Exercise 1 a) Explain how the notion of a resonator can be useful in characteriz
ID: 168445 • Letter: E
Question
Exercise 1 a) Explain how the notion of a resonator can be useful in characterizing the functioning of the outer ear. Be sure to specify the input and output signals, and the units in which they would be measured. b) Describe the fundamental problem our middle ear solves for listening to very low level sounds and how it solves it. Use the word 'impedance' in your answer and describe what structures of the middle ear are involved in solving the problem. c) The function of the basilar membrane can be linked to that of a filter bank. understand cochlear function. ii) What properties would the filter bank need to have in order to best mimic the functioning of the inner ear?Explanation / Answer
1.The external ear plays the role of an acoustic antenna: the pinna (together with the head) diffracts and focuses sound waves, the concha and the ear canal act as a resonator.
Acoustically, the eardrum is the final part of the external ear, which thus functions as a tube open only at one end.
Both the sound pressure levels and the phase of the acoustic waves change whilst being propagated from the free field environment, via the external ear, to the eardrum. These changes vary with the frequency of the sound and for each direction of the acoustic waves in the horizontal and vertical planes. They correspond to the transfer function (TF) of the external ear.
Ear canal: input = sound at ear canal entrance; output = sound at tympanic membrane; both
measure in pascals
2. The middle ear must perform impedance matching. Because the cochlea is filled with fluid that naturally has a higher mass (density) than air we need a greater pressure input to move it otherwise the sound energy would be reflected (just as it is reflected off the surface of water). In order to push the sound energy into the ear we need to increase the pressure. This is mainly achieved by the surface area ratio of TM to the oval window (this lets you gather many light air particles to collective push on a smaller number of fluid particles). The bones of the ear also add a level action and there is a buckling contribution. All these combine to give a pressure increase necessary to move the heavy cochlear fluids.
3.A. Filter bank is a collection or set of band-pass filters whose centre frequency varies over some range As the basilar membrane (BM) does a kind of frequency analysis,
its function can be compared to a filter bank.
B. Each auditory nerve fibre responds to the acoustic world through a single bandpass filter. filter bank should: span 20 Hz-20 kHz have bandwidths increasing with increasing frequency) spaced on a quasi-logarithmic scale.
Be nonlinear (increase bandwidth and decrease gain with increasing level)
For extra study
A filter bank is an array of band-pass filters that separates the input signal into multiple components, each one carrying a single frequency sub-band of the original signal. One application of a filter bank is a graphic equalizer, which can attenuate the components differently and recombine them into a modified version of the original signal. The process of decomposition performed by the filter bank is called analysis (meaning analysis of the signal in terms of its components in each sub-band); the output of analysis is referred to as a subband signal with as many subbands as there are filters in the filter bank. The reconstruction process is called synthesis, meaning reconstitution of a complete signal resulting from the filtering process.
the cochleagram creates a time-frequency representation of the input signal. By mimicking the components of the outer and middle ear, the signal is broken up into different frequencies that are naturally selected by the cochlea and hair cells. Because of the frequency selectivity of the basilar membrane, a filter bank is used to model the membrane, with each filter associated with a specific point on the basilar membrane
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