmetic = 'single';
Floating-Point to Fixed-Point Filter Conversion
• “Process Overview” on page 9-63
• “Design the Filter” on page 9-63
• “Quantize the Coefficients” on page 9-64
• “Dynamic Range Analysis” on page 9-67
• “Compare Magnitude Response and Magnitude Response Estimate” on page 9-68
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Fixed-Point Filter Design
Process Overview
The conversion from floating point to fixed point consists of two main parts: quantizing
the coefficients and performing the dynamic range analysis. Quantizing the coefficients
is a process of converting the coefficients to fixed-point numbers. The dynamic range
analysis is a process of fine tuning the scaling of each node to ensure that the fraction
lengths are set for full input range coverage and maximum precision. The following steps
describe this conversion process.
Design the Filter
Start by designing a regular, floating-point, equiripple bandpass filter, as shown in the
following figure.
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Fixed-Point Design
where the passband is from .45 to .55 of normalized frequency, the amount of ripple
acceptable in the passband is 1 dB, the first stopband is from 0 to .35 (normalized), the
second stopband is from .65 to 1 (normalized), and both stopbands provide 60 dB of
attenuation.
To design this filter, evaluate the following code, or type it at the MATLAB command
prompt:
f = fdesign.bandpass(.35,.45,.55,.65,60,1,60);
Hd = design(f, 'equiripple');
fvtool(Hd)
The last line of code invokes the Filter Visualization Tool, which displays the designed
filter. You use Hd, which is a double, floating-point filter, both as the baseline and a
starting point for the conversion.
Quantize the Coefficients
The first step in quantizing the coefficients is to find the valid word length for the
coefficients. Here again, the hardware usually dictates the maximum allowable setting.
However, if this constraint is large enough, there is room for some trial and error. Start
with the coefficient word length of 8 and determine if the resulting filter is sufficient for
your needs.
To set the coefficient word length of 8, evaluate or type the following code at the
MATLAB command prompt:
Hf = Hd;
Hf.Arithmetic = 'fixed';
set(Hf, 'CoeffWordLength', 8);
fvtool(Hf)
The resulting filter is shown in the following figure.
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Fixed-Point Filter Design
As the figure shows, the filter design constraints are not met. The attenuation is not
complete, and there is noise at the edges of the stopbands. You can experiment with
different coefficient word lengths if you like. For this example, however, the word length
of 12 is sufficient.
To set the coefficient word length of 12, evaluate or type the following code at the
MATLAB command prompt:
set(Hf, 'CoeffWordLength', 12);
fvtool(Hf)
The resulting filter satisfies the design constraints, as shown in the following figure.
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Fixed-Point Design
Now that the coefficient word length is set, there are other data width constraints that
might require attention. Type the following at the MATLAB command prompt:
>> info(Hf)
Discrete-Time FIR Filter (real)
------------------------------Filter Structure : Direct-Form FIR
Filter Length
: 48
Stable
: Yes
Linear Phase
: Yes (Type 2)
Arithmetic
: fixed
Numerator
: s12,14 -> [-1.250000e-001 1.250000e-001)
Input
: s16,15 -> [-1 1)
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Fixed-Point Filter Design
Filter Internals : Full Precision
Output
: s31,29 -> [-2 2) (auto determined)
Product
: s27,29 -> [-1.250000e-001 1.250000e-001)...
(auto determined)
Accumulator
: s31,29 -> [-2 2) (auto determined)
Round Mode
: No rounding
Overflow Mode
: No overflow
You see the output is 31 bits, the accumulator requires 31 bits and the multiplier
requires 27 bits. A typical piece of hardware might have a 16 bit data bus, a 24 bit
multiplier, and an accumulator with 4 guard bits. Another reasonable assumption is
that the data comes from a 12 bit ADC. To reflect these constraints type or evaluate the
following code:
set
set
set
set
set
(Hf,
(Hf,
(Hf,
(Hf,
(Hf,
'InputWordLength', 12);
'FilterInternals', 'SpecifyPrecision');
'ProductWordLength', 24);
'AccumWordLength', 28);
'OutputWordLength', 16);
Although the filter is basically done, if you try to filter some data with it at this stage,
you may get erroneous results due to overflows. Such overflows occur because you have
defined the constraints, but you have not tuned the filter coefficients to handle properly
the range of input data where the filter is designed to operate. Next, the dynamic range
analysis is necessary to ensure no overflows.
Dynamic Range Analysis
The purpose of the dynamic range analysis is to fine tune the scaling of the coefficients.
The ideal set of coefficients is valid for the full range of input data, while the fraction
lengths maximize precision. Consider carefully the range of input data to use for this
step. If you provide data that covers the largest dynamic range in the filter, the resulting
scaling is more conservative, and some precision is lost. If you provide data that covers
a very narrow input range, the precision can be much greater, but an input out of
the design range may produce an overflow. In this example, you use the worst-case
input signal, covering a full dynamic range, in order to ensure that no overflow ever
occurs. This worst-case input signal is a scaled version of the sign of the flipped impulse
response.
To scale the coefficients based on the full dynamic range, type or evaluate the following
code:
x = 1.9*sign(fliplr(impz(Hf)));
Hf = autoscale(Hf, x);
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Fixed-Point Design
To check that the coefficients are in range (no overflows) and have maximum possible
precision, type or evaluate the following code:
fipref('LoggingMode', 'on', 'DataTypeOverride', 'ForceOff');
y = filter(Hf, x);
fipref('LoggingMode', 'off');
R = qreport(Hf)
Where R is shown in the following figure:
The report shows no overflows, and all data falls within the designed range. The
conversion has completed successfully.
Compare Magnitude Response and Magnitude Response Estimate
You can use the fvtool GUI to analysis on your quantized filter, to see the effects of the
quantization on stopband attenuation, etc. Two important last checks when analyzing a
quantized filter are the Magnitude Response Estimate and the Round-off Noise Power
Spectrum. The value of the Magnitude Response Estimate analysis can be seen in the
following example.
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Fixed-Point Filter Design
View the Magnitude Response Estimate
Begin by designing a simple lowpass filter using the command.
h = design(fdesign.lowpass, 'butter','SOSScaleNorm','Linf');
Now set the arithmetic to fixed-point.
h.arithmetic = 'fixed';
Open the filter using fvtool.
fvtool(h)
When fvtool displays the filter using the Magnitude response view, the quantized filter
seems to match the original filter quite well.
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Fixed-Point Design
However if you look at the Magnitude Response Estimate plot from the Analysis
menu, you will see that the actual filter created may not perform nearly as well as
indicated by the Magnitude Response plot.
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Fixed-Point Filter Design
This is because by using the noise-based method of the Magnitude Response
Estimate, you estimate the complex frequency response for your filter as determined
by applying a noise- like signal to the filter input. Magnitude Response Estimate
uses the Monte Carlo trials to generate a noise signal that contains complete frequency
content across the range 0 to Fs. For more information about analyzing filters in this
way, refer to the section titled “Analyzing Filters with a Noise-Based Method” in the
User Guide.
For more information, refer to McClellan, et al., Computer-Based Exercises for Signal
Processing Using MATLAB 5, Prentice-Hall, 1998. See Project 5: Quantization Noise in
Digital Filters, page 231.
Create an FIR Filter Using Integer Coefficients
Review of Fixed-Point Numbers
Terminology of Fixed-Point Numbers
DSP System Toolbox functions assume fixed-point quantities are represented in
two's complement format, and are described using the WordLength and FracLength
parameters. It is common to represent fractional quantities of WordLength 16 with the
leftmost bit representing the sign and the remaining bits representing the fraction to the
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Fixed-Point Design
right of the binary point. Often the FracLength is thought of as the number of bits to the
right of the binary point. However, there is a problem with this interpretation when the
FracLength is larger than the WordLength, or when the FracLength is negative.
To work around these cases, you can use the following interpretation of a fixed-point
quantity:
The register has a WordLength of B, or in other words it has B bits. The bits are
numbered from left to right from 0 to B-1. The most significant bit (MSB) is the
leftmost bit, bB-1. The least significant bit is the right-most bit, b0. You can think of the
FracLength as a quantity specifying how to interpret the bits stored and resolve the
value they represent. The value represented by the bits is determined by assigning a
weight to each bit:
In this figure, L is the integer FracLength. It can assume any value, depending on the
quantization step size. L is necessary to interpret the value that the bits represent. This
value is given by the equation
value = -bB-1 2 B-1-L +
B -2
 bk 2k- L
k =0
.
The value 2–L is the smallest possible difference between two numbers represented in this
format, otherwise known as the quantization step. In this way, it is preferable to think
of the FracLength as the negative of the exponent used to weigh the right-most, or leastsignificant, bit of the fixed-point number.
To reduce the number of bits used to represent a given quantity, you can discard the
least-significant bits. This method minimizes the quantization error since the bits
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Fixed-Point Filter Design
you are removing carry the least weight. For instance, the following figure illustrates
reducing the number of bits from 4 to 2:
This means that the FracLength has changed from L to L – 2.
You can think of integers as being represented with a FracLength of L = 0, so that the
quantization step becomes .
Suppose B = 16 and L = 0. Then the numbers that can be represented are the integers
{ -32768, -32767,..., -1, 0,1 ..., 32766, 32767} .
If you need to quantize these numbers to use only 8 bits to represent them, you will want
to discard the LSBs as mentioned above, so that B=8 and L = 0–8 = –8. The increments,
or quantization step then becomes 2 -( -8) = 2 8 = 256 . So you will still have the same
range of values, but with less precision, and the numbers that can be represented become
{ -32768, -32512,..., -256 ,0, 256 ,...32256, 32512} .
With this quantization the largest possible error becomes about 256/2 when rounding to
the nearest, with a special case for 32767.
Integers and Fixed-Point Filters
This section provides an example of how you can create a filter with integer coefficients.
In this example, a raised-cosine filter with floating-point coefficients is created, and the
filter coefficients are then converted to integers.
Define the Filter Coefficients
To illustrate the concepts of using integers with fixed-point filters, this example will use
a raised-cosine filter:
b = rcosdesign(.25, 12.5, 8, 'sqrt');
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Fixed-Point Design
The coefficients of b are normalized so that the passband gain is equal to 1, and are
all smaller than 1. In order to make them integers, they will need to be scaled. If you
wanted to scale them to use 18 bits for each coefficient, the range of possible values for
the coefficients becomes:
[ -2 -17 , 217 - 1] == [ -131072,131071 ]
Because the largest coefficient of b is positive, it will need to be scaled as close as possible
to 131071 (without overflowing) in order to minimize quantization error. You can
determine the exponent of the scale factor by executing:
B = 18; % Number of bits
L = floor(log2((2^(B-1)-1)/max(b)));
bsc = b*2^L;
% Round towards zero to avoid overflow
Alternatively, you can use the fixed-point numbers autoscaling tool as follows:
bq = fi(b, true, B); % signed = true, B = 18 bits
L = bq.FractionLength;
It is a coincidence that B and L are both 18 in this case, because of the value of the
largest coefficient of b. If, for example, the maximum value of b were 0.124, L would be
20 while B (the number of bits) would remain 18.
Build the FIR Filter
First create the filter using the direct form, tapped delay line structure:
h = dfilt.dffir(bsc);
In order to set the required parameters, the arithmetic must be set to fixed-point:
h.Arithmetic = 'fixed';
h.CoeffWordLength = 18;
You can check that the coefficients of h are all integers:
all(h.Numerator == round(h.Numerator))
ans =
1
Now you can examine the magnitude response of the filter using fvtool:
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Fixed-Point Filter Design
fvtool(h, 'Color', 'white')
This shows a large gain of 117 dB in the passband, which is due to the large values of the
coefficients— this will cause the output of the filter to be much larger than the input. A
method of addressing this will be discussed in the following sections.
Set the Filter Parameters to Work with Integers
You will need to set the input parameters of your filter to appropriate values for working
with integers. For example, if the input to the filter is from a A/D converter with 12 bit
resolution, you should set the input as follows:
h.InputWordLength = 12;
h.InputFracLength = 0;
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The info method returns a summary of the filter settings.
info(h)
Discrete-Time FIR Filter (real)
------------------------------Filter Structure : Direct-Form FIR
Filter Length
: 101
Stable
: Yes
Linear Phase
: Yes (Type 1)
Arithmetic
: fixed
Numerator
: s18,0 -> [-131072 131072)
Input
: s12,0 -> [-2048 2048)
Filter Internals : Full Precision
Output
: s31,0 -> [-1073741824 1073741824) (auto determined)
Product
: s29,0 -> [-268435456 268435456) (auto determined)
Accumulator
: s31,0 -> [-1073741824 1073741824) (auto determined)
Round Mode
: No rounding
Overflow Mode
: No overflow
In this case, all the fractional lengths are now set to zero, meaning that the filter h is set
up to handle integers.
Create a Test Signal for the Filter
You can generate an input signal for the filter by quantizing to 12 bits using the
autoscaling feature, or you can follow the same procedure that was used for the
coefficients, discussed previously. In this example, create a signal with two sinusoids:
n = 0:999;
f1 = 0.1*pi; % Normalized frequency of first sinusoid
f2 = 0.8*pi; % Normalized frequency of second sinusoid
x = 0.9*sin(0.1*pi*n) + 0.9*sin(0.8*pi*n);
xq = fi(x, true, 12); % signed = true, B = 12
xsc = fi(xq.int, true, 12, 0);
Filter the Test Signal
To filter the input signal generated above, enter the following:
ysc = filter(h, xsc);
Here ysc is a full precision output, meaning that no bits have been discarded in the
computation. This makes ysc the best possible output you can achieve given the 12–bit
input and the 18–bit coefficients. This can be verified by filtering using double-precision
floating-point and comparing the results of the two filtering operations:
hd = double(h);
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Fixed-Point Filter Design
xd = double(xsc);
yd = filter(hd, xd);
norm(yd-double(ysc))
ans =
0
Now you can examine the output compared to the input. This example is plotting only
the last few samples to minimize the effect of transients:
idx = 800:950;
xscext = double(xsc(idx)');
gd = grpdelay(h, [f1 f2]);
yidx = idx + gd(1);
yscext = double(ysc(yidx)');
stem(n(idx)', [xscext, yscext]);
axis([800 950 -2.5e8 2.5e8]);
legend('input', 'output');
set(gcf, 'color', 'white');
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Fixed-Point Design
It is difficult to compare the two signals in this figure because of the large difference in
scales. This is due to the large gain of the filter, so you will need to compensate for the
filter gain:
stem(n(idx)', [2^18*xscext, yscext]);
axis([800 950 -5e8 5e8]);
legend('scaled input', 'output');
You can see how the signals compare much more easily once the scaling has been done,
as seen in the above figure.
Truncate the Output WordLength
If you examine the output wordlength,
ysc.WordLength
ans =
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Fixed-Point Filter Design
31
you will notice that the number of bits in the output is considerably greater than in
the input. Because such growth in the number of bits representing the data may not
be desirable, you may need to truncate the wordlength of the output. As discussed in
“Terminology of Fixed-Point Numbers” on page 9-71the best way to do this is to
discard the least significant bits, in order to minimize error. However, if you know there
are unused high order bits, you should discard those bits as well.
To determine if there are unused most significant bits (MSBs), you can look at where
the growth in WordLength arises in the computation. In this case, the bit growth occurs
to accommodate the results of adding products of the input (12 bits) and the coefficients
(18 bits). Each of these products is 29 bits long (you can verify this using info(h)).
The bit growth due to the accumulation of the product depends on the filter length and
the coefficient values- however, this is a worst-case determination in the sense that no
assumption on the input signal is made besides, and as a result there may be unused
MSBs. You will have to be careful though, as MSBs that are deemed unused incorrectly
will cause overflows.
Suppose you want to keep 16 bits for the output. In this case, there is no bit-growth due
to the additions, so the output bit setting will be 16 for the wordlength and –14 for the
fraction length.
Since the filtering has already been done, you can discard some bits from ysc:
yout = fi(ysc, true, 16, -14);
Alternatively, you can set the filter output bit lengths directly (this is useful if you plan
on filtering many signals):
specifyall(h);
h.OutputWordLength = 16;
h.OutputFracLength = -14;
yout2 = filter(h, xsc);
You can verify that the results are the same either way:
norm(double(yout) - double(yout2))
ans =
0
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Fixed-Point Design
However, if you compare this to the full precision output, you will notice that there is
rounding error due to the discarded bits:
norm(double(yout)-double(ysc))
ans =
1.446323386867543e+005
In this case the differences are hard to spot when plotting the data, as seen below:
stem(n(yidx), [double(yout(yidx)'), double(ysc(yidx)')]);
axis([850 950 -2.5e8 2.5e8]);
legend('Scaled Input', 'Output');
set(gcf, 'color', 'white');
Scale the Output
Because the filter in this example has such a large gain, the output is at a different
scale than the input. This scaling is purely theoretical however, and you can scale the
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Fixed-Point Filter Design
data however you like. In this case, you have 16 bits for the output, but you can attach
whatever scaling you choose. It would be natural to reinterpret the output to have a
weight of 2^0 (or L = 0) for the LSB. This is equivalent to scaling the output signal down
by a factor of 2^(-14). However, there is no computation or rounding error involved. You
can do this by executing the following:
yri = fi(yout.int, true, 16, 0);
stem(n(idx)', [xscext, double(yri(yidx)')]);
axis([800 950 -1.5e4 1.5e4]);
legend('input', 'rescaled output');
This plot shows that the output is still larger than the input. If you had done the filtering
in double-precision floating-point, this would not be the case— because here more bits
are being used for the output than for the input, so the MSBs are weighted differently.
You can see this another way by looking at the magnitude response of the scaled filter:
[H,w] = freqz(h);
plot(w/pi, 20*log10(2^(-14)*abs(H)));
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Fixed-Point Design
This plot shows that the passband gain is still above 0 dB.
To put the input and output on the same scale, the MSBs must be weighted equally. The
input MSB has a weight of 2^11, whereas the scaled output MSB has a weight of 2^(29–
14) = 2^15. You need to give the output MSB a weight of 2^11 as follows:
yf = fi(zeros(size(yri)), true, 16, 4);
yf.bin = yri.bin;
stem(n(idx)', [xscext, double(yf(yidx)')]);
legend('input', 'rescaled output');
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Fixed-Point Filter Design
This operation is equivalent to scaling the filter gain down by 2^(-18).
[H,w] = freqz(h);
plot(w/pi, 20*log10(2^(-18)*abs(H)));
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9-83
9
Fixed-Point Design
The above plot shows a 0 dB gain in the passband, as desired.
With this final version of the output, yf is no longer an integer. However this is only due
to the interpretation- the integers represented by the bits in yf are identical to the ones
represented by the bits in yri. You can verify this by comparing them:
max(abs(yf.int - yri.int))
ans =
0
Configure Filter Parameters to Work with Integers Using the set2int Method
• “Set the Filter Parameters to Work with Integers” on page 9-85
• “Reinterpret the Output” on page 9-86
9-84
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Fixed-Point Filter Design
Set the Filter Parameters to Work with Integers
The set2int method provides a convenient way of setting filter parameters to work with
integers. The method works by scaling the coefficients to integer numbers, and setting
the coefficients and input fraction length to zero. This makes it possible for you to use
floating-point coefficients directly.
h = dfilt.dffir(b);
h.Arithmetic = 'fixed';
The coefficients are represented with 18 bits and the input signal is represented with 12
bits:
g = set2int(h, 18, 12);
g_dB = 20*log10(g)
g_dB =
1.083707984390332e+002
The set2int method returns the gain of the filter by scaling the coefficients to integers,
so the gain is always a power of 2. You can verify that the gain we get here is consistent
with the gain of the filter previously. Now you can also check that the filter h is set up
properly to work with integers:
info(h)
Discrete-Time FIR Filter (real)
------------------------------Filter Structure : Direct-Form FIR
Filter Length
: 101
Stable
: Yes
Linear Phase
: Yes (Type 1)
Arithmetic
: fixed
Numerator
: s18,0 -> [-131072 131072)
Input
: s12,0 -> [-2048 2048)
Filter Internals : Full Precision
Output
: s31,0 -> [-1073741824 1073741824) (auto determined)
Product
: s29,0 -> [-268435456 268435456) (auto determined)
Accumulator: s31,0 -> [-1073741824 1073741824) (auto determined)
Round Mode
: No rounding
Overflow Mode
: No overflow
Here you can see that all fractional lengths are now set to zero, so this filter is set up
properly for working with integers.
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9-85
9
Fixed-Point Design
Reinterpret the Output
You can compare the output to the double-precision floating-point reference output, and
verify that the computation done by the filter h is done in full precision.
yint = filter(h, xsc);
norm(yd - double(yint))
ans =
0
You can then truncate the output to only 16 bits:
yout = fi(yint, true, 16);
stem(n(yidx), [xscext, double(yout(yidx)')]);
axis([850 950 -2.5e8 2.5e8]);
legend('input', 'output');
Once again, the plot shows that the input and output are at different scales. In order to
scale the output so that the signals can be compared more easily in a plot, you will need
9-86
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Fixed-Point Filter Design
to weigh the MSBs appropriately. You can compute the new fraction length using the
gain of the filter when the coefficients were integer numbers:
WL = yout.WordLength;
FL = yout.FractionLength + log2(g);
yf2 = fi(zeros(size(yout)), true, WL, FL);
yf2.bin = yout.bin;
stem(n(idx)', [xscext, double(yf2(yidx)')]);
axis([800 950 -2e3 2e3]);
legend('input', 'rescaled output');
This final plot shows the filtered data re-scaled to match the input scale.
