another fir filter core generator - kik

another fir filter core generator - kik
FIR FILTER SOFT CORE GENERATOR
Anatoli Sergyienko*, Vladislav Vasylienko*, Oleg Maslennikow**
* National Technical University of Ukraine "KPI", Kiev, Ukraine,
email: aser@comsys.ntu-kpi.kiev.ua
** Technical University of Koszalin, Poland, email: oleg@ie.tu.koszalin.pl
ABSTRACT
A new FIR filter soft core generator is represented which utilizes structural properties of
FPGA, minimizes its hardware volume. It provides the design of highly pipelined structures with
extremely high clock frequency which are described on VHDL.
1. INTRODUCTION
The modern system on the chip (SOC) technology is based on a set of principles, one of
them is the core generator use. Due to its flexibility, and reusability the core generator can
substitute the very large library of cores of a single type. Tunable core generators help to
optimize the speed, hardware, and energy consumption of the resulting project.
Finite impulse responce (FIR) filters are widely used in digital signal processing
systems due to their high throughput, easy procedures of their characteristic calculation, phase
characteristic linearity. The implementation of FIR filters in FPGA has a set of advantages,
like short design period, high throughput, hardware utilization effectiveness, and any rate of
calculating precision because of full adaptation of implemented structure to the filtering
algorithm. In many special applications, like high speed communications, FPGA is the only
solution for FIR filter implementation.
The FIR filter core generators can support the development of high speed FIR filters
with given filter length, impulse characteristic, signal-to-noise ratio. The Xilinx FIR core
generator is well known due to high speed, small hardware volume of generated filters [1].
This generator generates so called firm cores, which are represented by the netlist. This is the
source of such serious disadvantages like small range of parameter representation, and that
this generator is tied to the small set of FPGA chip families. Due to the high measurements of
generated relatively placed macros these filters are stiff and fit only large devices, and
therefore they have improper device area utilization.
In this paper the another FIR filter core generator is represented which generates filter
cores described on VHDL, with increased throughput, minimized hardware, wide range of
filter length, data and coefficient length, and which are implemented in the large set of FPGA
families.
2. METHODS OF COEFFICIENT MULTIPLICATION IN FPGAS
FIR filter computation, or convolution consists in deriving the following sum of
products
K
yn = ∑ ak ⋅ xn−k +1 ,
k =1
where xn-k+1 is the input data sample, ak is the filter impulse response coefficient, K is the
impulse response length, yn is the output result sample with index n. To derive one resulting
sample the filter has to implement averagely K multiplications and additions. Therefore the
convolution is rather computation intensive.
Initially FPGAs were not intended for computation intensive applications like
convolution. Therefore the multiplication units were firstly programmed as a set of logic
equations or as a set of AND gates with an adder tree. When the application of FPGA in the
intensive signal processing became clear and widely propagated, in the new FPGA families
some elements were added which support the high speed multiplications. For example in
Xilinx Virtex™ configurable logic blocks (CLB) the additional AND gates were added which
support the multiplication, and then in VirtexII™ devices the separate multiply units were
introduced.
In the most applications the convolution procedure has the multiplication to the constant
coefficients. And the use of combinatorial circuits of multipliers for such a multiplication is
rather abundance. Besides, the number of multiply units in the new FPGA families is not
enough for many DSP applications. Therefore a set of techniques were proposed to utilize the
property of constant coefficient multipliers (KCM). For example, taking into account that the
average number of one bits in the m bit constant coefficient is equal to m/2 the KCM can be
designed which consists of a tree of m/2-1 adders.
A.Peled and B.Liu have invented in1974 the method of deriving the sum of products
named the distributed arithmetic. The method consists in the storing of up to 2K combinations
of sums of K coefficients in the ROM. If the i-th bit silice of the input data set is inputted to
the address input of this ROM then the read data is the proper sum of partial products. The
whole sum of products is derived when up to m such sums of partial products are added in the
result accumulator with the proper bit shift.
