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Re: synthesizing with wavelet packets

Date1998-09-22 07:32
FromPedro Batista
SubjectRe: synthesizing with wavelet packets
Re wrote,

>Note that the Numerical Recipes code as it stands performs
>octave-band analysis, that is, it will yield nine bands
>of wavelet coefs in the range Nyquist freq - 40 Hz (if sr=44 kHz).
>This is good for applications like denoising and compression,
>but not generally for the kind of spectral manipulation that
>computer musicians might desire - I think that would require at
>least three bands per octave (and preferably variable bandwidth).

Hum, I'm not quite sure I can follow... How do you come up to the "nine 
bands
of wavelet coefs in the range Nyquist freq - 40 Hz (if sr=44 kHz)" ? I'm not 
by the slightest chance an expert on this stuff, you know
As I see it, each successive aplication of the filters analyses data an 
octave lower, and thought that was all there is to it, but I've never really 
studyed the nr code, nor implemented it yet

>I also found exactly one article about wavelets and music.
>It's by Peter Meijer (author of the Java image/sound applet).

There are more articles around. Not too digestable, some of them, but there 
is wickerhauser's original article, as well as some followups, even a GA 
approach to find best wave-packets for synthesis (get'em all from 
www.mathsoft.com/wavelets.html). And who doesnt need more data compression 
and denoising in their music? :)
No, really, I think theres promissing ground for the future, altho I agree 
some has to be perfected first, if there is to be a real useful musical 
usage

>His conclusion is that variable-
>windowed Fourier transforms might be at least as good as wavelets.
>(Intuitively, I'd think that it seems good to have co/sines as
>the base, because we know what to do with them, and what happens
>when we manipulate them.)

I'm not defending one thing over the other. Its all a matter of what you 
have, or dont. If there is a better method, I'm sure someone will use it, 
but so far I have no knowledge of it. And as you say, the great advantage of 
wavelets, over sines and cosines, is their compat localization in freq AND 
in space

>Note that most articles you find on the net are either very general
>or require a bit of maths.

yep, I could use a math degree, or at least a couple o'brains more