Fixed-Point Filtering in Simulink
• “Fixed-Point Filtering Blocks” on page 9-88
• “Filter Implementation Blocks” on page 9-88
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9-87
9
Fixed-Point Design
• “Filter Design and Implementation Blocks” on page 9-88
Fixed-Point Filtering Blocks
The following DSP System Toolbox blocks enable you to design and/or realize a variety of
fixed-point filters:
• CIC Decimation
• CIC Interpolation
• Filter Realization Wizard
• FIR Decimation
• FIR Interpolation
• Two-Channel Analysis Subband Filter
• Two-Channel Synthesis Subband Filter
Filter Implementation Blocks
The FIR Decimation, FIR Interpolation, Two-Channel Analysis Subband Filter, and TwoChannel Synthesis Subband Filter blocks are all implementation blocks. They allow you
to implement filters for which you already know the filter coefficients.
Filter Design and Implementation Blocks
The Filter Realization Wizard block invokes part of the Filter Design and Analysis
Tool from Signal Processing Toolbox software. This block allows you both to design
new filters and to implement filters for which you already know the coefficients. In
its implementation stage, the Filter Realization Wizard creates a filter realization
using Sum, Gain, and Delay blocks. You can use this block to design and/or implement
numerous types of fixed-point and floating-point single-channel filters. See the Filter
Realization Wizard reference page for more information about this block.
The CIC Decimation and CIC Interpolation blocks allow you to design and implement
Cascaded Integrator-Comb filters. See their block reference pages for more information.
9-88
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10
C Code Generation
Learn how to generate code for signal processing applications.
• “Understanding C Code Generation” on page 10-2
• “Functions and System Objects Supported for C Code Generation” on page 10-4
• “C Code Generation from MATLAB” on page 10-12
• “C Code Generation from Simulink” on page 10-13
• “How to Run a Generated Executable Outside MATLAB” on page 10-18
• “DSP System Toolbox Supported Hardware” on page 10-19
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10
C Code Generation
Understanding C Code Generation
In this section...
“C Code Generation with the Simulink Coder Product” on page 10-2
“Highly Optimized Generated ANSI C Code” on page 10-3
C Code Generation with the Simulink Coder Product
You can use the DSP System Toolbox, Simulink Coder, and Embedded Coder® products
together to generate code that you can use to implement your model for a practical
application. For instance, you can create an executable from your Simulink model to run
on a target chip.
This chapter introduces you to the basic concepts of code generation using these tools.
Shared Library Dependencies
In general, the code you generate from DSP System Toolbox blocks is portable ANSI
C code. After you generate the code, you can deploy it on another machine. For more
information on how to do so, see “Relocate Code to Another Development Environment”
in the Simulink Coder documentation.
There are a few DSP System Toolbox blocks that generate code with limited portability.
These blocks use precompiled shared libraries, such as DLLs, to support I/O for specific
types of devices and file formats. To find out which blocks use precompiled shared
libraries, open the DSP System Toolbox Block Support Table. You can identify blocks
that use precompiled shared libraries by checking the footnotes listed in the Code
Generation Support column of the table. All blocks that use shared libraries have the
following footnote:
Host computer only. Excludes Real-Time Windows (RTWIN) target.
Simulink Coder provides functions to help you set up and manage the build information
for your models. For example, one of the functions that Simulink Coder provides is
getNonBuildFiles. This function allows you to identify the shared libraries required
by blocks in your model. If your model contains any blocks that use precompiled shared
libraries, you can install those libraries on the target system. The folder that you install
the shared libraries in must be on the system path. The target system does not need to
have MATLAB installed, but it does need to be supported by MATLAB.
10-2
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Understanding C Code Generation
Highly Optimized Generated ANSI C Code
All DSP System Toolbox blocks generate highly optimized ANSI C code. This C code is
often suitable for embedded applications, and includes the following optimizations:
• Function reuse (run-time libraries) — The generated code reuses common
algorithmic functions via calls to shared utility functions. Shared utility functions are
highly optimized ANSI/ISO C functions that implement core algorithms such as FFT
and convolution.
• Parameter reuse (Simulink Coder run-time parameters) — In many cases,
if there are multiple instances of a block that all have the same value for a specific
parameter, each block instance points to the same variable in the generated code.
This process reduces memory requirements.
• Blocks have parameters that affect code optimization — Some blocks, such as
the Sine Wave block, have parameters that enable you to optimize the simulation for
memory or for speed. These optimizations also apply to code generation.
• Other optimizations — Use of contiguous input and output arrays, reusable inputs,
overwritable arrays, and inlined algorithms provide smaller generated C code that is
more efficient at run time.
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10-3
10
C Code Generation
Functions and System Objects Supported for C Code Generation
If you have a MATLAB Coder license, you can generate C and C++ code from MATLAB
code that contains DSP System Toolbox functions and System objects. For more
information about C and C++ code generation from MATLAB code, see the MATLAB
Coder documentation. For more information about generating code from System objects,
see “System Objects in MATLAB Code Generation”.
The following DSP System Toolbox functions and System objects are supported for C and
C++ code generation from MATLAB code.
Name
Remarks and Limitations
Estimation
dsp.BurgAREstimator
“System Objects in MATLAB Code Generation”
dsp.BurgSpectrumEstimator
“System Objects in MATLAB Code Generation”
dsp.CepstralToLPC
“System Objects in MATLAB Code Generation”
dsp.CrossSpectrumEstimator
“System Objects in MATLAB Code Generation”
dsp.LevinsonSolver
“System Objects in MATLAB Code Generation”
dsp.LPCToAutocorrelation
“System Objects in MATLAB Code Generation”
dsp.LPCToCepstral
“System Objects in MATLAB Code Generation”
dsp.LPCToLSF
“System Objects in MATLAB Code Generation”
dsp.LPCToLSP
“System Objects in MATLAB Code Generation”
dsp.LPCToRC
“System Objects in MATLAB Code Generation”
dsp.LSFToLPC
“System Objects in MATLAB Code Generation”
dsp.LSPToLPC
“System Objects in MATLAB Code Generation”
dsp.RCToAutocorrelation
“System Objects in MATLAB Code Generation”
dsp.RCToLPC
“System Objects in MATLAB Code Generation”
dsp.SpectrumEstimator
“System Objects in MATLAB Code Generation”
dsp.TransferFunctionEstimator
“System Objects in MATLAB Code Generation”
Filters
ca2tf
10-4
All inputs must be constant. Expressions or
variables are allowed if their values do not
change.
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Functions and System Objects Supported for C Code Generation
Name
Remarks and Limitations
cl2tf
All inputs must be constant. Expressions or
variables are allowed if their values do not
change.
dsp.AdaptiveLatticeFilter
“System Objects in MATLAB Code Generation”
dsp.AffineProjectionFilter
“System Objects in MATLAB Code Generation”
dsp.AllpoleFilter
• “System Objects in MATLAB Code
Generation”
• Only the Denominator property is tunable
for code generation.
dsp.BiquadFilter
“System Objects in MATLAB Code Generation”
dsp.CICCompensationDecimator
“System Objects in MATLAB Code Generation”
dsp.CICCompensationInterpolator
“System Objects in MATLAB Code Generation”
dsp.CICDecimator
“System Objects in MATLAB Code Generation”
dsp.CICInterpolator
“System Objects in MATLAB Code Generation”
dsp.FarrowRateConverter
“System Objects in MATLAB Code Generation”
dsp.FastTransversalFilter
“System Objects in MATLAB Code Generation”
dsp.FilterCascade
• You cannot generate code directly from
dsp.FilterCascade. You can use the
generateFilteringCode method to
generate a MATLAB function. You can
generate C/C++ code from this MATLAB
function.
• “System Objects in MATLAB Code
Generation”
dsp.FilteredXLMSFilter
“System Objects in MATLAB Code Generation”
dsp.FIRDecimator
“System Objects in MATLAB Code Generation”
dsp.FIRFilter
• “System Objects in MATLAB Code
Generation”
• Only the Numerator property is tunable for
code generation.
dsp.FIRHalfbandDecimator
“System Objects in MATLAB Code Generation”
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10-5
10
C Code Generation
Name
Remarks and Limitations
dsp.FIRHalfbandInterpolator
“System Objects in MATLAB Code Generation”
dsp.FIRInterpolator
“System Objects in MATLAB Code Generation”
dsp.FIRRateConverter
“System Objects in MATLAB Code Generation”
dsp.FrequencyDomainAdaptiveFilter
“System Objects in MATLAB Code Generation”
dsp.IIRFilter
• Only the Numerator and Denominator
properties are tunable for code generation.
• “System Objects in MATLAB Code
Generation”
dsp.KalmanFilter
“System Objects in MATLAB Code Generation”
dsp.LMSFilter
“System Objects in MATLAB Code Generation”
dsp.RLSFilter
“System Objects in MATLAB Code Generation”
dsp.SampleRateConverter
“System Objects in MATLAB Code Generation”
firceqrip
All inputs must be constant. Expressions or
variables are allowed if their values do not
change.
fireqint
All inputs must be constant. Expressions or
variables are allowed if their values do not
change.
firgr
• All inputs must be constant. Expressions or
variables are allowed if their values do not
change.
• Does not support syntaxes that have cell
array input.
firhalfband
All inputs must be constant. Expressions or
variables are allowed if their values do not
change.
firlpnorm
• All inputs must be constant. Expressions or
variables are allowed if their values do not
change.
• Does not support syntaxes that have cell
array input.
10-6
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Functions and System Objects Supported for C Code Generation
Name
Remarks and Limitations
firminphase
All inputs must be constant. Expressions or
variables are allowed if their values do not
change.
firnyquist
All inputs must be constant. Expressions or
variables are allowed if their values do not
change.
firpr2chfb
All inputs must be constant. Expressions or
variables are allowed if their values do not
change.
ifir
All inputs must be constant. Expressions or
variables are allowed if their values do not
change.
iircomb
All inputs must be constant. Expressions or
variables are allowed if their values do not
change.
iirgrpdelay
• All inputs must be constant. Expressions or
variables are allowed if their values do not
change.
• Does not support syntaxes that have cell
array input.
iirlpnorm
• All inputs must be constant. Expressions or
variables are allowed if their values do not
change.
• Does not support syntaxes that have cell
array input.
iirlpnormc
• All inputs must be constant. Expressions or
variables are allowed if their values do not
change.
• Does not support syntaxes that have cell
array input.
iirnotch
All inputs must be constant. Expressions or
variables are allowed if their values do not
change.
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10-7
10
C Code Generation
Name
Remarks and Limitations
iirpeak
All inputs must be constant. Expressions or
variables are allowed if their values do not
change.
tf2ca
All inputs must be constant. Expressions or
variables are allowed if their values do not
change.
tf2cl
All inputs must be constant. Expressions or
variables are allowed if their values do not
change.
Math Operations
dsp.ArrayVectorAdder
“System Objects in MATLAB Code Generation”
dsp.ArrayVectorDivider
“System Objects in MATLAB Code Generation”
dsp.ArrayVectorMultiplier
“System Objects in MATLAB Code Generation”
dsp.ArrayVectorSubtractor
“System Objects in MATLAB Code Generation”
dsp.CumulativeProduct
“System Objects in MATLAB Code Generation”
dsp.CumulativeSum
“System Objects in MATLAB Code Generation”
dsp.LDLFactor
“System Objects in MATLAB Code Generation”
dsp.LevinsonSolver
“System Objects in MATLAB Code Generation”
dsp.LowerTriangularSolver
“System Objects in MATLAB Code Generation”
dsp.LUFactor
“System Objects in MATLAB Code Generation”
dsp.Normalizer
“System Objects in MATLAB Code Generation”
dsp.UpperTriangularSolver
“System Objects in MATLAB Code Generation”
Quantizers
dsp.ScalarQuantizerDecoder
“System Objects in MATLAB Code Generation”
dsp.ScalarQuantizerEncoder
“System Objects in MATLAB Code Generation”
dsp.VectorQuantizerDecoder
“System Objects in MATLAB Code Generation”
dsp.VectorQuantizerEncoder
“System Objects in MATLAB Code Generation”
Scopes
10-8
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Functions and System Objects Supported for C Code Generation
Name
Remarks and Limitations
dsp.SpectrumAnalyzer
This System object does not generate code. It is
automatically declared as an extrinsic variable
using the coder.extrinsic function.
dsp.TimeScope
This System object does not generate code. It is
automatically declared as an extrinsic variable
using the coder.extrinsic function.
Signal Management
dsp.Counter
“System Objects in MATLAB Code Generation”
dsp.DelayLine
“System Objects in MATLAB Code Generation”
Signal Operations
dsp.Convolver
“System Objects in MATLAB Code Generation”
dsp.DCBlocker
“System Objects in MATLAB Code Generation”
dsp.Delay
“System Objects in MATLAB Code Generation”
dsp.DigitalDownConverter
“System Objects in MATLAB Code Generation”
dsp.DigitalUpConverter
“System Objects in MATLAB Code Generation”
dsp.Interpolator
“System Objects in MATLAB Code Generation”
dsp.NCO
“System Objects in MATLAB Code Generation”
dsp.PeakFinder
“System Objects in MATLAB Code Generation”
dsp.PhaseExtractor
“System Objects in MATLAB Code Generation”
dsp.PhaseUnwrapper
“System Objects in MATLAB Code Generation”
dsp.VariableFractionalDelay
“System Objects in MATLAB Code Generation”
dsp.VariableIntegerDelay
“System Objects in MATLAB Code Generation”
dsp.Window
• This object has no tunable properties for code
generation.
• “System Objects in MATLAB Code
Generation”
dsp.ZeroCrossingDetector
“System Objects in MATLAB Code Generation”
Sinks
dsp.AudioPlayer
“System Objects in MATLAB Code Generation”
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10-9
10
C Code Generation
Name
Remarks and Limitations
dsp.AudioFileWriter
“System Objects in MATLAB Code Generation”
dsp.UDPSender
“System Objects in MATLAB Code Generation”
Sources
dsp.AudioFileReader
“System Objects in MATLAB Code Generation”
dsp.AudioRecorder
“System Objects in MATLAB Code Generation”
dsp.SignalSource
“System Objects in MATLAB Code Generation”
dsp.SineWave
• This object has no tunable properties for code
generation.
• “System Objects in MATLAB Code
Generation”
dsp.UDPReceiver
“System Objects in MATLAB Code Generation”
Statistics
dsp.Autocorrelator
“System Objects in MATLAB Code Generation”
dsp.Crosscorrelator
“System Objects in MATLAB Code Generation”
dsp.Histogram
• This object has no tunable properties for code
generation.
• “System Objects in MATLAB Code
Generation”
dsp.Maximum
“System Objects in MATLAB Code Generation”
dsp.Mean
“System Objects in MATLAB Code Generation”
dsp.Median
“System Objects in MATLAB Code Generation”
dsp.Minimum
“System Objects in MATLAB Code Generation”
dsp.PeakToPeak
“System Objects in MATLAB Code Generation”
dsp.PeakToRMS
“System Objects in MATLAB Code Generation”
dsp.RMS
“System Objects in MATLAB Code Generation”
dsp.StandardDeviation
“System Objects in MATLAB Code Generation”
dsp.StateLevels
“System Objects in MATLAB Code Generation”
dsp.Variance
“System Objects in MATLAB Code Generation”
Transforms
10-10
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Functions and System Objects Supported for C Code Generation
Name
Remarks and Limitations
dsp.AnalyticSignal
“System Objects in MATLAB Code Generation”
dsp.DCT
“System Objects in MATLAB Code Generation”
dsp.FFT
“System Objects in MATLAB Code Generation”
dsp.IDCT
“System Objects in MATLAB Code Generation”
dsp.IFFT
“System Objects in MATLAB Code Generation”
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10-11
10
C Code Generation
C Code Generation from MATLAB
When you have a license for the MATLAB Coder product, you can generate standalone
C and C++ from MATLAB code. See the MATLAB Coder documentation for details on
supported functionality and workflow.
10-12
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C Code Generation from Simulink
C Code Generation from Simulink
In this section...
“Open and Run the Model” on page 10-13
“Generate Code from the Model” on page 10-15
“Build and Run the Generated Code” on page 10-15
Note: You must have both the DSP System Toolbox and Simulink Coder products
installed on your computer to complete the procedures in this section.
Open and Run the Model
The ex_codegen_dsp model implements a simple adaptive filter to remove noise from
a signal while simultaneously identifying a filter that characterizes the noise frequency
content. To open this model, enter
open_system('ex_codegen_dsp')
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10-13
10
C Code Generation
Run the model and observe the output in both scopes. This model saves the filter
weights each time they adapt. You can plot the last set of coefficients using the following
command:
plot(filter_wts(:,:,1201))
10-14
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C Code Generation from Simulink
Generate Code from the Model
To generate code from the model, you must first ensure that you have write permission
in your current folder. The code generation process creates a new subfolder inside the
current MATLAB working folder. MATLAB saves all of the files created by the code
generation process in that subfolder, including those which contain the generated C
source code.
To start the code generation process, click the Build Model icon (
) on your model
toolbar. After the model finishes generating code, the Code Generation Report appears,
allowing you to inspect the generated code. You may also notice that the build process
created a new subfolder inside of your current MATLAB working folder. The name of
this folder consists of the model name, followed by the suffix _grt_rtw. In the case
of this example, the subfolder that contains the generated C source code is named
ex_codegen_dsp_grt_rtw.
Build and Run the Generated Code
Setup the C/C++ Compiler
If you want to build and run the generated code, you need to have access to a C compiler.
For more information about which compilers are supported in the current release, see
http://www.mathworks.com/support/compilers/current_release/.
To setup your compiler, run the following command:
mex –setup
Build the Generated Code
After your compiler is setup, you can build and run the generated code. The
ex_codegen_dsp model is currently configured to generate code only. To build the
generated code, you must first make the following changes:
1
Open the Model Configuration Parameters dialog, navigate to the Code
Generation tab, and clear the Generate Code Only checkbox.
2
Click OK to apply your changes and close the dialog box.
3
From the model toolbar, click the Build Model icon (
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).
10-15
10
C Code Generation
Because you re-configured the model to generate and build code, the code generation
process continues until the code is compiled and linked.
Run the Generated Code
To run the generated code, enter the following command at the MATLAB prompt:
!ex_codegen_dsp
Running the generated code creates a MAT-file which contains the same variables as
those generated by simulating the model. The variables in the MAT-file are named with
a prefix of rt_. After you run the generated code, you can load the variables from the
MAT-file by typing the following command at the MATLAB prompt:
load ex_codegen_dsp.mat
You can now compare the variables from the generated code with the variables from the
model simulation. To plot the last set of coefficients from the generated code, enter the
following command at the MATLAB prompt:
plot(rt_filter_wts(:,:,1201))
The last set of coefficients from the generated code are shown in the following figure.
10-16
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C Code Generation from Simulink
For further information on generating code from Simulink, see the “Simulink Coder”
documentation.
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10-17
10
C Code Generation
How to Run a Generated Executable Outside MATLAB
To run your generated standalone executable application in Shell, you need to set the
environment variables as follows:
Platform
Command
Mac
setenv DYLD_LIBRARY_PATH
$DYLD_LIBRARY_PATH: $MATLABROOT/
bin/maci64 (csh/tcsh)
export DYLD_LIBRARY_PATH
$DYLD_LIBRARY_PATH: $MATLABROOT/
bin/maci64 (Bash)
Linux
setenv LD_LIBRARY_PATH
$LD_LIBRARY_PATH: $MATLABROOT/
bin/glnxa64 (csh/tcsh)
export LD_LIBRARY_PATH
$LD_LIBRARY_PATH: $MATLABROOT/
bin/glnxa64 (Bash)
Windows
set PATH = $MATLABROOT\bin\win32;
%PATH%
set PATH = $MATLABROOT\bin\win64;
%PATH%
10-18
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DSP System Toolbox Supported Hardware
DSP System Toolbox Supported Hardware
As of this release, DSP System Toolbox supports the following hardware.
Support Package
Vendor
Platforms
Earliest Release
Available
Last Release
Available
“ARM Cortex-M
Processors”
ARM
Windows, Mac,
Linux®
R2013b
Current
“ARM Cortex-A
Processors”
ARM
Windows, Mac,
Linux
R2014b
Current
For a complete list of supported hardware, see Hardware Support.
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‫‪10-20‬‬
11
Define New System Objects
• “Summary List of Methods for Defining New System Objects” on page 11-3
• “Define Basic System Objects” on page 11-5
• “Change Number of Step Inputs or Outputs” on page 11-7
• “Specify System Block Input and Output Names” on page 11-11
• “Validate Property and Input Values” on page 11-13
• “Initialize Properties and Setup One-Time Calculations” on page 11-16
• “Set Property Values at Construction Time” on page 11-19
• “Reset Algorithm State” on page 11-21
• “Define Property Attributes” on page 11-23
• “Hide Inactive Properties” on page 11-27
• “Limit Property Values to Finite String Set” on page 11-29
• “Process Tuned Properties” on page 11-32
• “Release System Object Resources” on page 11-34
• “Define Composite System Objects” on page 11-36
• “Define Finite Source Objects” on page 11-39
• “Save System Object” on page 11-41
• “Load System Object” on page 11-44
• “Clone System Object” on page 11-47
• “Define System Object Information” on page 11-48
• “Define System Block Icon” on page 11-50
• “Add Header to System Block Dialog” on page 11-52
• “Add Property Groups to System Object and Block Dialog” on page 11-54
• “Set Output Size” on page 11-58
• “Set Output Data Type” on page 11-60
• “Set Output Complexity” on page 11-62
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11
Define New System Objects
• “Specify Whether Output Is Fixed- or Variable-Size” on page 11-64
• “Specify Discrete State Output Specification” on page 11-66
• “Use Update and Output for Nondirect Feedthrough” on page 11-68
• “Enable For Each Subsystem Support” on page 11-71
• “Methods Timing” on page 11-73
• “System Object Input Arguments and ~ in Code Examples” on page 11-76
• “What Are Mixin Classes?” on page 11-77
• “Best Practices for Defining System Objects” on page 11-78
11-2
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Summary List of Methods for Defining New System Objects
Summary List of Methods for Defining New System Objects
The following Impl methods comprise the System objects API for defining new System
objects. For more information see “Define New System Objects”.
