Prof. Eliathamby Ambikairajah, School of EE&T Term 3,
2024 1 ELEC3104: Mini-Project – Cochlear Signal Processing TLT – Level 3 (Credit
Level): Using the Level 2 IIR cochlear filter
bank model, implement a spectral analysis system. Complete TLT-Level 2 first and ensure that you are on the right track before
proceeding to TLT – Level 3 Short-time Spectrum Analyser 2 ✓ You should use the IIR filter bank that you have designed in TLT-Level 2 to implement a short-time spectrum analyser. The
bank of filters separates the frequency spectrum of interest (88 Hz to 7723 Hz) into
N (=128) frequency bands.
✓ In this mini-project we will continue to use two spatial differentiations in order to sharpen the magnitude response of the
filters.
✓ The spatially differentiated bandpass filter output is then passed through a hair cell model (a rectifier followed by a first- order lowpass filter). The output of the hair cell model is a measure of energy (E) of the signal in a particular frequency band. Ouput Energy
is read (switch
closed)
once every 16 ms or so. k1 k2 k3 km kN Note: 1 –
are the gain factors
Gain Factor Calculation (1
) 3 1. Input Signal: For each filter n (where
= 1 , 2 , … … ) provide a sine wave of amplitude 1. The sine wave should have a
centre frequency corresponding to the centre frequency of the filter under consideration. 2. Filter Output: Apply the sine wave to the filter and compute the filter's output. 3. Maximum Value: Measure the absolute maximum value of the filter's output, denoted as
()
for the nth filter. 4. Gain Calculation: The gain factor
for the nth filter is calculated using the formula:
= 1
() 5. Repeat for All Filters: Repeat steps 1 to 4 for all N filters to obtain the gain values 1
. Gain Factor Calculation for Filters 1
Spatial Differentiation and Inner hair cell model 4 ✓ Spatial differentiation of the membrane displacement
represents coupling between the cilia of the inner hair cells,
through the fluid in the subtectorial space. ✓ Spatial differentiation refers to taking the derivative with
respect to the position (along the basilar membrane). A discrete
model is given by:
[n]=[n]- +1[n]
{. . 1[n]=1[n]- 2[n]} ✓ The second spatial differentiation is given by:
[n]=[n]- +1[n] {. . 1[n]=1[n]- 2[n]} Spatial Differentiation ✓ The model of an inner hair cell is a capacitor model, in which the input
voltage corresponds to the spatially differentiated membrane
displacement output of the filter bank model.
✓ Bending the inner hair cell cilia (Half-wave rectification) is simulated by
charging of the capacitor, and returning to the initial position of the cilia
is equivalent to discharging the capacitor. ✓ This model is given by the following input-output relationship: [] = 1 − 0 ǁ[] + 0[ − 1]
where 0 =
−2π
Where,
is the output electrical energy,
Inner hair cell model ǁ
is the spatially differentiated displacement after half- wave rectification. Cut-off frequency () of the hair cell model is based on the rate at which
the switch is closed. (every 16 ms – 62.5 Hz). Therefore,
≤ 31.25 .
Let’s choose =30Hz; Sampling frequency ()=16000Hz.
Are you on the right track? 5 ✓ If your implementation of the spatial differentiation is
correct, you should get the magnitude response similar
to the one shown in the diagram on the left, for the filter
84 with a centre frequency of 1640 Hz.
✓ You might notice that the centre frequency of each filter
has shifted slightly with each spatial differentiation, and
the filter shapes have become sharper, with a steeper
slope. Why do you think this is the case? Filter 84 (= 1.64 kHz) Are you on the right track? 6 ✓ Apply a sum of two sinusoidal components (704.6 Hz [Filter no:60] and 2.88 kHz [Filter
no: 100]) at the input []. ✓ Plot the output {1[]
[]} of each filter against the filter number at a particular
time instant .
✓ Repeat the above step for the output {1[]
[]} and for the output
{1[]
[]}
✓ Do you notice any differences between these three plots? If so, why? Explain briefly. ✓ The inner hair cell output shows the spectral components present in the input signal. ✓ If your implementation of the spatial differentiation is correct, you
should get results that are very similar to the diagram on the left for a
sum of
two sinusoidal input. ✓ The figure on the left
shows the spatially differentiated basilar membrane
displacement (e1[n] to eN[n] } and the corresponding inner hair cell output
in response to a sum of two sinusoidal components applied at the input
(704.6 Hz [Filter no:60] and 2.88 kHz [Filter no: 100]).
TLT-Level 3: An alternative inner hair cell model 7 • A second method of implementing the inner hair cell model is shown below: • In this model the positive cycle of the spatially differentiated (twice) membrane displacement is accumulated at each
sampling instant and then the accumulated value is digitally filtered
(Post-filtering) at the end of each 16 ms frame. The
accumulator is reset at the end of 16 ms frame. • Replace the previous hair cell model with the above model. • What is the main difference between the above hair cell model and the previous hair cell model in slide 4, TLT level 3?
Discuss your understanding with your lab demonstrator. An alternative inner hair cell model ∑ Spatially
differentiated
membrane
displacement Half-wave
rectifier Reset after 16 ms Accumulate for
16 ms + T Sampling period (T) = 16 ms Inner hair cell
output q(k) First order post
filter p(k) p(k-1)Delay Are you on the right track? 8 • Apply a signal which is a sum of six sinusoids, 1000-2000 samples, of equal amplitude and frequencies of your choice, to the input
of the filter bank. Plot the output of the spectrum analyser (i.e the output of each filter in dB against the filter number) at a
particular time instant.
• Plot the magnitude spectrum (using FFT) of the input signal and compare it with the filter bank
output.
Discuss the results that
you get. • Note that the sampling frequency of the input signal is 16kHz and the output signal has a sampling interval of 16ms (62.5Hz).
Explain why it is necessary to have a lower sampling rate at the output?
What are the implications for the cut-off of the output
LPF (see hair cell model) if we require a sampling of the output (close the switch) twice as often (125Hz)? • Apply your own recorded voice at 16 kHz sampling frequency as an input and observe the hair cell output at a particular time
instant. What do you notice? Discuss your observations with your lab demonstrator. Final Implementation 51作业君版权所有
