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Re: Gammatone analysis/synthesis

At 3:59 PM 9/26/96, Joe Pompei wrote:
>        Has anyone here experimented with resynthesizing audio signals after
>they have been decomposed with gammatone filters?
>        The gammatone 'transform' is in no way orthogonal or easily invertible
>(like wavelets), but perhaps by using discrete frequencies, experimenting with
>the filter length, or using other tricks resynthesis can be done with minimal
>error.  Anyone have experience with this?  All of the gammatone references I
>have explore analysis only.

Resynthesis from non-orthogonal filterbank analysis, even with nonlinear
operations like rectification thrown in, is possible using techniques
like "convex projection" and a little bit of iterating.

Shihab Shamma and his colleagues have published on Auditory Model
inversion, as have Malcolm Slaney, Dan Naar, and I.  But none of used
gammatones in those papers.  See for example:

Malcolm Slaney, Daniel Naar, and Richard F. Lyon, "Auditory Model
Inversion for Sound Separation," Proceedings IEEE International
Conference on Acoustics, Speech, and Signal Processing, Adelaide,
April 1994.

The answer for you will depend very much on what you mean by
gammatone analysis.  Do you mean you have all the filtered signals,
or just their magnitudes at some lower frame rate?  If the latter,
then a careful iterated convex projection is required, and may not
come out as good as you would like.  But if the former, then just
add them up, with a phase correction that you can get most
conveniently by filtering them backward (time-reversed) through
the same filters.  It won't be perfect, but darn close if you get
the channel gains right.

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