ELEC3104
28 March 2018
ELEC3104: Project – Cochlear Modelling
Dr Vidhyasaharan Sethu
And
Professor Eliathamby Ambikairajah
Additional Information
Contents
ELEC3104 Project Outline
Part A (Release – Week 5)
Introduction to Human Auditory System
Outer Ear
Middle Ear & Learning activity 1
Inner Ear & Learning activity 2
Organ of Corti
Part B (Release – Week 6)
Implementation of a parallel filterbank model of the cochlea for spectral analysis
In addition to the information provided to you in these slides, you are strongly encouraged to find and view animations and videos that describe the functioning of the peripheral auditory system and the cochlea in particular. Visualisation in the form of these animations will be very helpful in understanding cochlear signal processing.
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ELEC3104 Project Outline
This project will focus on understanding and modelling the spectral analyses carried out by the human cochlea.
It will involve modelling the following:
Understanding the analytical models describing the various elements of the peripheral auditory system Implementing a digital model of the peripheral auditory system in MATLAB
Demonstration and Validating your implementation
Presenting your work and your understanding
Your project will be assessed in week 10/11 as follows:
You will make a maximum of 10 minute presentation with slides outlining your understanding of the project, the underlying analytical model, your implementation and your validation. You should also demonstrate that your code works.
This will be followed by 5 minutes of questions about your understanding and implementation of the project as well as related signal processing concepts.
You should submit your presentation slides and code before the start of week 10 (as a single zip file on Moodle)
You will make this presentation to lab demonstrators.
In week 10, there will be a survey about the project that you must undertake.
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ELEC3104 Project Outline
It is expected that you will work on this project from week 5 onwards and make regular progress.
While these are not individually assessed, expected completion times for different stages of the project are listed in the following slides.
A recommended time frame for learning and reflection is provided below:
Week 5/6 – Understanding the relevant biological aspects of the Human Auditory System
Week 6 – Activities 1 & 2 completed and estimation of filterbank parameters
Weeks 7 – 8 – MATLAB implementation of the parallel filterbank cochlea model with digital auditory filters
Week 9 – Validating your implementation of your filters in terms of appropriateness of impulse response, magnitude response, etc and preparation of final presentation
Week 10/11 – Final Presentation.
You can discuss your project with your lab demonstrators in the scheduled tutorial-labs and they will be able to answer questions you may have. Your head demonstrator, Saad Irtza, will also be available outside lab hours for answering questions (please make an appointment via email). For administrative matters contact Dr. Sethu.
You are strongly encouraged to start immediately. Catching up at a later stage will be very hard. Please discuss your progress with your lab demonstrators every week in your scheduled lab class to ensure that you are on track.
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Introduction to the Human Auditory System
The human auditory system is responsible for converting pressure variations caused by the sound waves that reach the ear into nerve impulses that are interpreted by the brain.
Electrical signals.
The Human Auditory System is designed to assess frequency (pitch) and amplitude (loudness).
L
The peripheral auditory system is divided into the Outer Ear, Middle Ear, and Inner Ear.
The peripheral auditory system and in particular the cochlea can be viewed as a real-time spectrum analyser.
Sounds
Level
The primary role of the cochlea is to transform the incoming complex sound wave at the ear drum into electrical signals.
Moderate
60dB (normal conversation)
The human ear can respond to minute pressure variations in the air if they are in the audible frequency range, roughly 20 Hz – 20 kHz
Painful and dangerous
130dB(Jackhammers); 140dB(Gunshots) *Use hearing protection
Faint
20dB (A faint Whisper is 30dB)
Soft (Quiet)
40dB
Loud
80dB (alarm clocks, vacuum cleaners)
Very Loud
90dB(Blenders);110dB (Concerts, car horns)
Uncomfortable
120dB (jet planes during take off)
Over 85 dB for extended periods can cause permanent hearing loss
Zero decibels (0 dB) represent the absolute threshold of human hearing, below which we cannot hear a sound.
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Outer Ear (Air Vibration): A resonator
The pinna surround the ear canal and functions as sound wave reflectors and attenuators .
Electrical signals.
The sound waves enter a tube-like structure called ear canal and it serves as a sound amplifier.
L
The sound waves travel through the canal and reach the eardrum and cause it to vibrate
The length (L) of the human ear canal 20 is 2.8 cm (and 7 mm in diameter)
Speed of sound (c) = 340.3 m/sec ;
The resonant frequency (f) of the
canal is = = 3,038Hz.
0
The human outer ear is most sensitive at about 3kHz and provides about 20dB (decibels) of gain to the eardrum at around 3000Hz.