• cloneImpl
• getDiscreteStateImpl
• getDiscreteStateSpecificationImpl
• getHeaderImpl
• getIconImpl
• getInputNamesImpl
• getNumInputsImpl
• getNumOutputsImpl
• getOutputDataTypeImpl
• getOutputNamesImpl
• getOutputSizeImpl
• getPropertyGroupsImpl
• infoImpl
• isInactivePropertyImpl
• isInputDirectFeedthroughImpl
• isOutputComplexImpl
• isOutputFixedSizeImpl
• loadObjectImpl
• outputImpl
• processTunedPropertiesImpl
• propagatedInputComplexity
• propagatedInputDataType
• propagatedInputFixedSize
• propagatedInputSize
• releaseImpl
• resetImpl
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11-3
11
Define New System Objects
• saveObjectImpl
• setProperties
• setupImpl
• stepImpl
• supportsMultipleInstanceImpl
• updateImpl
• validateInputsImpl
• validatePropertiesImpl
11-4
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Define Basic System Objects
Define Basic System Objects
This example shows how to create a basic System object that increments a number by
one.
The class definition file contains the minimum elements required to define a System
object.
Create the Class Definition File
1
Create a MATLAB file named AddOne.m to contain the definition of your System
object.
edit AddOne.m
2
Subclass your object from matlab.System. Insert this line as the first line of your
file.
classdef AddOne < matlab.System
3
Add the stepImpl method, which contains the algorithm that runs when users call
the step method on your object. You always set the stepImpl method access to
protected because it is an internal method that users do not directly call or run.
All methods, except static methods, expect the System object handle as the first
input argument. You can use any name for your System object handle.
In this example, instead of passing in the object handle, ~ is used to indicate that
the object handle is not used in the function. Using ~ instead of an object handle
prevents warnings about unused variables from occurring.
By default, the number of inputs and outputs are both one. To change the number
of inputs or outputs, use the getNumInputsImpl or getNumOutputsImpl method,
respectively.
methods (Access = protected)
function y = stepImpl(~,x)
y = x + 1;
end
end
Note: Instead of manually creating your class definition file, you can use an option on
the New > System Object menu to open a template. The Basic template opens a simple
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11-5
11
Define New System Objects
System object template. The Advanced template includes more advanced features of
System objects, such as backup and restore. The Simulink Extension template includes
additional customizations of the System object for use in the Simulink MATLAB System
block. You then can edit the template file, using it as guideline, to create your own
System object.
Complete Class Definition File for Basic System Object
classdef AddOne < matlab.System
% ADDONE Compute an output value one greater than the input value
% All methods occur inside a methods declaration.
% The stepImpl method has protected access
methods (Access = protected)
function y = stepImpl(~,x)
y = x + 1;
end
end
end
See Also
matlab.System | getNumInputsImpl | getNumOutputsImpl | stepImpl
Related Examples
•
“Change Number of Step Inputs or Outputs” on page 11-7
More About
•
11-6
“System Design and Simulation in MATLAB”
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Change Number of Step Inputs or Outputs
Change Number of Step Inputs or Outputs
This example shows how to specify two inputs and two outputs for the step method.
If you specify the inputs and outputs to the stepImpl method, you do not need to
specify the getNumInputsImpl and getNumOutputsImpl methods. If you have
a variable number of inputs or outputs (using varargin or varargout), include the
getNumInputsImpl or getNumOutputsImpl method, respectively, in your class
definition file.
Note: You should only use getNumInputsImpl or getNumOutputsImpl methods to
change the number of System object inputs or outputs. Do not use any other handle
objects within a System object to change the number of inputs or outputs.
You always set the getNumInputsImpl and getNumOutputsImpl methods access to
protected because they are internal methods that users do not directly call or run.
Update the Algorithm for Multiple Inputs and Outputs
Update the stepImpl method to specify two inputs and two outputs. You do not need to
implement associated getNumInputsImpl or getNumOutputsImpl methods.
methods (Access = protected)
function [y1,y2] = stepImpl(~,x1,x2)
y1 = x1 + 1
y2 = x2 + 1;
end
end
Update the Algorithm and Associated Methods
Update the stepImpl method to use varargin and varargout. In this case, you must
implement the associated getNumInputsImpl and getNumOutputsImpl methods to
specify two or three inputs and outputs.
methods (Access = protected)
function varargout = stepImpl(obj,varargin)
varargout{1} = varargin{1}+1;
varargout{2} = varargin{2}+1;
if (obj.numInputsOutputs = 3)
varargout{3} = varargin{3}+1;
end
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11-7
11
Define New System Objects
end
function validatePropertiesImpl(obj)
if ~((obj.numInputsOutputs == 2) ||...
(obj.numInputsOutputs == 3))
error('Only 2 or 3 input and outputs allowed.');
end
end
function numIn = getNumInputsImpl(obj)
numIn = 3;
if (obj.numInputsOutputs == 2)
numIn = 2;
end
end
function numOut = getNumOutputsImpl(obj)
numOut = 3;
if (obj.numInputsOutputs == 2)
numOut = 2;
end
end
end
Use this syntax to run the algorithm with two inputs and two outputs.
x1 = 3;
x2 = 7;
[y1,y2] = step(AddOne,x1,x2);
To change the number of inputs or outputs, you must release the object before rerunning
it.
release(AddOne)
x1 = 3;
x2 = 7;
x3 = 10
[y1,y2,y3] = step(AddOne,x1,x2,x3);
Complete Class Definition File with Multiple Inputs and Outputs
classdef AddOne < matlab.System
% ADDONE Compute output values one greater than the input values
% This property is nontunable and cannot be changed
11-8
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Change Number of Step Inputs or Outputs
% after the setup or step method has been called.
properties (Nontunable)
numInputsOutputs = 3;
% Default value
end
% All methods occur inside a methods declaration.
% The stepImpl method has protected access
methods (Access = protected)
function varargout = stepImpl(obj,varargin)
if (obj.numInputsOutputs = 2)
varargout{1} = varargin{1}+1;
varargout{2} = varargin{2}+1;
else
varargout{1} = varargin{1}+1;
varargout{2} = varargin{2}+1;
varargout{3} = varargin{3}+1;
end
end
function validatePropertiesImpl(obj)
if ~((obj.numInputsOutputs == 2) ||
(obj.numInputsOutputs == 3))
error('Only 2 or 3 input and outputs allowed.');
end
end
function numIn = getNumInputsImpl(obj)
numIn = 3;
if (obj.numInputsOutputs == 2)
numIn = 2;
end
end
function numOut = getNumOutputsImpl(obj)
numOut = 3;
if (obj.numInputsOutputs == 2)
numOut = 2;
end
end
end
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11-9
11
Define New System Objects
end
See Also
getNumInputsImpl | getNumOutputsImpl
Related Examples
•
“Validate Property and Input Values” on page 11-13
•
“Define Basic System Objects” on page 11-5
More About
•
11-10
“System Object Input Arguments and ~ in Code Examples” on page 11-76
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Specify System Block Input and Output Names
Specify System Block Input and Output Names
This example shows how to specify the names of the input and output ports of a System
object–based block implemented using a MATLAB System block.
Define Input and Output Names
This example shows how to use getInputNamesImpl and getOutputNamesImpl to
specify the names of the input port as “source data” and the output port as “count.”
If you do not specify the getInputNamesImpl and getOutputNamesImpl methods, the
object uses the stepImpl method input and output variable names for the input and
output port names, respectively. If the stepImpl method uses varargin and varargout
instead of variable names, the port names default to empty strings.
methods (Access = protected)
function inputName = getInputNamesImpl(~)
inputName = 'source data';
end
function outputName = getOutputNamesImpl(~)
outputName = 'count';
end
end
Complete Class Definition File with Named Inputs and Outputs
classdef MyCounter < matlab.System
% MyCounter Count values above a threshold
properties
Threshold = 1
end
properties (DiscreteState)
Count
end
methods
function obj = MyCounter(varargin)
setProperties (obj,nargin,varargin{:});
end
end
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11-11
11
Define New System Objects
methods (Access = protected)
function setupImpl(obj)
obj.Count = 0;
end
function resetImpl(obj)
obj.Count = 0;
end
function y = stepImpl(obj,u)
if (u > obj.Threshold)
obj.Count = obj.Count + 1;
end
y = obj.Count;
end
function inputName = getInputNamesImpl(~)
inputName = 'source data';
end
function outputName = getOutputNamesImpl(~)
outputName = 'count';
end
end
end
See Also
getInputNamesImpl | getNumInputsImpl | getNumOutputsImpl |
getOutputNamesImpl
Related Examples
•
“Change Number of Step Inputs or Outputs” on page 11-7
More About
•
11-12
“System Object Input Arguments and ~ in Code Examples” on page 11-76
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Validate Property and Input Values
Validate Property and Input Values
This example shows how to verify that the user’s inputs and property values are valid.
Validate Properties
This example shows how to validate the value of a single property using
set.PropertyName syntax. In this case, the PropertyName is Increment.
methods
% Validate the properties of the object
function set.Increment(obj,val)
if val >= 10
error('The increment value must be less than 10');
end
obj.Increment = val;
end
end
This example shows how to validate the value of two interdependent properties using the
validatePropertiesImpl method. In this case, the UseIncrement property value
must be true and the WrapValue property value must be less than the Increment
property value.
methods (Access = protected)
function validatePropertiesImpl(obj)
if obj.UseIncrement && obj.WrapValue < obj.Increment
error('Wrap value must be less than increment value');
end
end
end
Validate Inputs
This example shows how to validate that the first input is a numeric value.
methods (Access = protected)
function validateInputsImpl(~,x)
if ~isnumeric(x)
error('Input must be numeric');
end
end
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11-13
11
Define New System Objects
end
Complete Class Definition File with Property and Input Validation
classdef AddOne < matlab.System
% ADDONE Compute an output value by incrementing the input value
% All properties occur inside a properties declaration.
% These properties have public access (the default)
properties (Logical)
UseIncrement = true
end
properties (PositiveInteger)
Increment = 1
WrapValue = 10
end
methods
% Validate the properties of the object
function set.Increment(obj, val)
if val >= 10
error('The increment value must be less than 10');
end
obj.Increment = val;
end
end
methods (Access = protected)
function validatePropertiesImpl(obj)
if obj.UseIncrement && obj.WrapValue < obj.Increment
error('Wrap value must be less than increment value');
end
end
% Validate the inputs to the object
function validateInputsImpl(~,x)
if ~isnumeric(x)
error('Input must be numeric');
end
end
function out = stepImpl(obj,in)
if obj.UseIncrement
out = in + obj.Increment;
11-14
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Validate Property and Input Values
else
out = in + 1;
end
end
end
end
Note: All inputs default to variable-size inputs. See “Change Input Complexity or
Dimensions” for more information.
See Also
validateInputsImpl | validatePropertiesImpl
Related Examples
•
“Define Basic System Objects” on page 11-5
More About
•
“Methods Timing” on page 11-73
•
“Property Set Methods”
•
“System Object Input Arguments and ~ in Code Examples” on page 11-76
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11-15
11
Define New System Objects
Initialize Properties and Setup One-Time Calculations
This example shows how to write code to initialize and set up a System object.
In this example, you allocate file resources by opening the file so the System object can
write to that file. You do these initialization tasks one time during setup, rather than
every time you call the step method.
Define Public Properties to Initialize
In this example, you define the public Filename property and specify the value of that
property as the nontunable string, default.bin. Users cannot change nontunable
properties after the setup method has been called. Refer to the Methods Timing section
for more information.
properties (Nontunable)
Filename = 'default.bin'
end
Define Private Properties to Initialize
Users cannot access private properties directly, but only through methods of the System
object. In this example, you define the pFileID property as a private property. You also
define this property as hidden to indicate it is an internal property that never displays to
the user.
properties (Hidden,Access = private)
pFileID;
end
Define Setup
You use the setupImpl method to perform setup and initialization tasks. You should
include code in the setupImpl method that you want to execute one time only. The
setupImpl method is called once during the first call to the step method. In this
example, you allocate file resources by opening the file for writing binary data.
methods
function setupImpl(obj)
obj.pFileID = fopen(obj.Filename,'wb');
if obj.pFileID < 0
error('Opening the file failed');
11-16
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Initialize Properties and Setup One-Time Calculations
end
end
end
Although not part of setup, you should close files when your code is done using them. You
use the releaseImpl method to release resources.
Complete Class Definition File with Initialization and Setup
classdef MyFile < matlab.System
% MyFile write numbers to a file
% These properties are nontunable. They cannot be changed
% after the setup or step method has been called.
properties (Nontunable)
Filename = 'default.bin' % the name of the file to create
end
% These properties are private. Customers can only access
% these properties through methods on this object
properties (Hidden,Access = private)
pFileID; % The identifier of the file to open
end
methods (Access = protected)
% In setup allocate any resources, which in this case
% means opening the file.
function setupImpl(obj)
obj.pFileID = fopen(obj.Filename,'wb');
if obj.pFileID < 0
error('Opening the file failed');
end
end
% This System object™ writes the input to the file.
function stepImpl(obj,data)
fwrite(obj.pFileID,data);
end
% Use release to close the file to prevent the
% file handle from being left open.
function releaseImpl(obj)
fclose(obj.pFileID);
end
end
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11-17
11
Define New System Objects
end
See Also
releaseImpl | setupImpl | stepImpl
Related Examples
•
“Release System Object Resources” on page 11-34
•
“Define Property Attributes” on page 11-23
More About
•
11-18
“Methods Timing” on page 11-73
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Set Property Values at Construction Time
Set Property Values at Construction Time
This example shows how to define a System object constructor and allow it to accept
name-value property pairs as input.
Set Properties to Use Name-Value Pair Input
Define the System object constructor, which is a method that has the same name as
the class (MyFile in this example). Within that method, you use the setProperties
method to make all public properties available for input when the user constructs the
object. nargin is a MATLAB function that determines the number of input arguments.
varargin indicates all of the object’s public properties.
methods
function obj = MyFile(varargin)
setProperties(obj,nargin,varargin{:});
end
end
Complete Class Definition File with Constructor Setup
classdef MyFile < matlab.System
% MyFile write numbers to a file
% These properties are nontunable. They cannot be changed
% after the setup or step method has been called.
properties (Nontunable)
Filename ='default.bin' % the name of the file to create
Access = 'wb' % The file access string (write, binary)
end
% These properties are private. Customers can only access
% these properties through methods on this object
properties (Hidden,Access = private)
pFileID; % The identifier of the file to open
end
methods
% You call setProperties in the constructor to let
% a user specify public properties of object as
% name-value pairs.
function obj = MyFile(varargin)
setProperties(obj,nargin,varargin{:});
end
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11-19
11
Define New System Objects
end
methods (Access = protected)
% In setup allocate any resources, which in this case is
% opening the file.
function setupImpl(obj)
obj.pFileID = fopen(obj.Filename,obj.Access);
if obj.pFileID < 0
error('Opening the file failed');
end
end
% This System object™ writes the input to the file.
function stepImpl(obj,data)
fwrite(obj.pFileID,data);
end
% Use release to close the file to prevent the
% file handle from being left open.
function releaseImpl(obj)
fclose(obj.pFileID);
end
end
end
See Also
nargin | setProperties
Related Examples
11-20
•
“Define Property Attributes” on page 11-23
•
“Release System Object Resources” on page 11-34
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Reset Algorithm State
Reset Algorithm State
This example shows how to reset an object state.
Reset Counter to Zero
pCount is an internal counter property of the System object obj. The user calls the
reset method, which calls the resetImpl method. In this example , pCount resets to 0.
Note: When resetting an object’s state, make sure you reset the size, complexity, and
data type correctly.
methods (Access = protected)
function resetImpl(obj)
obj.pCount = 0;
end
end
Complete Class Definition File with State Reset
classdef Counter < matlab.System
% Counter System object™ that increments a counter
properties (Access = private)
pCount
end
methods (Access = protected)
% In step, increment the counter and return
% its value as an output
function c = stepImpl(obj)
obj.pCount = obj.pCount + 1;
c = obj.pCount;
end
% Reset the counter to zero.
function resetImpl(obj)
obj.pCount = 0;
end
end
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11-21
11
Define New System Objects
end
See “Methods Timing” on page 11-73 for more information.
See Also
resetImpl
More About
•
11-22
“Methods Timing” on page 11-73
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Define Property Attributes
Define Property Attributes
This example shows how to specify property attributes.
Property attributes, which add details to a property, provide a layer of control to your
properties. In addition to the MATLAB property attributes, System objects can use these
three additional attributes—nontunable, logical, and positiveInteger. To specify
multiple attributes, separate them with commas.
Specify Property as Nontunable
Use the nontunable attribute for a property when the algorithm depends on the value
being constant once data processing starts. Defining a property as nontunable may
improve the efficiency of your algorithm by removing the need to check for or react to
values that change. For code generation, defining a property as nontunable allows the
memory associated with that property to be optimized. You should define all properties
that affect the number of input or output ports as nontunable.
System object users cannot change nontunable properties after the setup or step
method has been called. In this example, you define the InitialValue property, and set
its value to 0.
properties (Nontunable)
InitialValue = 0;
end
Specify Property as Logical
Logical properties have the value, true or false. System object users can enter 1 or
0 or any value that can be converted to a logical. The value, however, displays as true
or false. You can use sparse logical values, but they must be scalar values. In this
example, the Increment property indicates whether to increase the counter. By default,
Increment is tunable property. The following restrictions apply to a property with the
Logical attribute,
• Cannot also be Dependent or PositiveInteger
• Default value must be true or false. You cannot use 1 or 0 as a default value.
properties (Logical)
Increment = true
end
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11-23
11
Define New System Objects
Specify Property as Positive Integer
In this example, the private property pCount is constrained to accept only real, positive
integers. You cannot use sparse values. The following restriction applies to a property
with the PositiveInteger attribute,
• Cannot also be Dependent or Logical
properties (PositiveInteger)
Count
end
Specify Property as DiscreteState
If your algorithm uses properties that hold state, you can assign those properties the
DiscreteState attribute . Properties with this attribute display their state values
when users call getDiscreteStateImpl via the getDiscreteState method. The
following restrictions apply to a property with the DiscreteState attribute,
• Numeric, logical, or fi value, but not a scaled double fi value
• Does not have any of these attributes: Nontunable, Dependent, Abstract,
Constant, or Transient.
• No default value
• Not publicly settable
• GetAccess = Public by default
• Value set only using the setupImpl method or when the System object is locked
during resetImpl or stepImpl
In this example, you define the Count property.
properties (DiscreteState)
Count;
end
Complete Class Definition File with Property Attributes
classdef Counter < matlab.System
% Counter Increment a counter to a maximum value
% These properties are nontunable. They cannot be changed
% after the setup or step method has been called.
properties (Nontunable)
11-24
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Define Property Attributes
% The inital value of the counter
InitialValue = 0
end
properties (Nontunable, PositiveInteger)
% The maximum value of the counter
MaxValue = 3
end
properties (Logical)
% Whether to increment the counter
Increment = true
end
properties (DiscreteState)
% Count state variable
Count
end
methods (Access = protected)
% In step, increment the counter and return its value
% as an output
function c = stepImpl(obj)
if obj.Increment && (obj.Count < obj.MaxValue)
obj.Count = obj.Count + 1;
else
disp(['Max count, ' num2str(obj.MaxValue) ',reached'])
end
c = obj.Count;
end
% Setup the Count state variable
function setupImpl(obj)
obj.Count = 0;
end
% Reset the counter to one.
function resetImpl(obj)
obj.Count = obj.InitialValue;
end
end
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11-25
11
Define New System Objects
end
More About
11-26
•
“Class Attributes”
•
“Property Attributes”
•
“What You Cannot Change While Your System Is Running”
•
“Methods Timing” on page 11-73
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Hide Inactive Properties
Hide Inactive Properties
This example shows how to hide the display of a property that is not active for a
particular object configuration.
Hide an inactive property
You use the isInactivePropertyImpl method to hide a property from displaying. If
the isInactiveProperty method returns true to the property you pass in, then that
property does not display.
methods (Access = protected)
function flag = isInactivePropertyImpl(obj,propertyName)
if strcmp(propertyName,'InitialValue')
flag = obj.UseRandomInitialValue;
else
flag = false;
end
end
end
Complete Class Definition File with Hidden Inactive Property
classdef Counter < matlab.System
% Counter Increment a counter
% These properties are nontunable. They cannot be changed
% after the setup or step method has been called.
properties (Nontunable)
% Allow the user to set the initial value
UseRandomInitialValue = true
InitialValue = 0
end
% The private count variable, which is tunable by default
properties (Access = private)
pCount
end
methods (Access = protected)
% In step, increment the counter and return its value
% as an output
function c = stepImpl(obj)
obj.pCount = obj.pCount + 1;
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11-27
11
Define New System Objects
c = obj.pCount;
end
% Reset the counter to either a random value or the initial
% value.
function resetImpl(obj)
if obj.UseRandomInitialValue
obj.pCount = rand();
else
obj.pCount = obj.InitialValue;
end
end
% This method controls visibility of the object's properties
function flag = isInactivePropertyImpl(obj,propertyName)
if strcmp(propertyName,'InitialValue')
flag = obj.UseRandomInitialValue;
else
flag = false;
end
end
end
end
See Also
isInactivePropertyImpl
11-28
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Limit Property Values to Finite String Set
Limit Property Values to Finite String Set
This example shows how to limit a property to accept only a finite set of string values.
