Matlab Model Task

Signal Processing – Modelling an Auditory System
An auditory system mimics the behaviour of a biological cochlea found in humans and other
mammals. The system converts a 1D discrete-time audio signal to a 2D time-frequency signal
called an auditory spectrogram. From this spectrogram, audio information can be extracted
as shown in Table 1. Its application includes hearing aids, speech and musical information
retrieval, audio multimedia systems, and brain modelling.
The objective of this project is to model an auditory system using MATLAB. Note that this
project is an individual task.
Index Audio Information Responsible For
1 Intensity Sound loudness.
2 Direction Indicates where a sound is coming from.
3 Pitch Difference between musical notes and also male

and female voices.

4 Timbre Sound colour and shape indicating from which

specific source a sound is coming from.
Table 1: Information extractable from an auditory spectrogram.

To convert a one-dimensional (1D) sound signal into a two-dimensional (2D) time-frequency
representation, a cochlear filterbank is used. A cochlear filterbank comprises multiple
gammatone filters either in parallel or cascaded form. The bandwidth of each gammatone
filter increases with increasing frequency so that a high centre frequency filter has a higher
bandwidth than a filter with low centre frequency as shown in Figure 1(a).
A gammatone filter behaves like a bandpass filter. Each gammatone filter is tuned to a specific
centre frequency so that it only responds to a specific frequency. So, when the input signal
resonates close to the centre frequency of the filter, the filter will output a resonating signal
at its centre frequency. Hence, a filterbank will have a bank of gammatone filters whose
centre frequencies are tuned from low to high for the entire spectrum of a sound signal.

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Figure 1: Increasing bandwidth with increasing centre frequency in the gain response of gammatone filters. (a) x-axis is
linearly scaled where intervals between frequencies are the same; (b) x-axis is logarithmically-scaled where intervals between
frequencies are nonlinear.
Ideally, the varying filters tuned differently will react to the different frequencies in the input
signal and will output multiple signals. These signals are then half-wave rectified, where all
negative values are set to 0 and only positive values are maintained. They can be visualised
as a 2D image known as an auditory spectrogram, as shown in Figure 2.
An alternative method of showing an auditory spectrogram is by calculating the short-time
Fourier transform (STFT) on a sound signal.

Figure 2: Block diagram of auditory system

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MATLAB Model Tasks
Implement an auditory system in MATLAB using the following steps:
1. Modify the sample code in gammatonegram.tgz according to your specifications from
Table 2 based on your right-most digit in your student number. After your changes are
introduced, ensure the following:
- The heights of the two spectrograms are the same as the number of channels in
your settings.
- The lowest centre frequency in your gain response display should be within ±8 Hz
of your lowest centre frequency setting.
Right-most index of
your student
number

Gammatone filter
with lowest centre
frequency

Number of channels,
�� (gammatone filters)

Gammatone
filter order, ��
0 60 Hz 90 2
1 70 Hz 92 3
2 80 Hz 94 4
3 90 Hz 96 5
4 100 Hz 98 6
5 110 Hz 100 2
6 120 Hz 102 3
7 130 Hz 104 4
8 140 Hz 106 5
9 150 Hz 108 6

Table 2: Cochlear filterbank specification

2. In the same script file, generate a time vector (a vector is also known as an array) ��1
that contains numbers from [0 to (� − 1)]/����. Ensure the division by �� is done after
generating the vector 0 to �� − 1. Note that �� is the length (in number of samples, not
time duration) of the sound signal stored in sa2.wav that is found in
gammatonegram.tgz and ���� is the sampling rate of the sound signal.
3. Use the sound signal found in sa2.wav provided in gammatonegram.tgz, as input to
your model. In MATLAB, display the waveform of the sound signal with respect to time
vector ��1 in figure 1 and label the x-axis to reflect time in seconds and y-axis to reflect
amplitude (unitless).
4. In the original figure 1 from gammatonegram.tgz, two spectrograms are shown.
Redesignate these spectrograms to figure 2. Identify the spectrogram generated by a
gammatone filterbank and change its title to reflect this. Also, identify the
spectrogram by the short-time Fourier transform (STFT) and change its title to reflect
this.
5. Generate a time vector �� that contains � number of samples in the range from 0 to
the time duration of the sound signal in sa2.wav. Here, �� is a fixed number dependent
on the length (number of samples) of the auditory spectrogram.
6. Calculate and plot the average power (in Watts) of the STFT and auditory
spectrograms at the top half and bottom half, respectively in MATLAB figure 3. Here,
average power is to be computed independently for each column of the two
spectrograms. Label the axes and title the graphs. Hint: See online Mathworks help