Outer ear is a low-Q bandpass filter (Representative figure only)
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Middle Ear: An Impedance Matcher
Sitting just behind the ear drum is an air filled chamber . Three tiny bones (the hammer, anvil and stirrup – known as auditory ossicles) are suspended in this chamber, forming a bridge-like connection between the ear drum and the inner ear membrane called the oval window
Electrical signals.
Middle ear transforms the vibrating
motion of the eardrum into motion of
the stapes via the two tiny bones, the 20 malleus and incus .
The pressure of the sound waves on the oval window is around 25 times higher than on the eardrum.
The pressure is increased due to the difference in size between the relatively large surface of the eardrum and the smaller surface of the oval window
0
L
Middle ear converts acoustic energy to mechanical energy and mechanical energy to hydraulic energy
6
dB
Middle Ear (Mechanical vibration): An amplifier
There is an impedance mismatch between the outer and inner ears
Ai r
𝐹 1.3 𝐹 [𝐹 – Force]
𝐴 𝐴 [𝐴 – Area]
Fluid
𝑃 1.3 . 19 .
𝑃 25 𝑃 [𝑃 – Pressure]
Since the sound Intensity 𝐼 is proportional ∝ to the square pressure 𝑃) , the sound intensity increases 625 times (or 28dB
20
Middle Ear Transfer function
0
The combined frequency response of the outer and middle ear is a band-pass response, with its peak dominated near 3 kHz.
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What is included in the outer ear?
What is included in the normal middle ear?
The outer ear is a:
The middle ear converts:
A. Pinna
B. Ossicles
C. Cochlea
D. Alloftheabove
A. Incus
B. Ossicles
C. Airfilledcavity D. Alloftheabove
A. Low-pass filter
B. High pass filter
C. LowQband-passfilter D. All-passfilter
A. Acoustic Energy to Electrical
B. Hydraulic Energy to Electrical C. AcousticEnergytoMechanical D. Mechanical Energy to Acoustic
The middle ear may be modelled as a cascade of two complex pairs of zeros (to remove very high and very low frequencies) and one complex pair of poles (to provide low-Q gain at the middle frequencies). The approximate frequency response of the middle ear can be seen in the figure below. Assuming a sampling frequency of 48kHz:
(a) obtain the transfer function of the middle ear filter, by suitably placing poles and zeros on the z-plane. Verify your results in MATLAB.
(b) Using placement of poles and zeros, estimate a model for the outer ear and cascade it with your previous model of the middle ear and show using MATLAB that the overall response matches the one shown in this figure.
Reflections
Learning Activity 1
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8
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Inner Ear
The inner ear consists of the cochlea responsible for converting the vibrations of sound waves into electrochemical impulses which are passed on to the brain via the auditory nerve.
The cochlea is a spiral shaped structure which is about 3.5 cm in length if uncoiled.
The cochlea is divided along its length by the basilar membrane (BM) which partitions the cochlear into two fluid canals (scala vestibuli and scala tympani).
The BM terminates just reaching the helicotrema, so there is a passage way between the scala vistibuli and the scala tymapni equalising the difference in pressure at the ends of the two scalas.
A longitudinal section of an uncoiled cochlea
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Basilar Membrane (Hydro Dynamical process)
The Basilar Membrane varies in width and stiffness along its length.
3.5 cm
At basal end it is narrow and stiff where as towards the apex it is wider and more flexible.
Basilar membrane
0.05155 cm
Each point along the basilar membrane has a characteristic frequency, 𝑓(𝑥), to which it is most responsive.
Base
Apex
The maximum membrane displacement occurring at the basal end for high frequencies (16kHz) and at the apical end for low frequencies (70Hz) .
If 𝑥 is the distance of a point on the basilar membrane from the stapes, then the frequency, 𝑓(𝑥), that produces a peak at this point may be approximately (example model only) given by:
When the vibrations of the eardrum are transmitted by the middle ear into movement of the stapes, the resulting pressure differences between the cochlear fluid chambers, generate a travelling wave that propagates down the cochlea and reach maximum amplitude of displacement on the basilar membrane at a particular point before slowing down and decaying rapidly
•
It is evident that a 16 kHz tone at the stapes will cause the BM to vibrate at a point 𝑥 0.
The location of the maximum amplitude of this travelling wave varies with the frequency of the eardrum vibrations
The basilar membrane is a resonant structure that vibrates, vertically in sympathy with pressure variations in the cochlear fluid.