Specify a Set of Valid String Values
String sets use two related properties. You first specify the user-visible property name
and default string value. Then, you specify the associated hidden property by appending
“Set” to the property name. You must use a capital “S” in “Set.”
In the “Set” property, you specify the valid string values as a cell array of the
matlab.system.Stringset class. This example uses Color and ColorSet as the
associated properties.
properties
Color = 'blue'
end
properties (Hidden,Transient)
ColorSet = matlab.system.StringSet({'red','blue','green'});
end
Complete Class Definition File with String Set
classdef Whiteboard < matlab.System
% Whiteboard Draw lines on a figure window
%
% This System object™ illustrates the use of StringSets
properties
Color = 'blue'
end
properties (Hidden,Transient)
% Let them choose a color
ColorSet = matlab.system.StringSet({'red','blue','green'});
end
methods (Access = protected)
function stepImpl(obj)
h = Whiteboard.getWhiteboard();
plot(h, ...
randn([2,1]),randn([2,1]), ...
'Color',obj.Color(1));
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11-29
11
Define New System Objects
end
function releaseImpl(obj)
cla(Whiteboard.getWhiteboard());
hold on
end
end
methods (Static)
function a = getWhiteboard()
h = findobj('tag','whiteboard');
if isempty(h)
h = figure('tag','whiteboard');
hold on
end
a = gca;
end
end
end
String Set System Object Example
%%
% Each call to step draws lines on a whiteboard
%% Construct the System object
hGreenInk = Whiteboard;
hBlueInk = Whiteboard;
% Change the color
% Note: Press tab after typing the first single quote to
% display all enumerated values.
hGreenInk.Color = 'green';
hBlueInk.Color = 'blue';
% Take a few steps
for i=1:3
hGreenInk.step();
hBlueInk.step();
end
%% Clear the whiteboard
hBlueInk.release();
%% Display System object used in this example
11-30
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Limit Property Values to Finite String Set
type('Whiteboard.m');
See Also
matlab.system.StringSet
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11-31
11
Define New System Objects
Process Tuned Properties
This example shows how to specify the action to take when a tunable property value
changes during simulation.
The processTunedPropertiesImpl method is useful for managing actions to prevent
duplication. In many cases, changing one of multiple interdependent properties causes
an action. With the processTunedPropertiesImpl method, you can control when that
action is taken so it is not repeated unnecessarily.
Control When a Lookup Table Is Generated
This example of processTunedPropertiesImpl causes the pLookupTable to be
regenerated when either the NumNotes or MiddleC property changes.
methods (Access = protected)
function processTunedPropertiesImpl(obj)
obj.pLookupTable = obj.MiddleC * ...
(1+log(1:obj.NumNotes)/log(12));
end
end
Complete Class Definition File with Tuned Property Processing
classdef TuningFork < matlab.System
% TuningFork Illustrate the processing of tuned parameters
%
properties
MiddleC = 440
NumNotes = 12
end
properties (Access = private)
pLookupTable
end
methods (Access = protected)
function resetImpl(obj)
obj.MiddleC = 440;
obj.pLookupTable = obj.MiddleC * ...
(1+log(1:obj.NumNotes)/log(12));
end
11-32
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Process Tuned Properties
function hz = stepImpl(obj,noteShift)
% A noteShift value of 1 corresponds to obj.MiddleC
hz = obj.pLookupTable(noteShift);
end
function processTunedPropertiesImpl(obj)
% Generate a lookup table of note frequencies
obj.pLookupTable = obj.MiddleC * ...
(1+log(1:obj.NumNotes)/log(12));
end
end
end
See Also
processTunedPropertiesImpl
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11-33
11
Define New System Objects
Release System Object Resources
This example shows how to release resources allocated and used by the System object.
These resources include allocated memory, files used for reading or writing, etc.
Release Memory by Clearing the Object
This method allows you to clear the axes on the Whiteboard figure window while keeping
the figure open.
methods
function releaseImpl(obj)
cla(Whiteboard.getWhiteboard());
hold on
end
end
Complete Class Definition File with Released Resources
classdef Whiteboard < matlab.System
% Whiteboard Draw lines on a figure window
%
% This System object™ shows the use of StringSets
%
properties
Color = 'blue'
end
properties (Hidden)
% Let user choose a color
ColorSet = matlab.system.StringSet({'red','blue','green'});
end
methods (Access = protected)
function stepImpl(obj)
h = Whiteboard.getWhiteboard();
plot(h, ...
randn([2,1]), randn([2,1]), ...
'Color',obj.Color(1));
end
function releaseImpl(obj)
cla(Whiteboard.getWhiteboard());
hold on
11-34
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Release System Object Resources
end
methods (Static)
function a = getWhiteboard()
h = findobj('tag','whiteboard');
if isempty(h)
h = figure('tag','whiteboard');
hold on
end
a = gca;
end
end
end
See Also
releaseImpl
Related Examples
•
“Initialize Properties and Setup One-Time Calculations” on page 11-16
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11-35
11
Define New System Objects
Define Composite System Objects
This example shows how to define System objects that include other System objects.
This example defines a filter System object from an FIR System object and an IIR System
object.
Store System Objects in Properties
To define a System object from other System objects, store those objects in your class
definition file as properties. In this example, FIR and IIR are separate System objects
defined in their own class-definition files. You use those two objects to calculate the pFir
and pIir property values.
properties (Nontunable, Access = private)
pFir % Store the FIR filter
pIir % Store the IIR filter
end
methods
function obj = Filter(varargin)
setProperties(obj,nargin,varargin{:});
obj.pFir = FIR(obj.zero);
obj.pIir = IIR(obj.pole);
end
end
Complete Class Definition File of Composite System Object
classdef Filter < matlab.System
% Filter System object with a single pole and a single zero
%
% This System object illustrates composition by
% composing an instance of itself.
%
properties (Nontunable)
zero = 0.01
pole = 0.5
end
properties (Nontunable,Access = private)
pZero % Store the FIR filter
pPole % Store the IIR filter
11-36
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Define Composite System Objects
end
methods
function obj = Filter(varargin)
setProperties(obj,nargin,varargin{:});
% Create instances of FIR and IIR as
% private properties
obj.pZero = Zero(obj.zero);
obj.pPole = Pole(obj.pole);
end
end
methods (Access = protected)
function setupImpl(obj,x)
setup(obj.pZero,x);
setup(obj.pPole,x);
end
function resetImpl(obj)
reset(obj.pZero);
reset(obj.pPole);
end
function y = stepImpl(obj,x)
y = step(obj.pZero,x) + step(obj.pPole,x);
end
function releaseImpl(obj)
release(obj.pZero);
release(obj.pPole);
end
end
end
Class Definition File for IIR Component of Filter
classdef Pole < matlab.System
properties
Den = 1
end
properties (Access = private)
tap = 0
end
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11-37
11
Define New System Objects
methods
function obj = Pole(varargin)
setProperties(obj,nargin,varargin{:},'Den');
end
end
methods (Access = protected)
function y = stepImpl(obj,x)
y = x + obj.tap * obj.Den;
obj.tap = y;
end
end
end
Class Definition File for FIR Component of Filter
classdef Zero < matlab.System
properties
Num = 1
end
properties (Access = private)
tap = 0
end
methods
function obj = Zero(varargin)
setProperties(obj,nargin,varargin{:},'Num');
end
end
methods (Access = protected)
function y = stepImpl(obj,x)
y = x + obj.tap * obj.Num;
obj.tap = x;
end
end
end
See Also
nargin
11-38
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Define Finite Source Objects
Define Finite Source Objects
This example shows how to define a System object that performs a specific number of
steps or specific number of reads from a file.
Use the FiniteSource Class and Specify End of the Source
1
Subclass from finite source class.
classdef RunTwice < matlab.System & ...
matlab.system.mixin.FiniteSource
2
Specify the end of the source with the isDoneImpl method. In this example, the
source has two iterations.
methods (Access = protected)
function bDone = isDoneImpl(obj)
bDone = obj.NumSteps==2
end
Complete Class Definition File with Finite Source
classdef RunTwice < matlab.System & ...
matlab.system.mixin.FiniteSource
% RunTwice System object that runs exactly two times
%
properties (Access = private)
NumSteps
end
methods (Access = protected)
function resetImpl(obj)
obj.NumSteps = 0;
end
function y = stepImpl(obj)
if ~obj.isDone()
obj.NumSteps = obj.NumSteps + 1;
y = obj.NumSteps;
else
y = 0;
end
end
function bDone = isDoneImpl(obj)
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11-39
11
Define New System Objects
bDone = obj.NumSteps==2;
end
end
end
See Also
matlab.system.mixin.FiniteSource
More About
11-40
•
“What Are Mixin Classes?” on page 11-77
•
“Subclassing Multiple Classes”
•
“System Object Input Arguments and ~ in Code Examples” on page 11-76
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Save System Object
Save System Object
This example shows how to save a System object.
Save System Object and Child Object
Define a saveObjectImpl method to specify that more than just public properties
should be saved when the user saves a System object. Within this method, use the
default [email protected] to save public properties to the struct,
s. Use the saveObject method to save child objects. Save protected and dependent
properties, and finally, if the object is locked, save the object’s state.
methods (Access = protected)
function s = saveObjectImpl(obj)
s = [email protected](obj);
s.child = matlab.System.saveObject(obj.child);
s.protected = obj.protected;
s.pdependentprop = obj.pdependentprop;
if isLocked(obj)
s.state = obj.state;
end
end
end
Complete Class Definition File with Save and Load
classdef MySaveLoader < matlab.System
properties (Access = private)
child
pdependentprop
end
properties (Access = protected)
protected = rand;
end
properties (DiscreteState = true)
state
end
properties (Dependent)
dependentprop
end
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11-41
11
Define New System Objects
methods
function obj = MySaveLoader(varargin)
[email protected]();
setProperties(obj,nargin,varargin{:});
end
end
methods (Access = protected)
function setupImpl(obj)
obj.state = 42;
end
function out = stepImpl(obj,in)
obj.state = in;
out = obj.state;
end
end
% Serialization
methods (Access = protected)
function s = saveObjectImpl(obj)
% Call the base class method
s = [email protected](obj);
% Save the child System objects
s.child = matlab.System.saveObject(obj.child);
% Save the protected & private properties
s.protected = obj.protected;
s.pdependentprop = obj.pdependentprop;
% Save the state only if object locked
if isLocked(obj)
s.state = obj.state;
end
end
function loadObjectImpl(obj,s,wasLocked)
% Load child System objects
obj.child = matlab.System.loadObject(s.child);
% Load protected and private properties
11-42
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Save System Object
obj.protected = s.protected;
obj.pdependentprop = s.pdependentprop;
% Load the state only if object locked
if wasLocked
obj.state = s.state;
end
% Call base class method to load public properties
[email protected](obj,s,wasLocked);
end
end
end
See Also
loadObjectImpl | saveObjectImpl
Related Examples
•
“Load System Object” on page 11-44
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11-43
11
Define New System Objects
Load System Object
This example shows how to load a System object.
Load System Object and Child Object
Define a loadObjectImpl method to load a previously saved System object. Within
this method, use the matlab.System.loadObject to assign the child object struct
data to the associated object property. Assign protected and dependent property data
to the associated object properties. If the object was locked when it was saved, assign
the object’s state to the associated property. Load the saved public properties with the
loadObjectImpl method.
methods (Access = protected)
function loadObjectImpl(obj,s,wasLocked)
obj.child = matlab.System.loadObject(s.child);
obj.protected = s.protected;
obj.pdependentprop = s.pdependentprop;
if wasLocked
obj.state = s.state;
end
[email protected](obj,s,wasLocked);
end
end
end
Complete Class Definition File with Save and Load
classdef MySaveLoader < matlab.System
properties (Access = private)
child
pdependentprop
end
properties (Access = protected)
protected = rand;
end
properties (DiscreteState = true)
state
end
properties (Dependent)
11-44
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Load System Object
dependentprop
end
methods
function obj = MySaveLoader(varargin)
[email protected]();
setProperties(obj,nargin,varargin{:});
end
end
methods (Access = protected)
function setupImpl(obj)
obj.state = 42;
end
function out = stepImpl(obj,in)
obj.state = in;
out = obj.state;
end
end
% Serialization
methods (Access = protected)
function s = saveObjectImpl(obj)
% Call the base class method
s = [email protected](obj);
% Save the child System objects
s.child = matlab.System.saveObject(obj.child);
% Save the protected & private properties
s.protected = obj.protected;
s.pdependentprop = obj.pdependentprop;
% Save the state only if object locked
if isLocked(obj)
s.state = obj.state;
end
end
function loadObjectImpl(obj,s,wasLocked)
% Load child System objects
obj.child = matlab.System.loadObject(s.child);
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11-45
11
Define New System Objects
% Load protected and private properties
obj.protected = s.protected;
obj.pdependentprop = s.pdependentprop;
% Load the state only if object locked
if wasLocked
obj.state = s.state;
end
% Call base class method to load public properties
[email protected](obj,s,wasLocked);
end
end
end
See Also
loadObjectImpl | saveObjectImpl
Related Examples
•
11-46
“Save System Object” on page 11-41
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Clone System Object
Clone System Object
This example shows how to clone a System object.
Clone System Object
You can define your own clone method, which is useful for copying objects without saving
their state. The default cloneImpl method copies both a System object™ and its current
state. If an object is locked, the default cloneImpl creates a cloned object that is also
locked. An example of when you may want to write your own clone method is for cloning
objects that handle resources. These objects cannot allocate resources twice and you
would not want to save their states. To write your clone method, use the saveObject
and loadObject methods to perform the clone within the cloneImpl method.
methods (Access = protected)
function obj2 = cloneImpl(obj1)
s = saveObject (obj1);
obj2 = loadObject(s);
end
end
Complete Class Definition File with Clone
classdef PassThrough < matlab.System
methods (Access = protected)
function y = stepImpl(~,u)
y = u;
end
function obj2 = cloneImpl(obj1)
s = matlab.System.saveObject(obj1);
obj2 = matlab.System.loadObject(s);
end
end
end
See Also
cloneImpl | loadObjectImpl | saveObjectImpl
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11-47
11
Define New System Objects
Define System Object Information
This example shows how to define information to display for a System object.
Define System Object Info
You can define your own info method to display specific information for your
System object. The default infoImpl method returns an empty struct. This
infoImpl method returns detailed information when the info method is called using
info(x,'details') or only count information if it is called using info(x).
methods (Access = protected)
function s = infoImpl(obj,varargin)
if nargin>1 && strcmp('details',varargin(1))
s = struct('Name','Counter',...
'Properties', struct('CurrentCount', ...
obj.pCount,'Threshold',obj.Threshold));
else
s = struct('Count',obj.pCount);
end
end
end
Complete Class Definition File with InfoImpl
classdef Counter < matlab.System
% Counter Count values above a threshold
properties
Threshold = 1
end
properties (DiscreteState)
Count
end
methods (Access = protected)
function setupImpl(obj)
obj.Count = 0;
end
function resetImpl(obj)
obj.Count = 0;
end
11-48
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Define System Object Information
function y = stepImpl(obj,u)
if (u > obj.Threshold)
obj.Count = obj.Count + 1;
end
y = obj.Count;
end
function s = infoImpl(obj,varargin)
if nargin>1 && strcmp('details',varargin(1))
s = struct('Name','Counter',...
'Properties', struct('CurrentCount', ...
obj.pCount,'Threshold',obj.Threshold));
else
s = struct('Count',obj.pCount);
end
end
end
See Also
infoImpl
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11-49
11
Define New System Objects
Define System Block Icon
This example shows how to define the block icon of a System object–based block
implemented using a MATLAB System block.
Use the CustomIcon Class and Define the Icon
1
Subclass from custom icon class.
classdef MyCounter < matlab.System & ...
matlab.system.mixin.CustomIcon
2
Use getIconImpl to specify the block icon as New Counter with a line break (\n)
between the two words.
methods (Access = protected)
function icon = getIconImpl(~)
icon = sprintf('New\nCounter');
end
end
Complete Class Definition File with Defined Icon
classdef MyCounter < matlab.System & ...
matlab.system.mixin.CustomIcon
% MyCounter Count values above a threshold
properties
Threshold = 1
end
properties (DiscreteState)
Count
end
methods
function obj = MyCounter(varargin)
setProperties(obj,nargin,varargin{:});
end
end
methods (Access = protected)
function setupImpl(obj)
obj.Count = 0;
end
11-50
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Define System Block Icon
function resetImpl(obj)
obj.Count = 0;
end
function y = stepImpl(obj,u)
if (u > obj.Threshold)
obj.Count = obj.Count + 1;
end
y = obj.Count;
end
function icon = getIconImpl(~)
icon = sprintf('New\nCounter');
end
end
end
See Also
matlab.system.mixin.CustomIcon | getIconImpl
More About
•
“What Are Mixin Classes?” on page 11-77
•
“Subclassing Multiple Classes”
•
“System Object Input Arguments and ~ in Code Examples” on page 11-76
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11-51
11
Define New System Objects
Add Header to System Block Dialog
This example shows how to add a header panel to a System object–based block
implemented using a MATLAB System block.
Define Header Title and Text
This example shows how to use getHeaderImpl to specify a panel title and text for the
MyCounter System object.
If you do not specify the getHeaderImpl, the block does not display any title or text for
the panel.
You always set the getHeaderImpl method access to protected because it is an
internal method that end users do not directly call or run.
methods (Static, Access = protected)
function header = getHeaderImpl
header = matlab.system.display.Header('MyCounter',...
'Title','My Enhanced Counter');
end
end
Complete Class Definition File with Defined Header
classdef MyCounter < matlab.System
% MyCounter Count values
properties
Threshold = 1
end
properties (DiscreteState)
Count
end
methods (Static, Access = protected)
function header = getHeaderImpl
header = matlab.system.display.Header('MyCounter',...
'Title','My Enhanced Counter',...
'Text', 'This counter is an enhanced version.');
end
end
11-52
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Add Header to System Block Dialog
methods (Access = protected)
function setupImpl(obj,u)
obj.Count = 0;
end
function y = stepImpl(obj,u)
if (u > obj.Threshold)
obj.Count = obj.Count + 1;
end
y = obj.Count;
end
function resetImpl(obj)
obj.Count = 0;
end
end
end
See Also
matlab.system.display.Header | getHeaderImpl
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11-53
11
Define New System Objects
Add Property Groups to System Object and Block Dialog
This example shows how to define property sections and section groups for System object
display. The sections and section groups display as panels and tabs, respectively, in the
MATLAB System block dialog.
Define Section of Properties
This example shows how to use matlab.system.display.Section and
getPropertyGroupsImpl to define two property group sections by specifying their
titles and property lists.
If you do not specify a property in getPropertyGroupsImpl, the block does not display
that property.
methods (Static, Access = protected)
function groups = getPropertyGroupsImpl
valueGroup = matlab.system.display.Section(...
'Title','Value parameters',...
'PropertyList',{'StartValue','EndValue'});
thresholdGroup = matlab.system.display.Section(...
'Title','Threshold parameters',...
'PropertyList',{'Threshold','UseThreshold'});
groups = [valueGroup,thresholdGroup];
end
end
Define Group of Sections
This example shows how to use matlab.system.display.SectionGroup,
matlab.system.display.Section, and getPropertyGroupsImpl to define two
tabs, each containing specific properties.
methods (Static, Access = protected)
function groups = getPropertyGroupsImpl
upperGroup = matlab.system.display.Section(...
'Title', 'Upper threshold', ...
'PropertyList',{'UpperThreshold'});
lowerGroup = matlab.system.display.Section(...
'Title','Lower threshold', ...
'PropertyList',{'UseLowerThreshold','LowerThreshold'});
thresholdGroup = matlab.system.display.SectionGroup(...
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Add Property Groups to System Object and Block Dialog
'Title', 'Parameters', ...
'Sections', [upperGroup,lowerGroup]);
valuesGroup = matlab.system.display.SectionGroup(...
'Title', 'Initial conditions', ...
'PropertyList', {'StartValue'});
groups = [thresholdGroup, valuesGroup];
end
end
Complete Class Definition File with Property Group and Separate Tab
classdef EnhancedCounter < matlab.System
% EnhancedCounter Count values considering thresholds
properties
UpperThreshold = 1;
LowerThreshold = 0;
end
properties (Nontunable)
StartValue = 0;
end
properties(Logical,Nontunable)
% Count values less than lower threshold
UseLowerThreshold = true;
end
properties (DiscreteState)
Count;
end
methods (Static, Access = protected)
function groups = getPropertyGroupsImpl
upperGroup = matlab.system.display.Section(...
'Title', 'Upper threshold', ...
'PropertyList',{'UpperThreshold'});
lowerGroup = matlab.system.display.Section(...
'Title','Lower threshold', ...
'PropertyList',{'UseLowerThreshold','LowerThreshold'});
thresholdGroup = matlab.system.display.SectionGroup(...
'Title', 'Parameters', ...
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11-55
11
Define New System Objects
'Sections',
[upperGroup,lowerGroup]);
valuesGroup = matlab.system.display.SectionGroup(...
'Title', 'Initial conditions', ...
'PropertyList', {'StartValue'});
groups = [thresholdGroup, valuesGroup];
end
end
methods (Access = protected)
function setupImpl(obj)
obj.Count = obj.StartValue;
end
function y = stepImpl(obj,u)
if obj.UseLowerThreshold
if (u > obj.UpperThreshold) || ...