This method was proposed by L.Mintzer as the effective method to derive the sum of
products in FPGAs [3]. It utilizes the property of 4 input look-up table (LUT) to be
programmed as a high speed 16 bit ROM. This method is widely used in many DSP
applications, and in the Xilinx FIR core generator as well [4]. To achieve the high throughput
all the sums of partial products to the i –th digits of multiplicants are calculated in parallel.
Therefore such filters are usually called parallel distributed arithmetic (PDA) FIR filters. The
disadvantage of the method consists in the extremally large ROM volume when the
coefficient number K is larger than 8,…,12, and more. To minimize this disadvantage the
filter is divided to a set of blocks, each of them calculates the sum of K=4 or 5 products.
Another way to get the multiplication to the constant coefficient was proposed in [5].
This method was shown in [6] as the effective multiply method for FPGAs. It based on the
ROM which stores in its i-th location the coefficient a multiplied by i. Therefore the ROM of
volume 2m represents the KCM to m bit dates. Such multiplier and the filter based on it are
called ROM based multiplier (RBM) and RBM filter, respectively. When the ROM volume is
too small then the input data is divided to l slices of p bits so as m≤lp, and the result is equal
to the sum of l partial products. In [5] was shown that such multipliers for ASIC
implementation are effective ones comparing to the usual 16x16 bit multipliers when the
amount of the ROM volume is less than ca. 4 kbytes, and therefore the optimum slice width is
p=4. The example of such KCM for 16 bit input data and 16 bit coefficients for 16 bit
precision product and p=4 is illustrated by the fig.1. Such implementation of KCM has the
following advantages.
• High throughput. The multiplier netlist has much of pipeline registers, and the
logical paths are rather short. Therefore the minimum clock period can be extremely short and
is equal to the delay of a single adder.
• Small hardware volume. The resulting hardware volume of RBM FIR filters is
equal or less than hardware volume of PDA filters. It is less according to the following
feature. Consider the coefficient a has a sequence of j equal (zero or one) bits. Then in the
ROM the j-p+1 bit wide slice will have bits which are equal to each other. On the netlist
synthesis stage such a bit slice will be minimized to the constant source. The FIR filters,
which are used in the applications, usually have more than 70% of coefficients, which have
more than j=4 equal most significant bits, and averagely 40% of coefficients having more
than 7 such bits. Therefore when the RBM FIR filter is described on the language like VHDL,
then the synthesized filter has in 1.1,...,1.6 times less hardware volume than the PDA filter
has, depending on the filter coefficient set.
x
RGD
1512
11 8 7
4 3
0
ROM1
17
0
ROM2
13
0
ROM3
9
0
ROM4
5
0
RG
RG
RG
SM1
17
RG
SM2
RG
0
9
RG
0
SM3
15
RG
0
ay
Fig.1. Example of the constant coefficient multiplier
• Increased equivalent coefficient bit length. Such a feature is connected with the fact
that when storing in the ROM, the coefficient code is rounded to m bits after multiplication of
the coefficient a to the constant i but not before the multiplication. Therefore the equivalent
coefficient length in RBM filters can be estimated by m-2, where m is the maximum word
length of the ROM. Note that in PDA filters the coefficient length is equal to m-p.
3.
DESCRIPTION OF THE FIR FILTER CORE GENERATOR
A FIR filter core generator is designed which utilizes ROM based multipliers. The
generated FIR filter structure is usual one, and contains the array of internal registers for input
data delay – one per tap, array of coefficient multipliers –one per tap, and an adder tree which
calculates the sum of delayed and weighted input dates. To support the high throughput the
circuit is deeply pipelined. Two types of structures are distinguished called filters with
nonsymmetrical (NSRBM) and symmetrical (SRBM) impulse characteristics. The last
structure utilizes the property of couples of equal coefficients which reduces in two times the
number of multipliers. The advantages of these structures were shown in [7].
The generated cores are described by a single VHDL file and are independent on the
FPGA family and vendor. This file can be compiled by any proper synthesis tool into the
netlist for FPGAs of such families like Xilinx XC4000, Spartan™, Virtex™, Altera
Flex10K™, Flex20K™, and others.