𝑓 𝑥 16000.0 10. 𝐻𝑧 0𝑥3.5𝑐𝑚
• A70HztonewillexcitetheBMatapointx=3.5 cm (i.e. at the apex)
= 3.5 cm
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Different frequencies stimulate different areas of the basilar membrane
When a tone (single sinusoid) is applied, the cochlear fluid oscillates in phase with the stimulating frequency causing a travelling wave pattern of the vibration on the basilar membrane
There will be one place where the resonant frequency of the membrane matches the stimulus frequency and this place will show the maximum amount of vibration
By measuring vibration at particular points on the membrane for a range of stimulus frequencies we can plot the frequency response of each place on the membrane
The essential function of the basilar membrane is to act as a frequency analyser (a set of band-pass filters each responding to a different frequency region) resolving an input sound at the eardrum into its constituent frequencies
Basilar Membrane
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The peripheral auditory system is often modelled as a bank of bandpass filters (auditory filters) with overlapping passbands.
Typically modelled using a finite number of bandpass filters, equally spaced along the Basilar Membrane.
Basilar Membrane
The wave motion along the BM is governed by the mechanical properties of the membrane and hydrodynamic properties of the surrounding fluid (scalas)
It appears that each point of the BM moves independently (i.e. a point on the basilar membrane is assumed to have no direct mechanical coupling to neighboring points).
However, the neighboring points are coupled through the surrounding fluid.
The resonant frequency (𝑓𝑥 versus the distance from the stapes
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Reflections
What is the travelling wave on the basilar membrane? Explain with a single tone at the eardrum
When the stapes is oscillating at 70Hz, why is the travelling wave not attenuated until it reaches close to the apical end? Learning Activity 2
One well known model of auditory filters is the gammatone filter model where the impulse response of an auditory filter is given by:
𝒈 𝒏 𝒂 𝒏𝑻 𝑵𝟏𝒆𝟐𝝅𝒃 𝟐𝟒.𝟕𝟎.𝟏𝟎𝟖𝒇𝒑 𝒏𝑻𝒄𝒐𝒔 𝟐𝝅𝒇𝒑𝒏𝑻
where, 𝑓 is the centre frequency, 𝑇 is the sampling period, 𝑛 is the discrete time sample index, 𝑁 is the order of the filter (for e.g.,
𝑁 4) and 𝑎 is a constant chosen such that the filter gain at the centre frequency is 0dB; 𝑏 1.14;
Calculate the impulse response, 𝑔𝑛, for four auditory filters of your choice from the low, mid and high frequency regions of the basilar membrane in MATLAB. You will notice that the impulse responses have infinite duration, and thus each impulse response will need to be truncated to, say, 160 coefficients (i.e., 0 𝑛 160). Plot the impulse responses of all four filters in the same screen.
(a) What major differences do you see between the impulse responses you have plotted and why?
(b) Using these impulses responses, find the magnitude responses of all four filters and plot them (frequency vs magnitude in dB) on the same screen so you can compare them. (Are they similar to the plot on the right?)
(c) The gains at the centre frequencies of the filters may not be equal, choose the scaling factor 𝑎 for each filter (see equation g[n]) such that the gain of each filter is normalised to 0dB at the centre frequency.
(d) Approximately estimate the 3dB bandwidths of all four filters from your plots. Do they vary with the centre frequency? If so, how do you think they are related?
(e) Explain your understanding of constant-Q filters and constant-Bandwidth filters
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Learning Activity 2
Attached to the basilar membrane and running its entire length is the organ of corti containing some 30,000 sensory hair cells.
The hairs (cilia) of these cells stick up from the organ of corti and are in contact with overlying Tectorial Membrane
There are two types of sensory hair cells:
One row of inner hair cells, whose cilia float freely in the fluid-filled region called subtectorial space
Cross section
Three rows of outer hair cells whose cilia are attached to the tectorial membrane
Most of the afferent fibres (neurons which carry signals to the brain) come from inner hair cells,
The efferent fibres (which receive signals from the brain) go mainly to outer hair cells.
When the basilar membrane deflects, due to pressure wave in the cochlear fluid, the tectorial membrane move and shear which causes the hairs of the outer hair cells to bend and also cause the fluid flow in the subtectorial space.
This in turn triggers the inner hair cells to transmit nerve impulses along the afferent fibres and eventually to brain.
The motion of each part of the basilar membrane as detected by the inner hair cells is transmitted as neural description to the brain.
A simplified Diagram of a Human Auditory System
Organ of Corti
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Mechanical to Neural Transduction (Electro Chemical)
The mechanical displacement to electrical energy transduction process takes place in the inner hair cells
Bending of the inner hair cell cilia due to basilar membrane displacement produces a change in the overall resistance (reduces it) of the inner hair cell, thus modulating current flow through the hair cell.