(u < obj.LowerThreshold)
obj.Count = obj.Count + 1;
end
else
if (u > obj.UpperThreshold)
obj.Count = obj.Count + 1;
end
end
y = obj.Count;
end
function resetImpl(obj)
obj.Count = obj.StartValue;
end
function flag = isInactivePropertyImpl(obj, prop)
flag = false;
switch prop
case 'LowerThreshold'
flag = ~obj.UseLowerThreshold;
end
end
end
11-56
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Add Property Groups to System Object and Block Dialog
end
See Also
matlab.system.display.Section | matlab.system.display.SectionGroup |
getPropertyGroupsImpl
More About
•
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11-57
11
Define New System Objects
Set Output Size
This example shows how to specify the size of a System object output using the
getOutputSizeImpl method. Use this method when Simulink cannot infer the output
size from the inputs during model compilation.
Subclass from both the matlab.System base class and the Propagates mixin class.
classdef CounterReset < matlab.System & ...
matlab.system.mixin.Propagates
Use the getOutputSizeImpl method to specify the output size.
methods (Access = protected)
function sizeout = getOutputSizeImpl(~)
sizeout = [1 1];
end
end
View the method in the complete class definition file.
classdef CounterReset < matlab.System & matlab.system.mixin.Propagates
% CounterReset Count values above a threshold
properties
Threshold = 1
end
properties (DiscreteState)
Count
end
methods (Access = protected)
function setupImpl(obj)
obj.Count = 0;
end
function y = stepImpl(obj,u1,u2)
% Add to count if u1 is above threshold
% Reset if u2 is true
if (u2)
obj.Count = 0;
elseif (u1 > obj.Threshold)
obj.Count = obj.Count + 1;
11-58
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Set Output Size
end
y = obj.Count;
end
function resetImpl(obj)
obj.Count = 0;
end
function [sz,dt,cp] = getDiscreteStateSpecificationImpl(~,name)
if strcmp(name,'Count')
sz = [1 1];
dt = 'double';
cp = false;
else
error(['Error: Incorrect State Name: 'name'.']);
end
end
function dataout = getOutputDataTypeImpl(~)
dataout = 'double';
end
function sizeout = getOutputSizeImpl(~)
sizeout = [1 1];
end
function cplxout = isOutputComplexImpl(~)
cplxout = false;
end
function fixedout = isOutputFixedSizeImpl(~)
fixedout = true;
end
end
end
See Also
matlab.system.mixin.Propagates | getOutputSizeImpl
More About
•
“What Are Mixin Classes?” on page 11-77
•
“Subclassing Multiple Classes”
•
“System Object Input Arguments and ~ in Code Examples” on page 11-76
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Define New System Objects
Set Output Data Type
This example shows how to specify the data type of a System object output using the
getOutputDataTypeImpl method. Use this method when Simulink cannot infer the
data type from the inputs during model compilation.
Subclass from both the matlab.System base class and the Propagates mixin class.
classdef CounterReset < matlab.System & ...
matlab.system.mixin.Propagates
Use the getOutputDataTypeImpl method to specify the output data type as a double.
methods (Access = protected)
function dataout = getOutputDataTypeImpl(~)
dataout = 'double';
end
end
View the method in the complete class definition file.
classdef CounterReset < matlab.System & matlab.system.mixin.Propagates
% CounterReset Count values above a threshold
properties
Threshold = 1
end
properties (DiscreteState)
Count
end
methods (Access = protected)
function setupImpl(obj)
obj.Count = 0;
end
function resetImpl(obj)
obj.Count = 0;
end
function y = stepImpl(obj,u1,u2)
% Add to count if u1 is above threshold
% Reset if u2 is true
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Set Output Data Type
if (u2)
obj.Count = 0;
elseif (u1 > obj.Threshold)
obj.Count = obj.Count + 1;
end
y = obj.Count;
end
function [sz,dt,cp] = getDiscreteStateSpecificationImpl(~,name)
if strcmp(name,'Count')
sz = [1 1];
dt = 'double';
cp = false;
else
error(['Error: Incorrect State Name: 'name'.']);
end
end
function dataout = getOutputDataTypeImpl(~)
dataout = 'double';
end
function sizeout = getOutputSizeImpl(~)
sizeout = [1 1];
end
function cplxout = isOutputComplexImpl(~)
cplxout = false;
end
function fixedout = isOutputFixedSizeImpl(~)
fixedout = true;
end
end
end
See Also
matlab.system.mixin.Propagates | getOutputDataTypeImpl
More About
•
“What Are Mixin Classes?” on page 11-77
•
“Subclassing Multiple Classes”
•
“System Object Input Arguments and ~ in Code Examples” on page 11-76
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11-61
11
Define New System Objects
Set Output Complexity
This example shows how to specify whether a System object output is complex or real
using the isOutputComplexImpl method. Use this method when Simulink cannot infer
the output complexity from the inputs during model compilation.
Subclass from both the matlab.System base class and the Propagates mixin class.
classdef CounterReset < matlab.System & ...
matlab.system.mixin.Propagates
Use the isOutputComplexImpl method to specify that the output is real.
methods (Access = protected)
function cplxout = isOutputComplexImpl(~)
cplxout = false;
end
end
View the method in the complete class definition file.
classdef CounterReset < matlab.System & matlab.system.mixin.Propagates
% CounterReset Count values above a threshold
properties
Threshold = 1
end
properties (DiscreteState)
Count
end
methods (Access = protected)
function setupImpl(obj)
obj.Count = 0;
end
function resetImpl(obj)
obj.Count = 0;
end
function y = stepImpl(obj,u1,u2)
% Add to count if u1 is above threshold
% Reset if u2 is true
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Set Output Complexity
if (u2)
obj.Count = 0;
elseif (u1 > obj.Threshold)
obj.Count = obj.Count + 1;
end
y = obj.Count;
end
function [sz,dt,cp] = getDiscreteStateSpecificationImpl(~,name)
if strcmp(name,'Count')
sz = [1 1];
dt = 'double';
cp = false;
else
error(['Error: Incorrect State Name: 'name'.']);
end
end
function dataout = getOutputDataTypeImpl(~)
dataout = 'double';
end
function sizeout = getOutputSizeImpl(~)
sizeout = [1 1];
end
function cplxout = isOutputComplexImpl(~)
cplxout = false;
end
function fixedout = isOutputFixedSizeImpl(~)
fixedout = true;
end
end
end
See Also
matlab.system.mixin.Propagates | isOutputComplexImpl
More About
•
“What Are Mixin Classes?” on page 11-77
•
“Subclassing Multiple Classes”
•
“System Object Input Arguments and ~ in Code Examples” on page 11-76
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11
Define New System Objects
Specify Whether Output Is Fixed- or Variable-Size
This example shows how to specify whether a System object output is fixed- or variablesize. Use the isOutputFixedSizeImpl method when Simulink cannot infer the output
type from the inputs during model compilation.
Subclass from both the matlab.System base class and the Propagates mixin class.
classdef CounterReset < matlab.System & ...
matlab.system.mixin.Propagates
Use the isOutputFixedSizeImpl method to specify that the output is fixed size.
methods (Access = protected)
function fixedout = isOutputFixedSizeImpl(~)
fixedout = true;
end
end
View the method in the complete class definition file.
classdef CounterReset < matlab.System & matlab.system.mixin.Propagates
% CounterReset Count values above a threshold
properties
Threshold = 1
end
properties (DiscreteState)
Count
end
methods (Access = protected)
function setupImpl(obj)
obj.Count = 0;
end
function resetImpl(obj)
obj.Count = 0;
end
function y = stepImpl(obj,u1,u2)
% Add to count if u1 is above threshold
% Reset if u2 is true
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Specify Whether Output Is Fixed- or Variable-Size
if (u2)
obj.Count = 0;
elseif (u1 > obj.Threshold)
obj.Count = obj.Count + 1;
end
y = obj.Count;
end
function [sz,dt,cp] = getDiscreteStateSpecificationImpl(~,name)
if strcmp(name,'Count')
sz = [1 1];
dt = 'double';
cp = false;
else
error(['Error: Incorrect State Name: 'name'.']);
end
end
function dataout = getOutputDataTypeImpl(~)
dataout = 'double';
end
function sizeout = getOutputSizeImpl(~)
sizeout = [1 1];
end
function cplxout = isOutputComplexImpl(~)
cplxout = false;
end
function fixedout = isOutputFixedSizeImpl(~)
fixedout = true;
end
end
end
See Also
matlab.system.mixin.Propagates | isOutputFixedSizeImpl
More About
•
“What Are Mixin Classes?” on page 11-77
•
“Subclassing Multiple Classes”
•
“System Object Input Arguments and ~ in Code Examples” on page 11-76
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11
Define New System Objects
Specify Discrete State Output Specification
This example shows how to specify the size, data type, and complexity of a discrete
state property using the getDiscreteStateSpecificationImpl method. Use this
method when your System object has a property with the DiscreteState attribute and
Simulink cannot infer the output specifications during model compilation.
Subclass from both the matlab.System base class and from the Propagates mixin
class.
classdef CounterReset < matlab.System & ...
matlab.system.mixin.Propagates
Use the getDiscreteStateSpecificationImpl method to specify the size and data
type. Also specify the complexity of a discrete state property, which is used in the counter
reset example.
methods (Access = protected)
function [sz,dt,cp] = getDiscreteStateSpecificationImpl(~,name)
sz = [1 1];
dt = 'double';
cp = false;
end
end
View the method in the complete class definition file.
classdef CounterReset < matlab.System & matlab.system.mixin.Propagates
% CounterReset Count values above a threshold
properties
Threshold = 1
end
properties (DiscreteState)
Count
end
methods (Access = protected)
function setupImpl(obj)
obj.Count = 0;
end
function resetImpl(obj)
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Specify Discrete State Output Specification
obj.Count = 0;
end
function y = stepImpl(obj,u1,u2)
% Add to count if u1 is above threshold
% Reset if u2 is true
if (u2)
obj.Count = 0;
elseif (u1 > obj.Threshold)
obj.Count = obj.Count + 1;
end
y = obj.Count;
end
function [sz,dt,cp] = getDiscreteStateSpecificationImpl(~,name)
sz = [1 1];
dt = 'double';
cp = false;
end
function dataout = getOutputDataTypeImpl(~)
dataout = 'double';
end
function sizeout = getOutputSizeImpl(~)
sizeout = [1 1];
end
function cplxout = isOutputComplexImpl(~)
cplxout = false;
end
function fixedout = isOutputFixedSizeImpl(~)
fixedout = true;
end
end
end
See Also
matlab.system.mixin.Propagates | getDiscreteStateSpecificationImpl
More About
•
“What Are Mixin Classes?” on page 11-77
•
“Subclassing Multiple Classes”
•
“System Object Input Arguments and ~ in Code Examples” on page 11-76
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11
Define New System Objects
Use Update and Output for Nondirect Feedthrough
This example shows how to implement nondirect feedthrough for a System object using
the updateImpl, outputImpl and isInputDirectFeedthroughImpl methods.
In nondirect feedthrough, the object’s outputs depend only on the internal states and
properties of the object, rather than the input at that instant in time. You use these
methods to separate the output calculation from the state updates of a System object.
This enables you to use that object in a feedback loop and prevent algebraic loops.
Subclass from the Nondirect Mixin Class
To use the updateImpl, outputImpl, and isInputDirectFeedthroughImpl
methods, you must subclass from both the matlab.System base class and the
Nondirect mixin class.
classdef IntegerDelaySysObj < matlab.System & ...
matlab.system.mixin.Nondirect
Implement Updates to the Object
Implement an updateImpl method to update the object with previous inputs.
methods (Access = protected)
function updateImpl(obj,u)
obj.PreviousInput = [u obj.PreviousInput(1:end-1)];
end
end
Implement Outputs from Object
Implement an outputImpl method to output the previous, not the current input.
methods (Access = protected)
function [y] = outputImpl(obj,~)
y = obj.PreviousInput(end);
end
end
Implement Whether Input Is Direct Feedthrough
Implement an isInputDirectFeedthroughImpl method to indicate that the input is
nondirect feedthrough.
methods (Access = protected)
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Use Update and Output for Nondirect Feedthrough
function flag = isInputDirectFeedthroughImpl(~,~)
flag = false;
end
end
Complete Class Definition File with Update and Output
classdef intDelaySysObj < matlab.System &...
matlab.system.mixin.Nondirect &...
matlab.system.mixin.CustomIcon
% intDelaySysObj Delay input by specified number of samples.
properties
InitialOutput = 0;
end
properties (Nontunable)
NumDelays = 1;
end
properties (DiscreteState)
PreviousInput;
end
methods (Access = protected)
function validatePropertiesImpl(obj)
if ((numel(obj.NumDelays)>1) || (obj.NumDelays <= 0))
error('Number of delays must be positive non-zero scalar value.');
end
if (numel(obj.InitialOutput)>1)
error('Initial Output must be scalar value.');
end
end
function setupImpl(obj)
obj.PreviousInput = ones(1,obj.NumDelays)*obj.InitialOutput;
end
function resetImpl(obj)
obj.PreviousInput = ones(1,obj.NumDelays)*obj.InitialOutput;
end
function [y] = outputImpl(obj,~)
y = obj.PreviousInput(end);
end
function updateImpl(obj, u)
obj.PreviousInput = [u obj.PreviousInput(1:end-1)];
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Define New System Objects
end
function flag = isInputDirectFeedthroughImpl(~,~)
flag = false;
end
end
end
See Also
matlab.system.mixin.Nondirect | isInputDirectFeedthroughImpl |
outputImpl | updateImpl
More About
11-70
•
“What Are Mixin Classes?” on page 11-77
•
“Subclassing Multiple Classes”
•
“System Object Input Arguments and ~ in Code Examples” on page 11-76
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Enable For Each Subsystem Support
Enable For Each Subsystem Support
This example shows how to enable using a System object in a Simulink For Each
subsystem. Include the supportsMultipleInstanceImpl method in your class
definition file. This method applies only when the System object is used in Simulink via
the MATLAB System block.
Use the supportsMultipleInstanceImpl method and have it return true to indicate
that the System object supports multiple calls in a Simulink For Each subsystem.
methods (Access = protected)
function flag = supportsMultipleInstanceImpl(obj)
flag = true;
end
end
View the method in the complete class definition file.
classdef RandSeed < matlab.System
% RANDSEED Random noise with seed for use in For Each subsystem
properties (DiscreteState)
count;
end
properties (Nontunable)
seed = 20;
end
properties (Nontunable,Logical)
useSeed = false;
end
methods (Access = protected)
function y = stepImpl(obj,u1)
% Initial use after reset/setup
% and use the seed
if (obj.useSeed && ~obj.count)
rng(obj.seed);
end
obj.count = obj.count + 1;
[m,n] = size(u1);
% Uses default rng seed
y = rand(m,n) + u1;
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Define New System Objects
end
function setupImpl(obj)
obj.count = 0;
end
function resetImpl(obj)
obj.count = 0;
end
function flag = supportsMultipleInstanceImpl(obj)
flag = obj.useSeed;
end
end
end
See Also
matlab.System | supportsMultipleInstanceImpl
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Methods Timing
Methods Timing
In this section...
“Setup Method Call Sequence” on page 11-73
“Step Method Call Sequence” on page 11-73
“Reset Method Call Sequence” on page 11-74
“Release Method Call Sequence” on page 11-75
Setup Method Call Sequence
This hierarchy shows the actions performed when you call the setup method.
Step Method Call Sequence
This hierarchy shows the actions performed when you call the step method.
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Define New System Objects
Reset Method Call Sequence
This hierarchy shows the actions performed when you call the reset method.
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Methods Timing
Release Method Call Sequence
This hierarchy shows the actions performed when you call the release method.
See Also
releaseImpl | resetImpl | setupImpl | stepImpl
Related Examples
•
“Release System Object Resources” on page 11-34
•
“Reset Algorithm State” on page 11-21
•
“Set Property Values at Construction Time” on page 11-19
•
“Define Basic System Objects” on page 11-5
More About
•
“What Are System Object Methods?”
•
“The Step Method”
•
“Common Methods”
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11-75
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Define New System Objects
System Object Input Arguments and ~ in Code Examples
All methods, except static methods, expect the System object handle as the first input
argument. You can use any name for your System object handle. In many examples,
instead of passing in the object handle, ~ is used to indicate that the object handle is
not used in the function. Using ~ instead of an object handle prevents warnings about
unused variables.
11-76
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What Are Mixin Classes?
What Are Mixin Classes?
Mixin classes are partial classes that you can combine in various combinations to form
desired behaviors using multiple inheritance. System objects are composed of a base
class, matlab.System and may include one or more mixin classes. You specify the base
class and mixin classes on the first line of your class definition file.
The following mixin classes are available for use with System objects.
• matlab.system.mixin.CustomIcon — Defines a block icon for System objects in
the MATLAB System block
• matlab.system.mixin.FiniteSource — Adds the isDone method to System
objects that are sources
• matlab.system.mixin.Nondirect — Allows the System object, when used in the
MATLAB System block, to support nondirect feedthrough by making the runtime
callback functions, output and update available
• matlab.system.mixin.Propagates — Enables System objects to operate in the
MATLAB System block using the interpreted execution
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Define New System Objects
Best Practices for Defining System Objects
A System object is a specialized kind of MATLAB object that is optimized for iterative
processing. Use System objects when you need to call the step method multiple times
or process data in a loop. When defining your own System object, use the following
suggestions to help your code run efficiently.
• Define all one-time calculations in the setupImpl method and cache the results in a
private property. Use the stepImpl method for repeated calculations.
• For parameters that do not change, define them in a locked object as Nontunable
properties.
• If the number of System object inputs does not change, do not implement the
getNumInputsImpl method. Also do not implement the getNumInputsImpl
method when you explicitly list the inputs in the stepImpl method instead of
using varargin. The same caveats apply to the outputs, getNumOutputsImpl and
varargout.
• Variables that do not need to retain their values between calls should have local scope
for that method.
• If properties are accessed more than once in the stepImpl method, or in the
updateImpl and outputImpl methods, cache those properties as local variables
inside the method. Iterative calculations using cached local variables run faster than
calculations that must access the properties of an object. When the calculations for
the method complete, you can save the local cached results back to the properties of
that System object. Copy frequently used tunable properties into private properties.
• For best practices for including System objects in code generation, see “System
Objects in MATLAB Code Generation”.
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12
HDL Code Generation
• “What is HDL Code Generation?” on page 12-2
• “Blocks With HDL Support” on page 12-3
• “System Objects With HDL Support” on page 12-5
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12
HDL Code Generation
What is HDL Code Generation?
You can use MATLAB and Simulink for rapid prototyping of hardware designs. DSP
System Toolbox blocks provide support for HDL code generation when used with HDL
Coder™. Using DSP System Toolbox with Filter Design HDL Coder™, you can generate
HDL code from digital filter designs and optimize filter implementation for hardware
speed or area. The HDL Coder products generate target-independent synthesizable
Verilog and VHDL code for FPGA programming or ASIC prototyping and design.
12-2
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Blocks With HDL Support
Blocks With HDL Support
Filtering
• Biquad Filter
• CIC Decimation
• CIC Interpolation
• DC Blocker
• Discrete FIR Filter
• FIR Decimation
• FIR Interpolation
• LMS Filter
Math Functions
• Complex to Magnitude-Angle HDL Optimized
Signal Operations
• Delay
• Downsample
• NCO
• NCO HDL Optimized
• Repeat
• Upsample
Signal Management
Indexing
• Multiport Selector
• Selector
• Variable Selector
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12-3
12
HDL Code Generation
Signal Attributes
• Convert 1-D to 2-D
• Data Type Conversion
• Frame Conversion
Sinks
These blocks can be used for simulation visibility in models that generate HDL code, but
are not included in the hardware implementation.
• Display
• Matrix Viewer
• To Workspace
• Spectrum Analyzer
• Time Scope
• Vector Scope
• Waterfall
Statistics
• Maximum
• Minimum
Transforms
• FFT HDL Optimized
• IFFT HDL Optimized
12-4
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System Objects With HDL Support
System Objects With HDL Support
The coder supports the following DSP System Toolbox System objects for HDL code
generation:
• dsp.BiquadFilter
• dsp.Delay
• dsp.DCBlocker
• dsp.FIRFilter
• dsp.HDLComplexToMagnitudeAngle
• dsp.HDLFFT, dsp.HDLIFFT
• dsp.HDLNCO
• dsp.Maximum, dsp.Minimum
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12-5
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‫‪12-6‬‬
13
Links to Category Pages
• “Signal Management Library” on page 13-2
• “Sinks Library” on page 13-3
• “Math Functions Library” on page 13-4
• “Filtering Library” on page 13-5
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13
Links to Category Pages
Signal Management Library
You can find the relevant blocks in the following pages:
• “Buffers, Switches, and Counters”
• “Signal Attributes and Indexing”
• “Signal Operations”
13-2
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Sinks Library
Sinks Library
You can find the relevant blocks in the following pages:
• “Signal Import and Export”
• “Scopes and Data Logging”
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13-3
13
Links to Category Pages
Math Functions Library
You can find the relevant blocks in the following pages:
• “Array and Matrix Mathematics”
• “Linear Algebra”
13-4
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Filtering Library
Filtering Library
You can find the relevant blocks in the following pages:
• “Filter Design”
• “Single-Rate Filters”
• “Multirate and Multistage Filters”
• “Adaptive Filters”
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‫‪13-6‬‬
14
Designing Lowpass FIR Filters
• “Lowpass FIR Filter Design” on page 14-2
• “Controlling Design Specifications in Lowpass FIR Design” on page 14-7
• “Designing Filters with Non-Equiripple Stopband” on page 14-13
• “Minimizing Lowpass FIR Filter Length” on page 14-18
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14
Designing Lowpass FIR Filters
Lowpass FIR Filter Design
This example shows how to design a lowpass FIR filter using fdesign . An ideal lowpass
filter requires an infinite impulse response. Truncating or windowing the impulse
response results in the so-called window method of FIR filter design.
