Subject: Re: Gammatone analysis/synthesis From: "Richard F. Lyon" <lyon(at)APPLE.COM> Date: Thu, 26 Sep 1996 17:27:01 -0700At 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. -=-=-=-=-=-=-=-=-=- mailto:lyon(at)research.apple.com -=-=-=-=-=-=-=-=-=-=-=- Dick Lyon Distinguished Scientist Apple Computer 301-3M Apple Research Labs One Infinite Loop phone: (408) 974-4245 Cupertino CA 95014 fax: (408) 974-8414 -=-=-=-=-=-=-=- http://www.research.apple.com/personal/lyon/ -=-=-=-=-=-=- & Visiting Associate, Caltech Computation and Neural Systems Program -=-=-=-=-=-=-=-=-=- http://www.pcmp.caltech.edu/~dick/ -=-=-=-=-=-=-=-=-=-