The modulation being directly proportional to the degree of bending of the cilia and the bending of the cilia is one direction only; in effect a half wave rectification of the basilar membrane displacement takes place.
Bending of the cilia releases neurotransmitter which passes into synapses of one or more nerve cells which fire to indicate vibration
The amount of firing is thus related to the amount of vibration
Since the neurotransmitter is only released when the cilia are bent in one direction, firing tends to be in phase with basilar membrane movement
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Reflections
What is the tectorial membrane in the Organ of Corti?
How many sensory hair cells would you typically find along the entire length of the Organ of Corti?
What is the subtectorial space?
How many rows of inner hair cells and how many rows of outer hair cells are there?
Which type of hair cells have their cilia floating freely in the subtectorial space?
Is the following statement true? – “Bending of the inner hair cell increases the modulation current through the hair cell”
Why do you think the basilar membrane is tapered?
If the stapes is oscillating at 1kHz, do all sections of the basilar membrane vibrate? Estimate the position (from the basal end of the basilar membrane) where the displacement will be at its maximum.
Give a step-by-step explanation of the processing of a single tone (for e.g., a tone of 2 kHz) by the peripheral auditory system from sound into neural firing. Ensure you take into consideration the properties of the outer and middle ear, basilar membrane and neural transduction.
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ELEC3104
28 March 2018
Project Part B
Project Implementation
For this project, you should implement a digital model of the peripheral auditory system comprising of a model of the outer ear and the middle ear (from Part A) and a parallel filterbank model (comprising of auditory filters) of the cochlea (Part B).
The parallel filterbank model of the cochlea can be implemented as many band-pass auditory filters connected in parallel.
Models implemented in Part A
Models implemented in Part B
You should infer the necessary design parameters (such as filter responses) from this simulation
Project Implementation
You will be provided with a simulation of an approximate mechanical model of the displacement of the basilar membrane in the form of a MATLAB function. You can provide it with any input stimuli and the function will output the displacement as a function of time of various equal sized segments of the basilar membrane.
Input Signal
Basilar Membrane Displacement
BM_passive()
Simulates mechanical movement of Basilar Membrane
Inputs:
2. Sampling frequency (Scalar)
Output:
Project Implementation
You will be provided with a simulation of an approximate mechanical model of the displacement of the basilar membrane in the form of a MATLAB function. You can provide it with any input stimuli and the function will output the displacement as a function of time of various equal sized segments of the basilar membrane.
function BM_passive() 1. Input signal (Vector of T samples)
1. Basilar membrane displacement at each time instant (T time points) for each section of the basilar membrane in the simulation (N segments) arranged as a TxN matrix
Parallel Filterbank Model
Spectral component signals
Project Implementation
You should understand how the characteristics of the model are related to the functioning of the cochlea explained in part A (slides 1-15)
Validate (against the provided simulation) that all parts of your model operate as desired in terms of impulse responses and frequency responses for a variety of input signals.
Once your model is working, use inputs of your choice (music, speech, etc.) and observe the output and explain it in terms of the auditory system and its spectral analyses.
Input Audio Outer Ear Middle Ear
Signal
Model Model
NOTE: The equations provided in these slides (frequency as a function of position, gammatone filter response, etc.) are example models only and may not match the characteristics of the provided simulation. It is your responsibility to infer all necessary model parameters from the simulation
Reflection You should reflect on your project to see the following:
What is the function of the basilar membrane and how does it respond to various input stimuli?
What will happen if you include the outer and middle ear models at the input of the transmission line model of the cochlea in terms of hair cell output?
Can you see how the ear performs spectral analyses?
When the input has multiple frequencies and one of the tones is removed after a period of time, how and when would the response change in your filterbank model and in the mechanical model?
Project Assessment (30%)
In week 10/11 you will be required to make a 10 minute presentation (followed by 10mins of Q&A) to lab demonstrators explaining your implementation (based on a working demonstration and suitable analyses) as well as your understanding (based on your verbal answers to questions from the demonstrators – the questions may cover all topics in the course and not restricted to your specific project implementation). Your project mark will be awarded by the lab demonstrators based on this presentation. You must pass the project to pass the course.
Assessment items
Quality of presentation slide & clarity and correctness of oral presentation (5/30 marks)
Completion of project including results and analyses (9/30 marks) Demonstrate the digital model is completely functional as required
Neatness of code (4/30 marks)
Code is commented and easy to follow
Modular code, appropriate variable names, etc.
Correct and clear answers to questions (12/30 marks) Demonstrating in-depth understanding of all relevant concepts
Ability to explain all components of the project