A Lowpass FIR Filter Design Using Various Windows
FIR filters are widely used due to the powerful design algorithms that exist for them,
their inherent stability when implemented in non-recursive form, the ease with which
one can attain linear phase, their simple extensibility to multirate cases, and the ample
hardware support that exists for them among other reasons. This example showcases
functionality in the DSP System Toolbox™ for the design of low pass FIR filters with a
variety of characteristics. Many of the concepts presented here can be extended to other
responses such as highpass, bandpass, etc.
Consider a simple design of a lowpass filter with a cutoff frequency of 0.4*pi radians per
sample:
Fc = 0.4;
N = 100;
Hf = fdesign.lowpass('N,Fc',N,Fc);
We can design this lowpass filter using the window method. For example, we can use a
Hamming window or a Dolph-Chebyshev window:
Hd1 = design(Hf,'window','window',@hamming,'systemobject',true);
Hd2 = design(Hf,'window','window',{@chebwin,50}, ...
'systemobject',true);
hfvt = fvtool(Hd1,Hd2,'Color','White');
legend(hfvt,'Hamming window design', ...
'Dolph-Chebyshev window design')
14-2
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Lowpass FIR Filter Design
The choice of filter was arbitrary. Since ideally the order should be infinite, in general,
a larger order results in a better approximation to ideal at the expense of a more costly
implementation. For instance, with a Dolph-Chebyshev window, we can decrease the
transition region by increasing the filter order:
Hf.FilterOrder = 200;
Hd3 = design(Hf,'window','window',{@chebwin,50},...
'systemobject',true);
hfvt2 = fvtool(Hd2,Hd3,'Color','White');
legend(hfvt2,'Dolph-Chebyshev window design. Order = 100',...
'Dolph-Chebyshev window design. Order = 200')
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14-3
14
Designing Lowpass FIR Filters
Minimum Order Lowpass Filter Design
In order to determine a suitable filter order, it is necessary to specify the amount of
passband ripple and stopband attenuation that will be tolerated. It is also necessary to
specify the width of the transition region around the ideal cutoff frequency. The latter
is done by setting the passband edge frequency and the stopband edge frequency. The
difference between the two determines the transition width.
Fp = 0.38;
Fst = 0.42;
Ap = 0.06;
Ast = 60;
setspecs(Hf,'Fp,Fst,Ap,Ast',Fp,Fst,Ap,Ast);
We can still use the window method, along with a Kaiser window, to design the low pass
filter.
Hd4 = design(Hf,'kaiserwin','systemobject',true);
14-4
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Lowpass FIR Filter Design
measure(Hd4)
ans =
Sampling Frequency
Passband Edge
3-dB Point
6-dB Point
Stopband Edge
Passband Ripple
Stopband Atten.
Transition Width
:
:
:
:
:
:
:
:
N/A (normalized frequency)
0.38
0.39539
0.4
0.42
0.016058 dB
60.092 dB
0.04
One thing to note is that the transition width as specified is centered around the cutoff
frequency of 0.4 pi. This will become the point at which the gain of the lowpass filter is
half the passband gain (or the point at which the filter reaches 6 dB of attenuation).
Optimal Minimum Order Designs
The Kaiser window design is not an optimal design and as a result the filter order
required to meet the specifications using this method is larger than it needs to be.
Equiripple designs result in the lowpass filter with the smallest possible order to meet a
set of specifications.
Hd5 = design(Hf,'equiripple','systemobject',true);
hfvt3 = fvtool(Hd4,Hd5,'Color','White');
legend(hfvt3,'Kaiser window design','Equiripple design')
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14-5
14
Designing Lowpass FIR Filters
In this case, 146 coefficients are needed by the equiripple design while 183 are needed by
the Kaiser window design.
14-6
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Controlling Design Specifications in Lowpass FIR Design
Controlling Design Specifications in Lowpass FIR Design
This example shows how to control the filter order, passband ripple, stopband
attenuation, and transition region width of a lowpass FIR filter.
Controlling the Filter Order and Passband Ripples and Stopband Attenuation
When targeting custom hardware, it is common to find cases where the number of
coefficients is constrained to a set number. In these cases, minimum order designs are
not useful because there is no control over the resulting filter order. As an example,
suppose that only 101 coefficients could be used and the passband ripple/stopband
attenuation specifications need to be met. We can still use equiripple designs for these
specifications. However, we lose control over the transition width which will increase.
This is the price to pay for reducing the order while maintaining the passband ripple/
stopband attenuation specifications.
Consider a simple design of a lowpass filter with a cutoff frequency of 0.4*pi radians per
sample:
Ap = 0.06;
Ast = 60;
Fp = 0.38;
Fst = 0.42;
Hf=fdesign.lowpass('Fp,Fst,Ap,Ast',Fp,Fst,Ap,Ast);
Design an equiripple filter:
Hd1 = design(Hf,'equiripple','systemobject',true);
Set the number of coefficients to 101, which means setting the order to 100:
N = 100;
% order = 100 -> 101 coefficients
Fc = 0.4;
setspecs(Hf,'N,Fc,Ap,Ast',N,Fc,Ap,Ast);
Design a second equiripple filter with the given constraint:
Hd2 = design(Hf,'equiripple','systemobject',true);
Measure the filter variables of the second equiripple filter, and compare the graphs of the
first and second filters:
measure(Hd2)
hfvt = fvtool(Hd1,Hd2,'Color','White');
legend(hfvt,'Equiripple design, 146 coeffcients', ...
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14-7
14
Designing Lowpass FIR Filters
'Equiripple design, 101 coefficients')
Sampling Frequency
Passband Edge
3-dB Point
6-dB Point
Stopband Edge
Passband Ripple
Stopband Atten.
Transition Width
:
:
:
:
:
:
:
:
N/A (normalized frequency)
0.37316
0.39285
0.4
0.43134
0.06 dB
60 dB
0.058177
Notice that the transition has increased by almost 50%. This is not surprising given the
almost 50% difference between 101 coefficients and 146 coefficients.
Controlling the Transition Region Width
Another option when the number of coefficients is set is to maintain the transition width
at the expense of control over the passband ripple/stopband attenuation.
14-8
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Controlling Design Specifications in Lowpass FIR Design
setspecs(Hf,'N,Fp,Fst',N,Fp,Fst);
Hd3 = design(Hf,'equiripple','systemobject',true);
measure(Hd3)
hfvt2 = fvtool(Hd1,Hd3,'Color','White');
legend(hfvt2,'Equiripple design, 146 coefficients',...
'Equiripple design, 101 coefficients')
Sampling Frequency
Passband Edge
3-dB Point
6-dB Point
Stopband Edge
Passband Ripple
Stopband Atten.
Transition Width
:
:
:
:
:
:
:
:
N/A (normalized frequency)
0.38
0.39407
0.4
0.42
0.1651 dB
40.4369 dB
0.04
Note that in this case, the differences between using 146 coefficients and using 101
coefficients is reflected in a larger passband ripple and a smaller stopband attenuation.
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14-9
14
Designing Lowpass FIR Filters
It is possible to increase the attenuation in the stopband while keeping the same filter
order and transition width by the use of weights. Weights are a way of specifying the
relative importance of the passband ripple versus the stopband attenuation. By default,
passband and stopband are equally weighted (a weight of one is assigned to each). If we
increase the stopband weight, we can increase the stopband attenuation at the expense of
increasing the stopband ripple as well.
Hd4 = design(Hf,'equiripple','Wstop',5,'systemobject',true);
measure(Hd4)
hfvt3 = fvtool(Hd3,Hd4,'Color','White');
legend(hfvt3,'Passband weight = 1, Stopband weight = 1',...
'Passband weight = 1, Stopband weight = 5')
Sampling Frequency
Passband Edge
3-dB Point
6-dB Point
Stopband Edge
Passband Ripple
Stopband Atten.
Transition Width
14-10
:
:
:
:
:
:
:
:
N/A (normalized frequency)
0.38
0.39143
0.39722
0.42
0.34529 dB
48.0068 dB
0.04
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Controlling Design Specifications in Lowpass FIR Design
Another possibility is to specify the exact stopband attenuation desired and lose control
over the passband ripple. This is a powerful and very desirable specification. One has
control over most parameters of interest.
setspecs(Hf,'N,Fp,Fst,Ast',N,Fp,Fst,Ast);
Hd5 = design(Hf,'equiripple','systemobject',true);
hfvt4 = fvtool(Hd4,Hd5,'Color','White');
legend(hfvt4,'Equiripple design using weights',...
'Equiripple design constraining the stopband')
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14-11
14
Designing Lowpass FIR Filters
14-12
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Designing Filters with Non-Equiripple Stopband
Designing Filters with Non-Equiripple Stopband
This example shows how to design lowpass filters with stopbands that are not equiripple.
Optimal Non-Equiripple Lowpass Filters
To start, set up the filter parameters and use fdesign to create a constructor for
designing the filter.
N = 100;
Fp = 0.38;
Fst = 0.42;
Hf = fdesign.lowpass('N,Fp,Fst',N,Fp,Fst);
Equiripple designs achieve optimality by distributing the deviation from the ideal
response uniformly. This has the advantage of minimizing the maximum deviation
(ripple). However, the overall deviation, measured in terms of its energy tends to be
large. This may not always be desirable. When low pass filtering a signal, this implies
that remnant energy of the signal in the stopband may be relatively large. When this is a
concern, least-squares methods provide optimal designs that minimize the energy in the
stopband.
Hd1 = design(Hf,'equiripple','systemobject',true);
Hd2 = design(Hf,'firls','systemobject',true);
hfvt = fvtool(Hd1,Hd2,'Color','White');
legend(hfvt,'Equiripple design','Least-squares design')
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14-13
14
Designing Lowpass FIR Filters
Notice how the attenuation in the stopband increases with frequency for the leastsquares designs while it remains constant for the equiripple design. The increased
attenuation in the least-squares case minimizes the energy in that band of the signal to
be filtered.
Equiripple Designs with Increasing Stopband Attenuation
An often undesirable effect of least-squares designs is that the ripple in the passband
region close to the passband edge tends to be large. For low pass filters in general, it
is desirable that passband frequencies of a signal to be filtered are affected as little
as possible. To this extent, an equiripple passband is generally preferable. If it is still
desirable to have an increasing attenuation in the stopband, we can use design options
for equiripple designs to achieve this.
Hd3 = design(Hf,'equiripple','StopbandShape','1/f',...
'StopbandDecay',4,'systemobject',true);
hfvt2 = fvtool(Hd2,Hd3,'Color','White');
14-14
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Designing Filters with Non-Equiripple Stopband
legend(hfvt2,'Least-squares design',...
'Equiripple design with stopband decaying as (1/f)^4')
Notice that the stopbands are quite similar. However the equiripple design has a
significantly smaller passband ripple,
mls = measure(Hd2);
meq = measure(Hd3);
mls.Apass
meq.Apass
ans =
0.3504
ans =
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14-15
14
Designing Lowpass FIR Filters
0.1867
Filters with a stopband that decays as (1/f)^M will decay at 6M dB per octave. Another
way of shaping the stopband is using a linear decay. For example given an approximate
attenuation of 38 dB at 0.4*pi, if an attenuation of 70 dB is desired at pi, and a linear
decay is to be used, the slope of the line is given by (70-38)/(1-0.4) = 53.333. Such a design
can be achieved from:
Hd4 = design(Hf,'equiripple','StopbandShape','linear',...
'StopbandDecay',53.333,'systemobject',true);
hfvt3 = fvtool(Hd3,Hd4,'Color','White');
legend(hfvt3,'Equiripple design with stopband decaying as (1/f)^4',...
'Equiripple design with stopband decaying linearly and a slope of 53.333')
Yet another possibility is to use an arbitrary magnitude specification and select two
bands (one for the passband and one for the stopband). Then, by using weights for the
second band, it is possible to increase the attenuation throughout the band.
14-16
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Designing Filters with Non-Equiripple Stopband
N = 100;
B = 2; % number of bands
F = [0 .38 .42:.02:1];
A = [1 1 zeros(1,length(F)-2)];
W = linspace(1,100,length(F)-2);
Harb = fdesign.arbmag('N,B,F,A',N,B,F(1:2),A(1:2),F(3:end),...
A(3:end));
Ha = design(Harb,'equiripple','B2Weights',W,...
'systemobject',true);
fvtool(Ha,'Color','White')
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14-17
14
Designing Lowpass FIR Filters
Minimizing Lowpass FIR Filter Length
This example shows how to minimize the number coefficients, by designing minimumphase or minimum-order filters.
Minimum-Phase Lowpass Filter Design
To start, set up the filter parameters and use fdesign to create a constructor for
designing the filter.
N = 100;
Fp = 0.38;
Fst = 0.42;
Ap = 0.06;
Ast = 60;
Hf = fdesign.lowpass('Fp,Fst,Ap,Ast',Fp,Fst,Ap,Ast);
So far, we have only considered linear-phase designs. Linear phase is desirable in many
applications. Nevertheless, if linear phase is not a requirement, minimum-phase designs
can provide significant improvements over linear phase counterparts. For instance,
returning to the minimum order case, a minimum-phase/minimum-order design for the
same specifications can be computed with:
Hd1 = design(Hf,'equiripple','systemobject',true);
Hd2 = design(Hf,'equiripple','minphase',true,...
'systemobject',true);
hfvt = fvtool(Hd1,Hd2,'Color','White');
legend(hfvt,'Linear-phase equiripple design',...
'Minimum-phase equiripple design')
14-18
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Minimizing Lowpass FIR Filter Length
Notice that the number of coefficients has been reduced from 146 to 117. As a second
example, consider the design with a stopband decaying in linear fashion. Notice the
increased stopband attenuation. The passband ripple is also significantly smaller.
setspecs(Hf,'N,Fp,Fst',N,Fp,Fst);
Hd3 = design(Hf,'equiripple','StopbandShape','linear',...
'StopbandDecay',53.333,'systemobject',true);
setspecs(Hf,'Fp,Fst,Ap,Ast',Fp,Fst,Ap,Ast);
Hd4 = design(Hf,'equiripple','StopbandShape','linear',...
'StopbandDecay',53.333,'minphase',true,'systemobject',true);
hfvt2 = fvtool(Hd3,Hd4,'Color','White');
legend(hfvt2,'Linear-phase equiripple design with linearly decaying stopband',...
'Minimum-phase equiripple design with linearly decaying stopband')
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14-19
14
Designing Lowpass FIR Filters
Minimum-Order Lowpass Filter Design Using Multistage Techniques
A different approach to minimizing the number of coefficients that does not involve
minimum-phase designs is to use multistage techniques. Here we show an interpolated
FIR (IFIR) approach.
Hd5 = ifir(Hf);
hfvt3 = fvtool(Hd1,Hd5,'Color','White');
legend(hfvt3,'Linear-phase equirriple design',...
'Linear-phase IFIR design')
14-20
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Minimizing Lowpass FIR Filter Length
The number of nonzero coefficients required in the IFIR case is 111. Less than both the
equiripple linear-phase and minimum-phase designs.
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‫‪14-22‬‬
15
FDATool: A Filter Design and Analysis
GUI
• “Overview” on page 15-2
• “Using FDATool” on page 15-6
• “Importing a Filter Design” on page 15-33
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15
FDATool: A Filter Design and Analysis GUI
Overview
In this section...
“FDATool” on page 15-2
“Filter Design Methods” on page 15-2
“Using the Filter Design and Analysis Tool” on page 15-3
“Analyzing Filter Responses” on page 15-4
“Filter Design and Analysis Tool Panels” on page 15-4
“Getting Help” on page 15-5
FDATool
The Filter Design and Analysis Tool (FDATool) is a user interface for designing and
analyzing filters quickly. FDATool enables you to design digital FIR or IIR filters by
setting filter specifications, by importing filters from your MATLAB workspace, or by
adding, moving or deleting poles and zeros. FDATool also provides tools for analyzing
filters, such as magnitude and phase response and pole-zero plots.
Filter Design Methods
FDATool gives you access to the following Signal Processing Toolbox filter design
methods.
15-2
Design Method
Function
Butterworth
butter
Chebyshev Type I
cheby1
Chebyshev Type II
cheby2
Elliptic
ellip
Maximally Flat
maxflat
Equiripple
firpm
Least-squares
firls
Constrained least-squares
fircls
Complex equiripple
cfirpm
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Overview
Design Method
Function
Window
fir1
When using the window method in FDATool, all Signal Processing Toolbox window
functions are available, and you can specify a user-defined window by entering its
function name and input parameter.
Advanced Filter Design Methods
The following advanced filter design methods are available if you have DSP System
Toolbox software.
Design Method
Function
Constrained equiripple FIR
firceqrip
Constrained-band equiripple FIR
fircband
Generalized remez FIR
firgr
Equiripple halfband FIR
firhalfband
Least P-norm optimal FIR
firlpnorm
Equiripple Nyquist FIR
firnyquist
Interpolated FIR
ifir
IIR comb notching or peaking
iircomb
Allpass filter (given group delay)
iirgrpdelay
Least P-norm optimal IIR
iirlpnorm
Constrained least P-norm IIR
iirlpnormc
Second-order IIR notch
iirnotch
Second-order IIR peaking (resonator)
iirpeak
Using the Filter Design and Analysis Tool
There are different ways that you can design filters using the Filter Design and Analysis
Tool. For example:
• You can first choose a response type, such as bandpass, and then choose from the
available FIR or IIR filter design methods.
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15-3
15
FDATool: A Filter Design and Analysis GUI
• You can specify the filter by its type alone, along with certain frequency- or timedomain specifications such as passband frequencies and stopband frequencies. The
filter you design is then computed using the default filter design method and filter
order.
Analyzing Filter Responses
Once you have designed your filter, you can display the filter coefficients and detailed
filter information, export the coefficients to the MATLAB workspace, and create a C
header file containing the coefficients, and analyze different filter responses in FDATool
or in a separate Filter Visualization Tool (fvtool). The following filter responses are
available:
• Magnitude response (freqz)
• Phase response (phasez)
• Group delay (grpdelay)
• Phase delay (phasedelay)
• Impulse response (impz)
• Step response (stepz)
• Pole-zero plots (zplane)
• Zero-phase response (zerophase)
Filter Design and Analysis Tool Panels
The Filter Design and Analysis Tool has sidebar buttons that display particular panels in
the lower half of the tool. The panels are
• Design Filter. See “Choosing a Filter Design Method” on page 15-7 for more
information. You use this panel to
• Design filters from scratch.
• Modify existing filters designed in FDATool.
• Analyze filters.
• Import filter. You use this panel to
• Import previously saved filters or filter coefficients that you have stored in the
MATLAB workspace.
15-4
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Overview
• Analyze imported filters.
• Pole/Zero Editor. See “Editing the Filter Using the Pole/Zero Editor” on page
15-17. You use this panel to add, delete, and move poles and zeros in your filter
design.
If you also have DSP System Toolbox product installed, additional panels are available:
• Set quantization parameters — Use this panel to quantize double-precision filters
that you design in FDATool, quantize double-precision filters that you import into
FDATool, and analyze quantized filters.
• Transform filter — Use this panel to change a filter from one response type to
another.
• Multirate filter design — Use this panel to create a multirate filter from your existing
FIR design, create CIC filters, and linear and hold interpolators.
If you have Simulink installed, this panel is available:
• Realize Model — Use this panel to create a Simulink block containing the filter
structure.
Getting Help
At any time, you can right-click or click the What's this? button,
, to get information
on the different parts of the tool. You can also use the Help menu to see complete Help
information.
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15-5
15
FDATool: A Filter Design and Analysis GUI
Using FDATool
To open FDATool, type
fdatool
at the MATLAB command prompt.
The Filter Design and Analysis Tool opens with the Design Filter panel displayed.
Note that when you open FDATool, Design Filter is not enabled. You must make a
change to the default filter design in order to enable Design Filter. This is true each
time you want to change the filter design. Changes to radio button items or drop down
menu items such as those under Response Type or Filter Order enable Design Filter
immediately. Changes to specifications in text boxes such as Fs, Fpass, and Fstop
require you to click outside the text box to enable Design Filter.
Choosing a Response Type
You can choose from several response types:
15-6
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Using FDATool
• Lowpass
• Raised cosine
• Highpass
• Bandpass
• Bandstop
• Differentiator
• Multiband
• Hilbert transformer
• Arbitrary magnitude
Additional response types are available if you have DSP System Toolbox software
installed.
To design a bandpass filter, select the radio button next to Bandpass in the Response
Type region of the GUI.
Note: Not all filter design methods are available for all response types. Once you choose
your response type, this may restrict the filter design methods available to you. Filter
design methods that are not available for a selected response type are removed from the
Design Method region of the GUI.
Choosing a Filter Design Method
You can use the default filter design method for the response type that you've selected,
or you can select a filter design method from the available FIR and IIR methods listed in
the GUI.
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15-7
15
FDATool: A Filter Design and Analysis GUI
To select the Remez algorithm to compute FIR filter coefficients, select the FIR radio
button and choose Equiripple from the list of methods.
Setting the Filter Design Specifications
• “Viewing Filter Specifications” on page 15-8
• “Filter Order” on page 15-9
• “Options” on page 15-9
• “Bandpass Filter Frequency Specifications” on page 15-10
• “Bandpass Filter Magnitude Specifications” on page 15-11
Viewing Filter Specifications
The filter design specifications that you can set vary according to response type and
design method. The display region illustrates filter specifications when you select
Analysis > Filter Specifications or when you click the Filter Specifications toolbar
button.
You can also view the filter specifications on the Magnitude plot of a designed filter by
selecting View > Specification Mask.
