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Re: temporal dynamics of cochlear filters

Hi Sandeep and list,

This is a good question in my opinion. I don't believe that there is a 
simple answer with respect to psychoacoustic filters.

The history of modern cochlear filters is long! Let us start with the 
invention of the gammatone filer bank [1]. You will notice that these 
filters were based on stochastic ensembles of neural recordings.
Subsequent developments generated the 'roex' filters which address 
filter change with signal level. It was later published that the optimum 
auditory filter is the gammachirp [2]. [2] also lists references for the 
roex filters.

You will notice that there is a very limited discussion on the speed of 
filter shape change. More recent references may well address your 
question, however I am not aware of these references. If you are intent 
on using psychoacoustics to answer your question, then you may well 
decide to conduct an analysis on the gammachirp impulse response.

If you decide that psychoacoustic models are limited in explaining the 
answer to your question, you may begin to look at the physiology. We are 
pretty sure now that the adaptation, compression and amplification of 
the inner ear is a function of non-linear mechanics AND the cochlear 
amplifier [3]. A very strong argument is for the high level (saturating) 
effects being due to the hair cells [4]. Whilst the reference [4] is 
with respect to two-tone suppression, it is thought that two-tone 
suppression is an expression of the mechanical or CA's nonlinearity.

So the physiology would suggest that changes in the state of the hair 
cells will determine the changes in the apparent filter shape. A recent 
review into the cochlear amplifier [5] suggests that the outer hair 
cells of the Organ of Corti are under the control of both the 
stereocillia at the apex of the cell and the efferent neurons at the 
base of the cell. For this reason, it is most likely that two time 
coefficients are of interest. One time constant being that of the 
mechanics and the mechanical response, the other being the time constant 
of the neural effects and the neural response.
The most popular models of the CA at the moment are based on augmenting 
the passive travelling wave. Unfortunately these models do not have a 
complete physiological basis and often resort to mathematical equations 
to close the gap [6]. Their suggestion is however that the mechanism of 
the cochlear amplifier is local to the cochlear.

If you consider the approach of the non-linear mechanics theory then [7] 
is a good start for looking into non-linear mechanical time frames.

Finally, you could have a look at the response nature of an active 
cochlear [8]. The experiments in [8] however are not conducted with 
sinusoids, but clicks. Our knowledge of the active cochlear is that its 
response will be strongly influenced by the nature of the signal which 
is put into it.

I hope that this helps you with a few directions and references.

The cochlear amplifier e-mail list:

[1] @INPROCEEDINGS{Johannesma:1972,
  author = {Johannesma, P.I.M.},
  title = {The pre-response stimulus ensemble of neurons in the cochlear 
  booktitle = {Symposium on Hearing Theory},
  year = {1972},
  pages = {58-69},
  publisher = {IPO, Eindhoven, Holland}

[2] ARTICLE{Irino:1997,
  author = {Irino, T. and Patterson, R.D.},
  title = {A time-domain, level-dependent auditory filter: the 
  journal = {Journal of the Acoustical Society of America},
  year = {1997},
  volume = {101},
  pages = {412-419},
  number = {1}

[3] @article{allen:1992b,
  title={{Micromechanical models of the cochlea}},
  author={Allen, J.B. and Neely, S.},
  journal={Physics Today},

[4] @ARTICLE{geisler:1990,
  author = {Geisler, C.D. and Yates, G.K. and Patuzzi, R.B. and 
Johnstone, B.M.},
  title = {{Saturation of outer hair cell receptor currents causes 
  journal = {Hearing Research},
  year = {1990},
  volume = {44},
  pages = {241--56},
  number = {2-3}

[5] @article{oghalai2004caa,
  title={{The cochlear amplifier: augmentation of the traveling wave 
within the inner ear.}},
  author={Oghalai, J.S.},
  journal={Current Opinion in Otolaryngology \& Head and Neck Surgery},

[6] The following book lists alot of references
  title = {The Cochlea},
  publisher = {Springer Verlag},
  year = {1996},
  editor = {Dallos, P. and Popper, A.N. and Fay, R.R.}

[7] @article{allen2001ncs,
  title={{Nonlinear cochlear signal processing}},
  author={Allen, J.B.},
  journal={Physiology of the Ear},

[8] @article{recio1998bmr,
  title={{Basilar-membrane responses to clicks at the base of the 
chinchilla cochlea}},
  author={Recio, A. and Rich, N.C. and Narayan, S.S. and Ruggero, M.A.},
  journal={The Journal of the Acoustical Society of America},

On Thu, Jun 12, 2008 at 06:07:59PM -0400, Sandeep Phatak wrote:
> Hi,
>     I have a question regarding the non-linearity of cochlear filters
> and I will appreciate if someone could point me to the relevant
> reference(s). My question is - when a tone burst (at say, 75 dB SPL)
> with sharp onset is presented to a normal cochlea, how long does it
> take for narrowly tuned cochlear filter (with CF at the tone
> frequency) to go to the widely-tuned, high-threshold state?
> Sandeep