The core generator is designed as the Win32 Delphi Dialog-Based Application. The
main window is shown on the fig.2.
Fig.2. FIR filter core generator parameterization window
The generator is implemented as the command line driven application as well. This
implementation is introduced in the HDL Wizard™ tool of the Active HDL package. The
customer can exchange the following parameters:
coefficient set which is given as decimal, octal, hexadecimal, binary integers or real
numbers;
input data width from 4 to 24 bits;
coefficient width from 4 to 24 bits;
number of taps from 4 to 100;
SRBM, NSRBM, and antisymmetric filters;
output precision up to full precision;
2's complement input data or unsigned input data;
the speed slow down which is provided by the control of the Clock Enable signal.
The regulated maximum parameters can have more high limits. The mentioned above
parameter limits are set as practical limits.
4. EXPERIMENTAL RESULTS
A set of FIR filters was generated by the new core generator and implemented in Xilinx
FPGAs using Foundation 3.1. synthesis and implementation tool. The impulse responses were
selected as practical ones which represent the low pass and band pass filters with sharp
frequency response characteristics and 60-70 db suppression rate. Some results for input and
output data width 16, coefficient width 16, and symmetrical impulse characteristic are shown
in the table 1. The results of the Xilinx FIR PDA core generator are shown in the last row of
the table for comparison.
The table analysis shows that the resulting filter structures have the high throughput,
and minimized hardware. The low hardware volume increase and low sampling frequency
degradation when the filter complexity increases can be seen comparing the results on the
Virtex devices.
Tabl.1. Parameters of designed FIR-filters and Xilinx PDA filter
Filter
type
SRBM
SRBM
SRBM
SPDA
Device type
Number of
taps, K
VirtexE-8
20
VirtexE-8
99
XC4000XV-07
20
XC4000XV-07
20
Hardware volume,
CLB (slices)
1022
5151
1008
1457
Maximum sampling
frequency, MHz
212
208
76
50
5. CONCLUSION
A new FIR filter soft core generator is represented which utilizes structural properties of
FPGA, minimizes its hardware volume. It provides the design of highly pipelined structures
with extremely high clock frequency, which is higher than 200 MHz for modern FPGA
families. The generated core is described by a single VHDL file and therefore is independent
on the FPGA vendor and family.
Now the core generator is modernized to generate the decimation, interpolation filters,
1/n -band filters, etc.
REFERENCES
[1] Parallel Distributed Arithmetic FIR filter. Product Specification. Available at
http://www.xilinx.com. Feb.8.1988.
[2] Peled A., Liu B. A New Hardware Realization of Digital Filters. IEEE Trans. on Acoustic Signal,
Speech Processing, V.ASSP-22, June, 1974.
[3] Mintzer L. FIR filters with the Xilinx FPGA. FPGA'92, ACM/SIGDA Workshop on FPGAs,
1992, pp. 129-134.
[4] Goslin G.R. A Guide to Using Field Programmable Gate Arrays (FPGAs) for ApplicationSpecific Digital Signal Processing Performance. Available at http://www.xilinx.com. 1995.
[5] Kanevski Ju.S., Nekrasov B.A., Sergyienko A.M. Issues of High-Performance FFT Procesor
Implementation. (In Rusian). Upravlajustshie Systemy i Mashiny, 1986. №4, pp.60-63.
[6] Chapman K. Constant Coefficient Multipliers for the XC4000E. Application Note. Available at
http://www.xilinx.com. December 11, 1996.
[7] Kaniewski J., Berezowski R., Gretkowski D., Maslennikov O., Soltan P. Modele VHDL filtrov
FIR przeznaczonych do realizaciji w ukladach FPGA. Materialy III Krajowej Konferencji
Naukowej "Reprogramowalne uklady cyfrowe", RUC'2000, Szczecin (Poland), 10-11 Kwietnia
2000. pp.269-276.
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