15-8
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Using FDATool
Filter Order
You have two mutually exclusive options for determining the filter order when you
design an equiripple filter:
• Specify order: You enter the filter order in a text box.
• Minimum order: The filter design method determines the minimum order filter.
Select the Minimum order radio button for this example.
Note that filter order specification options depend on the filter design method you choose.
Some filter methods may not have both options available.
Options
The available options depend on the selected filter design method. Only the FIR
Equiripple and FIR Window design methods have settable options. For FIR Equiripple,
the option is a Density Factor. See firpm for more information. For FIR Window
the options are Scale Passband, Window selection, and for the following windows, a
settable parameter:
Window
Parameter
Chebyshev (chebwin)
Sidelobe attenuation
Gaussian (gausswin)
Alpha
Kaiser (kaiser)
Beta
Taylor (taylorwin)
Nbar and Sidelobe level
Tukey (tukeywin)
Alpha
User Defined
Function Name, Parameter
You can view the window in the Window Visualization Tool (wvtool) by clicking the
View button.
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15-9
15
FDATool: A Filter Design and Analysis GUI
For this example, set the Density factor to 16.
Bandpass Filter Frequency Specifications
For a bandpass filter, you can set
• Units of frequency:
• Hz
• kHz
• MHz
• Normalized (0 to 1)
• Sampling frequency
• Passband frequencies
• Stopband frequencies
You specify the passband with two frequencies. The first frequency determines the
lower edge of the passband, and the second frequency determines the upper edge of the
passband.
Similarly, you specify the stopband with two frequencies. The first frequency determines
the upper edge of the first stopband, and the second frequency determines the lower edge
of the second stopband.
For this example:
• Keep the units in Hz (default).
• Set the sampling frequency (Fs) to 2000 Hz.
• Set the end of the first stopband (Fstop1) to 200 Hz.
• Set the beginning of the passband (Fpass1) to 300 Hz.
• Set the end of the passband (Fpass2) to 700 Hz.
15-10
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Using FDATool
• Set the beginning of the second stopband (Fstop2) to 800 Hz.
Bandpass Filter Magnitude Specifications
For a bandpass filter, you can specify the following magnitude response characteristics:
• Units for the magnitude response (dB or linear)
• Passband ripple
• Stopband attenuation
For this example:
• Keep Units in dB (default).
• Set the passband ripple (Apass) to 0.1 dB.
• Set the stopband attenuation for both stopbands (Astop1, Astop2) to 75 dB.
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15-11
15
FDATool: A Filter Design and Analysis GUI
Computing the Filter Coefficients
Now that you've specified the filter design, click the Design Filter button to compute the
filter coefficients.
Notice that the Design Filter button is disabled once you've computed the coefficients for
your filter design. This button is enabled again once you make any changes to the filter
specifications.
Analyzing the Filter
• “Displaying Filter Responses” on page 15-12
• “Using Data Tips” on page 15-14
• “Drawing Spectral Masks” on page 15-14
• “Changing the Sampling Frequency” on page 15-16
• “Displaying the Response in FVTool” on page 15-16
Displaying Filter Responses
You can view the following filter response characteristics in the display region or in a
separate window.
• Magnitude response
• Phase response
• Magnitude and Phase responses
• Group delay response
• Phase delay response
• Impulse response
• Step response
• Pole-zero plot
• Zero-phase response — available from the y-axis context menu in a Magnitude or
Magnitude and Phase response plot.
If you have DSP System Toolbox product installed, two other analyses are available:
magnitude response estimate and round-off noise power. These two analyses are the only
ones that use filter internals.
15-12
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Using FDATool
For descriptions of the above responses and their associated toolbar buttons and other
FDATool toolbar buttons, see fvtool.
You can display two responses in the same plot by selecting Analysis > Overlay
Analysis and selecting an available response. A second y-axis is added to the right side
of the response plot. (Note that not all responses can be overlaid on each other.)
You can also display the filter coefficients and detailed filter information in this region.
For all the analysis methods, except zero-phase response, you can access them from the
Analysis menu, the Analysis Parameters dialog box from the context menu, or by using
the toolbar buttons. For zero-phase, right-click the y-axis of the plot and select Zerophase from the context menu.
For example, to look at the filter's magnitude response, select the Magnitude Response
button
on the toolbar.
You can also overlay the filter specifications on the Magnitude plot by selecting View >
Specification Mask.
Note: You can use specification masks in FVTool only if FVTool was launched from
FDATool.
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15-13
15
FDATool: A Filter Design and Analysis GUI
Using Data Tips
You can click the response to add plot data tips that display information about particular
points on the response.
For information on using data tips, see “Display Data Values Interactively” in the
MATLAB documentation.
Drawing Spectral Masks
To add spectral masks or rejection area lines to your magnitude plot, click View > Userdefined Spectral Mask.
15-14
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Using FDATool
The mask is defined by a frequency vector and a magnitude vector. These vectors must be
the same length.
• Enable Mask — Select to turn on the mask display.
• Normalized Frequency — Select to normalize the frequency between 0 and 1
across the displayed frequency range.
• Frequency Vector — Enter a vector of x-axis frequency values.
• Magnitude Units — Select the desired magnitude units. These units should match
the units used in the magnitude plot.
• Magnitude Vector — Enter a vector of y-axis magnitude values.
The magnitude response below shows a spectral mask.
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15-15
15
FDATool: A Filter Design and Analysis GUI
Changing the Sampling Frequency
To change the sampling frequency of your filter, right-click any filter response plot and
select Sampling Frequency from the context menu.
To change the filter name, type the new name in Filter name. (In fvtool, if you have
multiple filters, select the desired filter and then enter the new name.)
To change the sampling frequency, select the desired unit from Units and enter the
sampling frequency in Fs. (For each filter in fvtool, you can specify a different
sampling frequency or you can apply the sampling frequency to all filters.)
To save the displayed parameters as the default values to use when FDATool or FVTool
is opened, click Save as Default.
To restore the default values, click Restore Original Defaults.
Displaying the Response in FVTool
To display the filter response characteristics in a separate window, select View > Filter
Visualization Tool (available if any analysis, except the filter specifications, is in the
display region) or click the Full View Analysis button:
This launches the Filter Visualization Tool (fvtool).
Note: If Filter Specifications are shown in the display region, clicking the Full View
Analysis toolbar button launches a “ MATLAB figure window” instead of FVTool. The
15-16
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Using FDATool
associated menu item is Print to figure, which is enabled only if the filter specifications
are displayed.
You can use this tool to annotate your design, view other filter characteristics, and print
your filter response. You can link FDATool and FVTool so that changes made in FDATool
are immediately reflected in FVTool. See fvtool for more information.
Editing the Filter Using the Pole/Zero Editor
• “Displaying the Pole-Zero Plot” on page 15-17
• “Changing the Pole-Zero Plot” on page 15-18
Displaying the Pole-Zero Plot
You can edit a designed or imported filter's coefficients by moving, deleting, or adding
poles and/or zeros using the Pole/Zero Editor panel.
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15-17
15
FDATool: A Filter Design and Analysis GUI
Note: You cannot generate MATLAB code (File > Generate MATLAB code) if your
filter was designed or edited with the Pole/Zero Editor.
You cannot move quantized poles and zeros. You can only move the reference poles and
zeros.
Click the Pole/Zero Editor button in the sidebar or select Edit > Pole/Zero Editor to
display this panel.
Poles are shown using x symbols and zeros are shown using o symbols.
Changing the Pole-Zero Plot
Plot mode buttons are located to the left of the pole/zero plot. Select one of the buttons to
change the mode of the pole/zero plot. The Pole/Zero Editor has these buttons from left to
right: move pole, add pole, add zero, and delete pole or zero.
15-18
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Using FDATool
The following plot parameters and controls are located to the left of the pole/zero plot and
below the plot mode buttons.
• Filter gain — factor to compensate for the filter's pole(s) and zero(s) gains
• Coordinates — units (Polar or Rectangular) of the selected pole or zero
• Magnitude — if polar coordinates is selected, magnitude of the selected pole or zero
• Angle — if polar coordinates is selected, angle of selected pole(s) or zero(s)
• Real — if rectangular coordinates is selected, real component of selected pole(s) or
zero(s)
• Imaginary — if rectangular coordinates is selected, imaginary component of selected
pole or zero
• Section — for multisection filters, number of the current section
• Conjugate — creates a corresponding conjugate pole or zero or automatically selects
the conjugate pole or zero if it already exists.
• Auto update — immediately updates the displayed magnitude response when poles
or zeros are added, moved, or deleted.
The Edit > Pole/Zero Editor has items for selecting multiple poles/zeros, for inverting
and mirroring poles/zeros, and for deleting, scaling and rotating poles/zeros.
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15-19
15
FDATool: A Filter Design and Analysis GUI
Moving one of the zeros on the vertical axis produces the following result:
15-20
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Using FDATool
• The selected zero pair is shown in green.
• When you select one of the zeros from a conjugate pair, the Conjugate check box and
the conjugate are automatically selected.
• The Magnitude Response plot updates immediately because Auto update is active.
Converting the Filter Structure
• “Converting to a New Structure” on page 15-21
• “Converting to Second-Order Sections” on page 15-23
Converting to a New Structure
You can use Edit > Convert Structure to convert the current filter to a new structure.
All filters can be converted to the following representations:
• Direct-form I
• Direct-form II
• Direct-form I transposed
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15-21
15
FDATool: A Filter Design and Analysis GUI
• Direct-form II transposed
• Lattice ARMA
Note: If you have DSP System Toolbox product installed, you will see additional
structures in the Convert structure dialog box.
In addition, the following conversions are available for particular classes of filters:
• Minimum phase FIR filters can be converted to Lattice minimum phase
• Maximum phase FIR filters can be converted to Lattice maximum phase
• Allpass filters can be converted to Lattice allpass
• IIR filters can be converted to Lattice ARMA
Note: Converting from one filter structure to another may produce a result with different
characteristics than the original. This is due to the computer's finite-precision arithmetic
and the variations in the conversion's roundoff computations.
For example:
• Select Edit > Convert Structure to open the Convert structure dialog box.
• Select Direct-form I in the list of filter structures.
15-22
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Using FDATool
Converting to Second-Order Sections
You can use Edit > Convert to Second-Order Sections to store the converted filter
structure as a collection of second-order sections rather than as a monolithic higher-order
structure.
Note: The following options are also used for Edit > Reorder and Scale Scale SecondOrder Sections, which you use to modify an SOS filter structure.
The following Scale options are available when converting a direct-form II structure
only:
• None (default)
• L-2 (L2 norm)
• L-infinity (L∞ norm)
The Direction (Up or Down) determines the ordering of the second-order sections. The
optimal ordering changes depending on the Scale option selected.
For example:
• Select Edit > Convert to Second-Order Sections to open the Convert to SOS
dialog box.
• Select L-infinity from the Scale menu for L∞ norm scaling.
• Leave Up as the Direction option.
Note: To convert from second-order sections back to a single section, use Edit >
Convert to Single Section.
Exporting a Filter Design
• “Exporting Coefficients or Objects to the Workspace” on page 15-24
• “Exporting Coefficients to an ASCII File” on page 15-25
• “Exporting Coefficients or Objects to a MAT-File” on page 15-25
• “Exporting to SPTool” on page 15-26
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15
FDATool: A Filter Design and Analysis GUI
• “Exporting to a Simulink Model” on page 15-26
• “Other Ways to Export a Filter” on page 15-27
Exporting Coefficients or Objects to the Workspace
You can save the filter either as filter coefficients variables or as a dfilt or mfilt filter
object variable. (Note that you must have DSP System Toolbox product installed to save
as an mfilt.) To save the filter to the MATLAB workspace:
1
Select File > Export. The Export dialog box appears.
2
Select Workspace from the Export To menu.
3
Select Coefficients from the Export As menu to save the filter coefficients or
select Objects to save the filter in a filter object.
4
For coefficients, assign variable names using the Numerator (for FIR filters) or
Numerator and Denominator (for IIR filters), or SOS Matrix and Scale Values
(for IIR filters in second-order section form) text boxes in the Variable Names region.
For objects, assign the variable name in the Discrete Filter (or Quantized Filter)
text box. If you have variables with the same names in your workspace and you want
to overwrite them, select the Overwrite Variables check box.
5
15-24
Click the Export button.
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Using FDATool
Exporting Coefficients to an ASCII File
To save filter coefficients to a text file,
1
Select File > Export. The Export dialog box appears.
2
Select Coefficients File (ASCII) from the Export To menu.
3
Click the Export button. The Export Filter Coefficients to .FCF File dialog box
appears.
4
Choose or enter a filename and click the Save button.
The coefficients are saved in the text file that you specified, and the MATLAB Editor
opens to display the file. The text file also contains comments with the MATLAB version
number, the Signal Processing Toolbox version number, and filter information.
Exporting Coefficients or Objects to a MAT-File
To save filter coefficients or a filter object as variables in a MAT-file:
1
Select File > Export. The Export dialog box appears.
2
Select MAT-file from the Export To menu.
3
Select Coefficients from the Export As menu to save the filter coefficients or
select Objects to save the filter in a filter object.
4
For coefficients, assign variable names using the Numerator (for FIR filters) or
Numerator and Denominator (for IIR filters), or SOS Matrix and Scale Values
(for IIR filters in second-order section form) text boxes in the Variable Names region.
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15
FDATool: A Filter Design and Analysis GUI
For objects, assign the variable name in the Discrete Filter (or Quantized Filter)
text box. If you have variables with the same names in your workspace and you want
to overwrite them, select the Overwrite Variables check box.
5
Click the Export button. The Export to a MAT-File dialog box appears.
6
Choose or enter a filename and click the Save button.
Exporting to SPTool
You may want to use your designed filter in SPTool to do signal processing and analysis.
1
Select File > Export. The Export dialog box appears.
2
Select SPTool from the Export To menu.
3
Assign the variable name in the Discrete Filter (or Quantized Filter) text box.
If you have variables with the same names in your workspace and you want to
overwrite them, select the Overwrite Variables check box.
4
Click the Export button.
SPTool opens and the current FDATool filter appears in the Filter area list as the
specified variable name followed by (Imported).
Note: If you are using the DSP System Toolbox software and export a quantized
filter, only the values of its quantized coefficients are exported. The reference
coefficients are not exported. SPTool does not restrict the coefficient values, so if you
edit them in SPTool by moving poles or zeros, the filter will no longer be in quantized
form.
Exporting to a Simulink Model
If you have the Simulink product installed, you can export a Simulink block of your filter
design and insert it into a new or existing Simulink model.
You can export a filter designed using any filter design method available in FDATool.
Note: If you have the DSP System Toolbox and Fixed-Point Designer installed, you can
export a CIC filter to a Simulink model.
15-26
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Using FDATool
1
After designing your filter, click the Realize Model sidebar button or select File >
Export to Simulink Model. The Realize Model panel is displayed.
2
Specify the name to use for your block in Block name.
3
To insert the block into the current (most recently selected) Simulink model, set the
Destination to Current. To inset the block into a new model, select New. To insert
the block into a user-defined subsystem, select User defined.
4
If you want to overwrite a block previously created from this panel, check
Overwrite generated `Filter' block.
5
6
Set the Input processing parameter to specify whether the generated filter
performs sample- or frame-based processing on the input. Depending on the type of
filter you design, one or both of the following options may be available:
• Columns as channels (frame based) — When you select this option, the
block treats each column of the input as a separate channel.
• Elements as channels (sample based) — When you select this option, the
block treats each element of the input as a separate channel.
7
Click the Realize Model button to create the filter block. When the Build model
using basic elements check box is selected, FDATool implements the filter as a
subsystem block using Sum, Gain, and Delay blocks.
If you double-click the Simulink Filter block, the filter structure is displayed.
Other Ways to Export a Filter
You can also send your filter to a C header file or generate MATLAB code to construct
your filter from the command line. For detailed instructions, see the following sections:
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15
FDATool: A Filter Design and Analysis GUI
• “Generating a C Header File” on page 15-28
• “Generating MATLAB Code” on page 15-29
Generating a C Header File
You may want to include filter information in an external C program. To create a C
header file with variables that contain filter parameter data, follow this procedure:
15-28
1
Select Targets > Generate C Header. The Generate C Header dialog box appears.
2
Enter the variable names to be used in the C header file. The particular filter
structure determines the variables that are created in the file
Filter Structure
Variable Parameter
Direct-form I
Direct-form II
Direct-form I
transposed
Direct-form II
transposed
Numerator, Numerator length*, Denominator,
Denominator length*, and Number of sections (inactive if
filter has only one section)
Lattice ARMA
Lattice coeffs, Lattice coeffs length*, Ladder coeffs, Ladder
coeffs length*, Number of sections (inactive if filter has
only one section)
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Using FDATool
Filter Structure
Variable Parameter
Lattice MA
Lattice coeffs, Lattice coeffs length*, and Number of
sections (inactive if filter has only one section)
Direct-form FIR Direct- Numerator, Numerator length*, and Number of sections
form FIR transposed
(inactive if filter has only one section)
*length variables contain the total number of coefficients of that type.
Note: Variable names cannot be C language reserved words, such as “for.”
3
Select Export Suggested to use the suggested data type or select Export As and
select the desired data type from the pull-down.
Note: If you do not have DSP System Toolbox software installed, selecting any
data type other than double-precision floating point results in a filter that does not
exactly match the one you designed in the FDATool. This is due to rounding and
truncating differences.
4
Click OK to save the file and close the dialog box or click Apply to save the file, but
leave the dialog box open for additional C header file definitions.
Generating MATLAB Code
You can generate MATLAB code that constructs the filter you designed in FDATool from
the command line. Select File > Generate MATLAB Code > Filter Design Function
and specify the filename in the Generate MATLAB code dialog box.
Note: You cannot generate MATLAB code (File > Generate MATLAB Code > Filter
Design Function) if your filter was designed or edited with the Pole/Zero Editor.
The following is generated MATLAB code for the default lowpass filter in FDATool.
function Hd = ExFilter
%EXFILTER Returns a discrete-time filter object.
%
% MATLAB Code
% Generated by MATLAB(R) 7.11 and the Signal Processing Toolbox 6.14.
%
% Generated on: 17-Feb-2010 14:15:37
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15
FDATool: A Filter Design and Analysis GUI
%
% Equiripple Lowpass filter designed using the FIRPM function.
% All frequency values are in Hz.
Fs = 48000; % Sampling Frequency
Fpass
Fstop
Dpass
Dstop
dens
=
=
=
=
=
9600;
12000;
0.057501127785;
0.0001;
20;
%
%
%
%
%
Passband Frequency
Stopband Frequency
Passband Ripple
Stopband Attenuation
Density Factor
% Calculate the order from the parameters using FIRPMORD.
[N, Fo, Ao, W] = firpmord([Fpass, Fstop]/(Fs/2), [1 0], [Dpass, Dstop]);
% Calculate the coefficients using the FIRPM function.
b = firpm(N, Fo, Ao, W, {dens});
Hd = dfilt.dffir(b);
% [EOF]
Managing Filters in the Current Session
You can store filters designed in the current FDATool session for cascading together,
exporting to FVTool or for recalling later in the same or future FDATool sessions.
You store and access saved filters with the Store filter and Filter Manager buttons,
respectively, in the Current Filter Information pane.
Store Filter — Displays the Store Filter dialog box in which you specify the filter name
to use when storing the filter in the Filter Manager. The default name is the type of the
filter.
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Using FDATool
Filter Manager — Opens the Filter Manager.
The current filter is listed below the listbox. To change the current filter, highlight the
desired filter. If you select Edit current filter, FDATool displays the currently selected
filter specifications. If you make any changes to the specifications, the stored filter is
updated immediately.
To cascade two or more filters, highlight the desired filters and press Cascade. A new
cascaded filter is added to the Filter Manager.
To change the name of a stored filter, press Rename. The Rename filter dialog box is
displayed.
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15-31
15
FDATool: A Filter Design and Analysis GUI
To remove a stored filter from the Filter Manager, press Delete.
To export one or more filters to FVTool, highlight the filter(s) and press FVTool.
Saving and Opening Filter Design Sessions
You can save your filter design session as a MAT-file and return to the same session
another time.
Select the Save session button
to save your session as a MAT-file. The first time
you save a session, a Save Filter Design File browser opens, prompting you for a session
name.
For example, save this design session as TestFilter.fda in your current working
directory by typing TestFilter in the File name field.
The .fda extension is added automatically to all filter design sessions you save.
Note: You can also use the File > Save session and File > Save session as to save a
session.
You can load existing sessions into the Filter Design and Analysis Tool by selecting the
Open session button,
or File > Open session . A Load Filter Design File browser
opens that allows you to select from your previously saved filter design sessions.
15-32
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Importing a Filter Design
Importing a Filter Design
In this section...
“Import Filter Panel” on page 15-33
“Filter Structures” on page 15-34
Import Filter Panel
The Import Filter panel allows you to import a filter. You can access this region by
clicking the Import Filter button in the sidebar.
The imported filter can be in any of the representations listed in the Filter Structure
pull-down menu. You can import a filter as second-order sections by selecting the check
box.
Specify the filter coefficients in Numerator and Denominator, either by entering them
explicitly or by referring to variables in the MATLAB workspace.
Select the frequency units from the following options in the Units menu, and for any
frequency unit other than Normalized, specify the value or MATLAB workspace variable
of the sampling frequency in the Fs field.
To import the filter, click the Import Filter button. The display region is automatically
updated when the new filter has been imported.
You can edit the imported filter using the Pole/Zero Editor panel.
