PowerPoint Presentation
Prof. , School of EE&T Term 3, 2022
Copyright By PowCoder代写 加微信 powcoder
ELEC3104: Mini-Project – Cochlear Signal Processing
Prof. , School of EE&T Term 3, 2022
ELEC3104: Mini-Project – Cochlear Signal Processing
TLT – Level 3 (Credit Level): Implementation of a cascaded filter bank
model of the cochlea for spectral analysis.
Complete TLT-Level 2 first, and ensure that you are on the right track before
proceeding to TLT – Level 3
TLT-Level 3: Short-time Spectrum Analyser
You should use the cochlear model that you have designed in TLT-Level 2 to implement a short-time spectrum analyser. The
cascaded filters separate the frequency spectrum of interest (96.5 Hz to 20000 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 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 (i.e: A Spectrum
analyser).
Hair cell model Hair cell model Hair cell model Hair cell model Hair cell model
Filter 2 Filter 3 Filter m Filter N
Input x[n]
s1[n] s2[n] s3[n] sm[n] sN[n]
Spatial differentiation
d1[n] d2[n] d3[n] dm[n] dN[n]
Spatial differentiation
e1[n] e2[n] e3[n] em[n] eN[n]
Digital filter model of the basilar membrane
v1[n] v2[n] v3[n] Vm[n] vN[n]
Energy (E1) Energy (E2) Energy (E3) Energy (Em) Energy (EN)
Ouput Energy 𝐸𝐸𝑚𝑚 is read (switch closed) once every 16 ms or so.
SOUND BASILAR
INNER HAIR
HAIR CELLS
PROCESSING
Inner Ear (Cochlea) Nerve Fibres
Organ of Corti
TLT-Level 3: Inner hair cell model
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:
𝑣𝑣𝑚𝑚[𝑛𝑛] = 1 − 𝑐𝑐0 𝑒𝑒𝑒𝑚𝑚[𝑛𝑛] + 𝑐𝑐0𝑣𝑣𝑚𝑚[𝑛𝑛 − 1] where 𝑐𝑐0 = 𝑒𝑒
Where, 𝑣𝑣 𝑛𝑛 is the output electrical energy.
Inner hair cell model
𝑒𝑒𝑒 𝑛𝑛 is the spatially differentiated displacement after half-wave rectification.
Cut-off frequency (𝑓𝑓𝑐𝑐) of the hair cell model is based on the rate at which the switch is closed. (every 16 ms – 62.5 Hz). Therefore 𝑓𝑓𝑐𝑐 ≤
31.25 𝐻𝐻𝐻𝐻. Let’s choose 𝑓𝑓𝑐𝑐=30Hz; Sampling frequency (𝑓𝑓𝑠𝑠)=48,000Hz;
Are you on the right track?
Apply a sum of two sinusoidal components (5.92 kHz and 1.01 kHz) at the
input 𝑥𝑥[𝑛𝑛].
The figure below shows the spatially differentiated basilar membrane
displacement {𝑒𝑒1[𝑛𝑛] 𝑡𝑡𝑡𝑡 𝑒𝑒𝑁𝑁[𝑛𝑛]} of each filter against the filter number at a
particular time instant and the corresponding inner hair cell output in
response to a sum of two sinusoidal components.
If your inner hair cell model implementation is correct, you should
observe something similar to what is shown below
The inner hair cell output shows the spectral components that present in
the input signal.
0 20 40 60 80 100 120
Displacement after two spatial differentiation
0 20 40 60 80 100 120
filter number
Inner hair cell output
5.92 kHz (filter no : 30)
5.92 kHz (filter no : 30)
1.01 kHz (filter no : 72)
1.01 kHz (filter no : 72)
TLT-Level 3: An alternative inner hair cell model
• 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
differentiated
displacement
Reset after 16 ms
Accumulate for
Sampling period (T) = 16 ms
Inner hair cell
output q(k)
First order post
p(k-1)Delay
TLT Level 3 : Final Implementation
• Apply a signal which is a sum of four sinusoids, 1000-2000 samples, of equal amplitude and frequencies of your choice, to the
input of the filter bank. Plot the output of your 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)?
• Discuss your results with your lab demonstrator.
Final Implementation
Slide Number 1
Slide Number 2
Slide Number 3
Slide Number 4
Slide Number 5
Slide Number 6
Slide Number 7
程序代写 CS代考 加微信: powcoder QQ: 1823890830 Email: powcoder@163.com