Re: Wavelet discussion

["Richard F. Lyon" <DickLyon@xxxxxxx>]

Jont Allen <jba@RESEARCH.ATT.COM> wrote:

> There is a little bit of the Emperor's new clothes syndrome
> about wavelets I'm afraid. If I'm wrong, I would like to hear
> about it.

I pretty much agree with Jont here.  As Ludger Solbach has responded,
wavelets offer some nice mathematical properties, but they do not
have much advantage for understanding the basilar membrane.  They
are of interest in hearing because compared to Fourier transforms,
they are "less awful" as a way to analyze and represent sound, since
constant-Q is a better approximation to cochlear bandwidths than
constant-BW is.

The IEEE Trans. on Info. Theory had a special issue on wavelets
(1993?) in which Shihab Shamma and his colleagues (Wang, Yang, and
Shamma if I recall correctly) presented a model of BM processing
with linear wavelet filtering followed by nonlinear processing.
They have had a more recent followup paper to explain the good
behaviors of the model better.  Sorry I don't have the refs handy,
as my office is all in boxes this week.

The main reasons to NOT use a wavelet formulation for the basilar
membrane are:
1) wavelets are inherently constant-Q, but the BM is between
constant-Q (near the base, or high frequencies) and constant-BW
(near the apex, or low frequencies).
2) wavelets are inherently linear, but BM filtering is strongly
nonlinear--compressive and adaptive.

Jont also points out that wavelet users largely ignore frequency
response.  This is true, but non inherent.

Dick Lyon, formerly <lyon@apple.com>