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15
FDATool: A Filter Design and Analysis GUI
Filter Structures
The available filter structures are:
• Direct Form, which includes direct-form I, direct-form II, direct-form I transposed,
direct-form II transposed, and direct-form FIR
• Lattice, which includes lattice allpass, lattice MA min phase, lattice MA max phase,
and lattice ARMA
• Discrete–time Filter (dfilt object)
The structure that you choose determines the type of coefficients that you need to specify
in the text fields to the right.
Direct-form
For direct-form I, direct-form II, direct-form I transposed, and direct-form II transposed,
specify the filter by its transfer function representation
H ( z) =
b(1) + b(2) z-1 + b(3) z -2 + º b( m + 1) z- m
a(1) + a(2) z -1 + a(3) Z -3 + º a(n + 1) z -n
• The Numerator field specifies a variable name or value for the numerator coefficient
vector b, which contains m+1 coefficients in descending powers of z.
• The Denominator field specifies a variable name or value for the denominator
coefficient vector a, which contains n+1 coefficients in descending powers of z. For FIR
filters, the Denominator is 1.
Filters in transfer function form can be produced by all of the Signal Processing Toolbox
filter design functions (such as fir1, fir2, firpm, butter, yulewalk). See “Transfer
Function” for more information.
Importing as second-order sections
For all direct-form structures, except direct-form FIR, you can import the filter in its
second-order section representation:
L
H ( z) = G
15-34
b0k + b1k z -1 + b2k z-2
-1
-2
k=1 a0 k + a1k z + a2k z
’
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Importing a Filter Design
The Gain field specifies a variable name or a value for the gain G, and the SOS Matrix
field specifies a variable name or a value for the L-by-6 SOS matrix
Ê b01
Á
Á b02
SOS = Á ·
Á
Á ·
Áb
Ë 0L
b11
b12
·
·
b1L
b21
b22
·
·
b2L
1 a11
1 a12
·
·
·
·
1 a1L
a22 ˆ
˜
a22 ˜
· ˜
˜
· ˜
a2 L ˜¯
whose rows contain the numerator and denominator coefficients bik and aik of the secondorder sections of H(z).
Filters in second-order section form can be produced by functions such as tf2sos,
zp2sos, ss2sos, and sosfilt. See “Second-Order Sections (SOS)” for more
information.
Lattice
For lattice allpass, lattice minimum and maximum phase, and lattice ARMA filters,
specify the filter by its lattice representation:
• For lattice allpass, the Lattice coeff field specifies the lattice (reflection) coefficients,
k(1) to k(N), where N is the filter order.
• For lattice MA (minimum or maximum phase), the Lattice coeff field specifies the
lattice (reflection) coefficients, k(1) to k(N), where N is the filter order.
• For lattice ARMA, the Lattice coeff field specifies the lattice (reflection) coefficients,
k(1) to k(N), and the Ladder coeff field specifies the ladder coefficients, v(1) to
v(N+1), where N is the filter order.
Filters in lattice form can be produced by tf2latc. See “Lattice Structure” for more
information.
Discrete-time Filter (dfilt object)
For Discrete-time filter, specify the name of the dfilt object. See dfilt for more
information.
Multirate Filter (mfilt object)
For Multirate filter, specify the name of the mfilt object. See mfilt in the DSP System
Toolbox product for more information.
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‫‪15-36‬‬
16
Designing a Filter in the Filterbuilder
GUI
• “Filterbuilder Design Process” on page 16-2
• “Designing a FIR Filter Using filterbuilder” on page 16-11
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16
Designing a Filter in the Filterbuilder GUI
Filterbuilder Design Process
In this section...
“Introduction to Filterbuilder” on page 16-2
“Design a Filter Using Filterbuilder” on page 16-2
“Select a Response” on page 16-2
“Select a Specification” on page 16-5
“Select an Algorithm” on page 16-5
“Customize the Algorithm” on page 16-7
“Analyze the Design” on page 16-9
“Realize or Apply the Filter to Input Data” on page 16-9
Introduction to Filterbuilder
The filterbuilder function provides a graphical interface to the fdesign object-object
oriented filter design paradigm and is intended to reduce development time during the
filter design process. filterbuilder uses a specification-centered approach to find the
best algorithm for the desired response.
Note: filterbuilder requires the Signal Processing Toolbox. The functionality of
filterbuilder is greatly expanded by the DSP System Toolbox. Many of the features
described or displayed below are only available if the DSP System Toolbox is installed.
You may verify your installation by typing ver at the command prompt.
Design a Filter Using Filterbuilder
The basic workflow in using filterbuilder is to choose the constraints and
specifications of the filter, and to use those as a starting point in the design. Postponing
the choice of algorithm for the filter allows the best design method to be determined
automatically, based upon the desired performance criteria. The following are the details
of each of the steps for designing a filter with filterbuilder.
Select a Response
When you open the filterbuilder tool by typing:
16-2
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Filterbuilder Design Process
filterbuilder
at the MATLAB command prompt, the Response Selection dialog box appears, listing
all possible filter responses available in DSP System Toolbox.
Note This step cannot be skipped because it is not automatically completed for you by the
software. You must select a response to initiate the filter design process.
After you choose a response, say bandpass, you start the design of the Specifications
Object, and the Bandpass Design dialog box appears. This dialog box contains a Main
pane, a Data Types pane and a Code Generation pane. The specifications of your filter
are generally set in the Main pane of the dialog box.
The Data Types pane provides settings for precision and data types, and the Code
Generation pane contains options for various implementations of the completed filter
design.
For the initial design of your filter, you will mostly use the Main pane.
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16-3
16
16-4
Designing a Filter in the Filterbuilder GUI
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Filterbuilder Design Process
The Bandpass Design dialog box contains all the parameters you need to determine
the specifications of a bandpass filter. The parameters listed in the Main pane depend
upon the type of filter you are designing. However, no matter what type of filter you have
chosen in the Response Selection dialog box, the filter design dialog box contains the
Main, Data Types, and Code Generation panes.
Select a Specification
To choose the specification for the bandpass filter, you can begin by selecting an Impulse
Response, Order Mode, and Filter Type in the Filter Specifications frame of the
Main Pane. You can further specify the response of your filter by setting frequency and
magnitude specifications in the appropriate frames on the Main Pane.
Note Frequency, Magnitude, and Algorithm specifications are interdependent
and may change based upon your Filter Specifications selections. When choosing
specifications for your filter, select your Filter Specifications first and work your
way down the dialog box- this approach ensures that the best settings for dependent
specifications display as available in the dialog box.
Select an Algorithm
The algorithms available for your filter depend upon the filter response and design
parameters you have selected in the previous steps. For example, in the case of a
bandpass filter, if the impulse response selected is IIR and the Order Mode field is set
to Minimum, the design methods available are Butterworth, Chebyshev type I or II,
or Elliptic, whereas if the Order Mode field is set to Specify, the design method
available is IIR least p-norm.
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16-5
16
16-6
Designing a Filter in the Filterbuilder GUI
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Filterbuilder Design Process
Customize the Algorithm
By expanding the Design options section of the Algorithm frame, you can further
customize the algorithm specified. The options available will depend upon the algorithm
and settings that have already been selected in the dialog box. In the case of a bandpass
IIR filter using the Butterworth method, design options such as Match Exactly are
available, as shown in the following figure.
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16-7
16
16-8
Designing a Filter in the Filterbuilder GUI
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Filterbuilder Design Process
Analyze the Design
To analyze the filter response, click on the View Filter Response button. The Filter
Visualization Tool opens displaying the magnitude plot of the filter response.
Realize or Apply the Filter to Input Data
When you have achieved the desired filter response through design iterations and
analysis using the Filter Visualization Tool, apply the filter to the input data. Again,
this step is never automatically performed for you by the software. To filter your data,
you must explicitly execute this step. In the Bandpass Design dialog box, click OK and
DSP System Toolbox creates the filter object and exports it to the MATLAB workspace.
The filter is then ready to be used to filter actual input data. The basic filter command
takes input data x, filters it through the Filter Object, and produces output y:
>> y = filter (Hbp, x)
To understand how the filtering commands work, type:
>> help dfilt/filter
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16-9
16
Designing a Filter in the Filterbuilder GUI
Tip If you have Simulink, you have the option of exporting this filter to a Simulink block
using the realizemdl command. To get help on this command, type:
>> help realizemdl
16-10
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Designing a FIR Filter Using filterbuilder
Designing a FIR Filter Using filterbuilder
FIR Filter Design
Example – Using Filterbuilder to Design a Finite Impulse Response (FIR) Filter
To design a lowpass FIR filter using filterbuilder:
1
Open the Filterbuilder GUI by typing the following at the MATLAB prompt:
filterbuilder
The Response Selection dialog box appears. In this dialog box, you can select from
a list of filter response types. Select Lowpass in the list box.
2
Hit the OK button. The Lowpass Design dialog box opens. Here you can specify the
writable parameters of the Lowpass filter object. The components of the Main frame
of this dialog box are described in the section titled Lowpass Filter Design Dialog Box
— Main Pane. In the dialog box, make the following changes:
• Enter a Fpass value of 0.55.
• Enter a Fstop value of 0.65.
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16-11
16
Designing a Filter in the Filterbuilder GUI
3
Click Apply, and the following message appears at the MATLAB prompt:
The variable 'Hlp' has been exported to the command window.
4
16-12
To check your design, click View Filter Response. The Filter Visualization tool
appears, showing a plot of the magnitude response of the filter.
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Designing a FIR Filter Using filterbuilder
You can change the design and click Apply, followed by View Filter Response, as
many times as needed until your design specifications are met.
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16-13
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‫‪16-14‬‬
‫‪A‬‬
‫‪Bibliography‬‬
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A
Advanced Filters
Advanced Filters
[1] Antoniou, A., Digital Filters: Analysis, Design, and Applications, Second Edition,
McGraw-Hill, Inc., 1993.
[2] Chirlian, P.M., Signals and Filters, Van Nostrand Reinhold, 1994.
[3] Fliege, N.J., Multirate Digital Signal Processing, John Wiley and Sons, 1994.
[4] Jackson, L., Digital Filtering and Signal Processing with MATLAB Exercises, Third
edition, Springer, 1995.
[5] Lapsley, P., J. Bier, A. Sholam, and E.A. Lee, DSP Processor Fundamentals:
Architectures and Features, IEEE Press, 1997.
[6] McClellan, J.H., C.S. Burrus, A.V. Oppenheim, T.W. Parks, R.W. Schafer, and H.W.
Schuessler, Computer-Based Exercises for Signal Processing Using MATLAB 5,
Prentice-Hall, 1998.
[7] Mayer-Baese, U., Digital Signal Processing with Field Programmable Gate Arrays,
Springer, 2001, refer to the BiQuad block diagram on pp. 126 and the IIR
Butterworth example on pp. 140.
[8] Moler, C., “Floating points: IEEE Standard unifies arithmetic model.” Cleve's Corner,
The MathWorks, Inc., 1996. See http://www.mathworks.com/company/newsletter/
pdf/Fall96Cleve.pdf.
[9] Oppenheim, A.V., and R.W. Schafer, Discrete-Time Signal Processing, Prentice-Hall,
1989.
[10] Shajaan, M., and J. Sorensen, “Time-Area Efficient Multiplier-Free Recursive Filter
Architectures for FPGA Implementation,” IEEE International Conference on
Acoustics, Speech, and Signal Processing, 1996, pp. 3269-3272.
A-2
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Adaptive Filters
Adaptive Filters
[1] Hayes, M.H., Statistical Digital Signal Processing and Modeling, John Wiley and
Sons, 1996.
[2] Haykin, S., Adaptive Filter Theory, Third Edition, Prentice-Hall, Inc., 1996.
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A-3
A
Multirate Filters
Multirate Filters
[1] Fliege, N.J., Multirate Digital Signal Processing, John Wiley and Sons, 1994.
[2] Harris, Fredric J, Multirate Signal Processing for Communication Systems, Prentice
Hall PTR, 2004.
[3] Hogenauer, E. B., “An Economical Class of Digital Filters for Decimation and
Interpolation,” IEEE Transactions on Acoustics, Speech, and Signal Processing,
Vol. ASSP-29, No. 2, April 1981, pp. 155-162.
[4] Lyons, Richard G., Understanding Digital Signal Processing, Prentice Hall PTR, 2004
[5] Mitra, S.K., Digital Signal Processing, McGraw-Hill, 1998.
[6] Orfanidis, S.J., Introduction to Signal Processing, Prentice-Hall, Inc., 1996.
A-4
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Frequency Transformations
Frequency Transformations
[1] Constantinides, A.G., “Spectral Transformations for Digital Filters,” IEEE
Proceedings, Vol. 117, No. 8, pp. 1585-1590, August 1970.
[2] Nowrouzian, B., and A.G. Constantinides, “Prototype Reference Transfer Function
Parameters in the Discrete-Time Frequency Transformations,” Proceedings
33rd Midwest Symposium on Circuits and Systems, Calgary, Canada, Vol. 2, pp.
1078-1082, August 1990.
[3] Feyh, G., J.C. Franchitti, and C.T. Mullis, “Allpass Filter Interpolation and Frequency
Transformation Problem,“ Proceedings 20th Asilomar Conference on Signals,
Systems and Computers, Pacific Grove, California, pp. 164-168, November 1986.
[4] Krukowski, A., G.D. Cain, and I. Kale, “Custom Designed High-Order Frequency
Transformations for IIR Filters,” 38th Midwest Symposium on Circuits and
Systems (MWSCAS'95), Rio de Janeiro, Brazil, August 1995.
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A-5
A
Fixed-Point Filters
Fixed-Point Filters
[1] Jackson, L., Digital Filtering and Signal Processing with MATLAB Exercises, Third
edition, Springer, 1995, pp.373–422.
[2] Dehner, G, “Noise optimized IIR digital filter design: tutorial and some new aspects,”
Signal Processing, Vol 83, Issue 8 (August 2003) pp.1565–1582.
A-6
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‫معرفی چند منبع در زمینه آموزش برنامه نویسی ‪ MATLAB‬یا متلب‬
‫کتاب های به زبان انگلیسی‬
‫عنوان‪Matlab, Third Edition: A Practical Introduction to :‬‬
‫‪Programming and Problem Solving‬‬
‫ترجمه عنوان‪ :‬متلب‪ :‬مقدمه ای عملی بر برنامه نويسی و حل مساله‪ ،‬چاپ سوم‬
‫مولفین‪Stormy Attaway :‬‬
‫سال چاپ‪2013 :‬‬
‫انتشارات‪Butterworth-Heinemann :‬‬
‫کتاب های به زبان فارسی‬
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‫مولفین‪ :‬برايان هان‪ ،‬دانیل تی‪ ،‬والنتین‬
‫مترجمین‪ :‬رامین موالنا پور‪ ،‬سارا موالناپور‪ ،‬نینا اسدی پور‬
‫انتشارات‪ :‬سها دانش‬
‫لینک دسترسی‪ :‬لینک‬
‫لینک دسترسی‪ :‬لینک‬
‫عنوان‪MATLAB For Dummies :‬‬
‫ترجمه عنوان‪ :‬تلب به زبان ساده‬
‫مولفین‪Jim Sizemore, John Paul Mueller :‬‬
‫سال چاپ‪2014 :‬‬
‫انتشارات‪For Dummies :‬‬
‫عنوان‪ :‬کاربرد ‪ MATLAB‬در علوم مهندسی‬
‫مولفین‪ :‬حیدرعلی شايانفر‪ ،‬حسین شايقی‬
‫انتشارات‪ :‬ياوريان‬
‫لینک دسترسی‪ :‬لینک‬
‫لینک دسترسی‪ :‬لینک‬
‫عنوان‪Essential MATLAB for Engineers and Scientists :‬‬
‫عنوان‪ :‬برنامه نويسی ‪ MATLAB‬برای مهندسان‬
‫ترجمه عنوان‪ :‬آنچه بايد مهندسین و دانشمندان از متلب بدانند‬
‫مولفین‪ :‬محمود کشاورز مهر‪ ،‬بهزاد عبدی‬
‫مولفین‪Brian Hahn, Daniel Valentine:‬‬
‫سال چاپ‪2013 :‬‬
‫انتشارات‪Academic Press :‬‬
‫انتشارات‪ :‬نوپردازان‬
‫لینک دسترسی‪ :‬لینک‬
‫لینک دسترسی‪ :‬لینک‬
‫عنوان‪MATLAB: An Introduction with Applications :‬‬
‫عنوان‪ :‬آموزش کاربردی مباحث پیشرفته با ‪MATLAB‬‬
‫ترجمه عنوان‪ :‬مقدمه ای بر متلب و کاربردهای آن‬
‫مولفین‪ :‬نیما جمشیدی‪ ،‬علی ابويی مهريزی‪ ،‬رسول مواليی‬
‫مولف‪Amos Gilat :‬‬
‫انتشارات‪ :‬عابد‬
‫سال چاپ‪2014 :‬‬
‫انتشارات‪Wiley :‬‬
‫لینک دسترسی‪ :‬لینک‬
‫لینک دسترسی‪ :‬لینک‬
‫عنوان‪MATLAB For Beginners: A Gentle Approach:‬‬
‫عنوان‪ :‬کاملترين مرجع آموزشی و کاربردی ‪MATLAB‬‬
‫ترجمه عنوان‪ :‬متلب برای افراد مبتدی با يک رويکرد تدريجی‬
‫مولفین‪ :‬علی اکبر علمداری‪ ،‬نسرين علمداری‬
‫مولف‪Peter I. Kattan:‬‬
‫انتشارات‪ :‬نگارنده دانش‬
‫سال چاپ‪2008 :‬‬
‫انتشارات‪CreateSpace Independent Publishing Platform :‬‬
‫لینک دسترسی‪ :‬لینک‬
‫لینک دسترسی‪ :‬لینک‬
‫عنوان‪MATLAB for Engineers :‬‬
‫عنوان‪ :‬برنامه نويسی ‪ MATLAB‬برای مهندسین‬
‫ترجمه عنوان‪ :‬متلب برای مهندسین‬
‫مولف‪ :‬استفن چاپمن‬
‫مولف‪Holly Moore :‬‬
‫سال چاپ‪2011 :‬‬
‫انتشارات‪Prentice Hall :‬‬
‫لینک دسترسی‪ :‬لینک‬
‫عنوان‪Mastering MATLAB :‬‬
‫ترجمه عنوان‪ :‬تسلط بر متلب‬
‫مولفین‪Duane C. Hanselman, Bruce L. Littlefield :‬‬
‫سال چاپ‪2011 :‬‬
‫انتشارات‪Prentice Hall :‬‬
‫لینک دسترسی‪ :‬لینک‬
‫مترجم‪ :‬سعدان زکائی‬
‫انتشارات‪ :‬دانشگاه صنعتی خواجه نصیرالدين طوسی‬
‫لینک دسترسی‪ :‬لینک‬
‫عنوان‪ :‬آموزش گام به گام محاسبات عددی با متلب‬
‫مولف‪ :‬کلیو مولر‬
‫مترجم‪ :‬رسول نصیری‬
‫انتشارات‪ :‬نشر گستر‬
‫لینک دسترسی‪ :‬لینک‬
‫منابع آموزشی آنالین‬
‫عنوان‪ :‬مجموعه فرادرسهای برنامهنويسی متلب‬
‫مدرس‪ :‬دکتر سید مصطفی کالمی هريس‬
‫مدت زمان‪ ۹ :‬ساعت و ‪ ۳‬دقیقه‬
‫زبان‪ :‬فارسی‬
‫ارائه دهنده‪ :‬فرادرس‬
‫لینک دسترسی‪ :‬لینک‬
‫عنوان‪ :‬مجموعه فرادرسهای متلب برای علوم و مهندسی‬
‫مدرس‪ :‬دکتر سید مصطفی کالمی هريس‬
‫مدت زمان‪ 14 :‬ساعت و ‪ 2۲‬دقیقه‬
‫زبان‪ :‬فارسی‬
‫ارائه دهنده‪ :‬فرادرس‬
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‫مدرس‪ :‬دکتر سید مصطفی کالمی هريس‬
‫مدت زمان‪ ۲ :‬ساعت و ‪ 12‬دقیقه‬
‫زبان‪ :‬فارسی‬
‫ارائه دهنده‪ :‬فرادرس‬
‫لینک دسترسی‪ :‬لینک‬
‫عنوان‪Introduction to Programming with MATLAB :‬‬
‫ترجمه عنوان‪ :‬آشنايی با برنامهنويسی متلب‬
‫مدرسین‪Akos Ledeczi, Michael Fitzpatrick, Robert Tairas :‬‬
‫زبان‪ :‬انگلیسی‬
‫ارائه دهنده‪Vanderbilt University :‬‬
‫لینک دسترسی‪ :‬لینک‬
‫عنوان‪Introduction to MATLAB :‬‬
‫ترجمه عنوان‪ :‬مقدمهای بر متلب‬
‫مدرس‪Danilo Šćepanović :‬‬
‫زبان‪ :‬انگلیسی‬
‫ارائه دهنده‪MIT OCW :‬‬
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‫عنوان‪Up and Running with MATLAB :‬‬
‫ترجمه عنوان‪ :‬شروع سريع کار با متلب‬
‫مدرس‪Patrick Royal :‬‬
‫زبان‪ :‬انگلیسی‬
‫ارائه دهنده‪lynda.com :‬‬
‫لینک دسترسی‪ :‬لینک‬
‫عنوان‪Modelling and Simulation using MATLAB :‬‬
‫ترجمه عنوان‪ :‬مدلسازی و شبیهسازی با استفاده از متلب‬
‫مدرسین‪ Prof. Dr.-Ing. Georg Fries :‬و دیگران‬
‫زبان‪ :‬انگلیسی‬
‫ارائه دهنده‪iversity.org :‬‬
‫لینک دسترسی‪ :‬لینک‬
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