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page on bandpower command. Also, the �� time vector is helpful for display of the
graphs and axis labels.
7. In Figure 1 displayed above, only the gain response of every 5 th channel of the
gammatone filterbank is displayed. Generate and display the gain response �� (the
equation has already been implemented for you in the second argument of the plot
line in demo_gammatone.m) of all the channels in the gammatone filterbank on a
linearly scaled x-axis and the same response on a logarithmically scaled x-axis in figure
4 in MATLAB. Plot the linearly-scaled gain response on top of MATLAB figure 4 and the
log-scaled gain response below it. In the graph, your settings from Table 2 can be
checked inspecting the peak of the first filter (left-most curve). This value should
within ±8 Hz of your setting from Table 2. The peak of the last filter (right-most curve)
should be close to but less than 8 kHz.
8. Display the centre frequencies of every 5 th channel from the gain response in the
command window using fprintf in a loop. The centre frequencies are the
maximum values of every channel in the gain response. The following string should be
displayed in a new line in the command for every 5 th channel: “Centre frequency of
channel ��: �� �� Hz” where �� is the channel number and �� �� is the centre frequency.
9. Generate two temporal profiles – one from the auditory spectrogram and another
from the STFT spectrogram. A temporal profile can be generated by summing all the
rows of a spectrogram.
10. Generate two spectral profiles – one from the auditory spectrogram and another from
the STFT spectrogram. A spectral profile can be generated by summing all the columns
of a spectrogram.
11. Display two temporal profiles and two spectral profiles in figure 5. The x-axis of each
temporal profile should be displayed with respect to ��2 (in seconds). The x-axis of each
spectral profile should be displayed with respect to � and �� vectors (in Hertz) that
correspond to the two spectrograms – these vectors have been automatically
generated for you in demo_gammatone.m. The amplitude (y-axis) for all four graphs
are unitless. Display:
a. The spectral profile from the STFT spectrogram on the top-left corner in
MATLAB figure 5;
b. The spectral profile from the auditory spectrogram on the top-right corner in
MATLAB figure 5;
c. The temporal profile from the STFT spectrogram on the bottom-left corner in
MATLAB figure 5.
d. The temporal profile from the auditory spectrogram on the bottom-right
corner in MATLAB figure 5.

12. Use 2D correlation coefficient (CC) to show the quantitative difference between the
following comparisons (note that only one CC should be generated per comparison).
Use fprintf to display the comparisons below one line at a time in your command
window.
a. Auditory spectrogram versus STFT spectrogram.
b. Auditory spectrogram bandpower versus STFT spectrogram bandpower.

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c. Auditory spectrogram temporal profile versus STFT spectrogram temporal
profile.
d. Auditory spectrogram spectral profile versus STFT spectrogram spectral
profile.

13. Use symbolic variables and display the impulse response of a ��-order gammatone
filter for channel 10 where �� can be found from Table 2 based on your right-most index
of your student number. Also substitute the numeric centre frequency for channel 10
into the �� �� variable. Display the equation in 6 significant figures. The impulse response
equation is defined by ��[��] in the Auditory Signal Processing.pdf slides.
Add comments to the code you have modified or introduced in MATLAB. Submit only the
MATLAB script files that you have modified on vUWS submission link under “Assessment 2”.
Progress Report (25%)
You are expected to complete up to task 4 from the MATLAB model section. Prepare a 2-page
progress report on the tasks. Describe what you have done to complete the tasks. If you are
unable to complete any task, explain what you are experiencing. Use any online English
grammar and vocabulary checking application to ensure that your report is coherent and
clear, e.g. Grammarly – marks will be given if you are able to convey your ideas clearly and
concisely.
Submit your progress report and your MATLAB script files that you have modified using the
Turnitin link in vUWS under “Assessment 1”.
Final Report (50%)
Prepare the final report with the results above using a standard format. The final report
should include the images as well as the correlation coefficient results and the gammatone
filter impulse response (screen capture – do not use your phone to capture any images). Use
any online English grammar and vocabulary checking application to ensure that your report
is coherent and clear, e.g. Grammarly – marks will be given if you are able to convey your
ideas clearly and concisely.
The sections to be included in the final report are:
1. Introduction. Objectives – alternatively, you can include a motivation statement on
why this project is important.
2. Components of the auditory model.
3. Modelling the auditory model using MATLAB using the specification from Table 2
clearly described. Also, mention about the filter order from Table 2 required to show
the gammatone impulse response. Also, address the following questions in your
report for additional marks:
a. The inner hair cell response has all its negative values set to 0. How can these
values be converted from negative to positive? Suggest a computational
method to differentiate the current positive values with the positive values
converted from the negative values.

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b. Suggest a computational method to attain temporal and spectral profiles with
their amplitudes between 0 to 1.

4. Results (screen capture of all the; screen capture of MATLAB command window
showing correlation coefficients (CC) and the symbolic equation). Comment on the CC
results to indicate the degree of difference between pairs of vectors and matrices in
task 12.
a. Address which CC result is highest and thus, most similar.
b. Conversely, address which CC result is lowest and thus, least similar.
5. Conclusion (discuss your experience in using MATLAB for modelling of the auditory
model, its usefulness, and difficulties).
6. References. Either Harvard-style or IEEE-style referencing is acceptable – See the last
slide in Auditory Signal Processing.pdf as an example.
Submit your final report and your MATLAB script files that you have modified using the
Turnitin link in vUWS under “Assessment 3”.
Resources
 Signal Processing Toolbox.
 Audio Toolbox.
 Auditory Filterbank Sample Code.
 Auditory Filterbank Documentation.