# AUDL 1001 final exam 2009 p+f 19.03.09

```AUDL1001
Examination 2009
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BSc AUDIOLOGY
AUDL1001 – SIGNALS AND SYSTEMS FOR HEARING AND SPEECH
(YEAR 1)
EXAMINATION 2009
Time allowed: 3 hours
1) Consider the amplitude responses of the following two systems.
System 1
20
gain (dB)
10
0
-10 0
500
1000
1500
2000
1500
2000
-20
-30
-40
frequency (Hz)
System 2
20
gain (dB)
10
0
-10 0
500
1000
-20
-30
-40
frequency (Hz)
CONTINUE
AUDL1001
Examination 2009
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AUDL1001
Examination 2009
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a) What kind of a filter does each represent?
b) Draw the amplitude response of System 2 on linear gain and linear frequency scales.
c) Now draw the amplitude response of a cascade of these two systems, System 1
followed by System 2, on dB and linear frequency scales.
d) What would be the amplitude response of the cascade if the position of the two
systems were reversed? Explain your reasoning.
(10 points total)
2) Draw input and output spectra of the following 4 signals passed through System 1 in
Question 1, over the frequency range 0-2 kHz, on dB and linear frequency scales. Ensure
that your labels are accurate and that your amplitude scales are consistent across the
input and output graphs.
a) A sinusoid at 300 Hz
b) White noise
c) An impulse
d) A periodic train of impulses with a period of 0.01 s
(10 points total)
3) Draw two cycles of a digital 50 Hz sinusoid at a peak voltage of 20 µV, sampled at 400
times per second. What processes are necessary to convert an analogue waveform to a
digital waveform? What are the limitations of these processes?
(15 points total)
TURN OVER
AUDL1001
Examination 2009
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AUDL1001
Examination 2009
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4) Consider a periodic train of very narrow pulses at 100 Hz, whose fundamental component
is at a level of 10 dB re 1 mV. This signal passes through a high-pass filter which has a
passband gain of -10 dB at 400 Hz and upwards, and a low frequency slope which rolls
off at 12 dB/octave from there.
a) Draw the amplitude spectrum of the input wave on a linear amplitude scale over the
frequency range 0 – 1000 Hz (use a linear frequency scale).
b) Draw the frequency response of the system using dB gain and log frequency over the
range 100 – 1000 Hz.
c) Using dB amplitude scales, draw the amplitude spectrum of the input wave, and the
output of this system to it, over the frequency range 100 – 1000 Hz.
d) Would the input waveform be changed after passing through the system? Give
reasons for your answer (you do not need to draw the output wave).
(20 points total)
5) It is often said that the function of the basilar membrane can be likened to that of a filter
bank. Describe what a filter bank is, and how the notion of a filter bank can be used to
understand cochlear function and the relevant aspects of auditory nerve firing patterns.
What properties would the filter bank need to have in order to best mimic the functioning
of the inner ear?
(20 points total)
CONTINUE
AUDL1001
Examination 2009
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AUDL1001
Examination 2009
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6) Almost all systems clip signals that are too large to be handled by them, so any system
can only be considered to be linear time-invariant (LTI) over some limited range of levels.
Suppose you had a system that acted as a perfect amplifier with a gain of 4. However, the
magnitude of the output voltage is strictly limited to 10 V peak-to-peak (so the minimum
voltage is -5 V and the maximum 5 V).
a) Draw the frequency response of the system, on dB and linear frequency scales (0-3
kHz), assuming the input voltage to be 1 V.
b) Draw output waveforms for 2 cycles of a 400 Hz sinusoid when:
i) the peak voltage of the input is 1 V, and
ii) the peak voltage of the input is 2 V.
In terms of a general description, what kinds of output waves do you obtain in the two
cases (aperiodic, simple, complex, periodic)?
c) Make your best guess as to what the spectrum of the output to a 2 V input sinusoid at
400 Hz would look like, and draw it (using linear scales on both axes).
d) Draw the input/output function of the system for a 400 Hz sinusoid for peak voltages
ranging from 0 V to 3 V.
e) Is the system homogeneous? Why or why not?
f) Is the system it time-invariant? Why or why not?
g) From what you have shown above, what are the two ways you can show that this
system is not LTI for input voltages ranging from 0-3 V?
(25 points total)
END OF PAPER
AUDL1001
Examination 2009
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