Walsh Transforms (was Re: Sliders galore)

[Sean Costello]

Hi all:

OK, I'll bite: What, exactly, are Walsh transforms? More importantly,
how useful are they to synth-DIY, or synthesis in general? I have a
somewhat primitive understanding, that they do Fourier-type things with
square waves. How controllable are they? Are there easy transforms that
produce useful sonic results, or is it like FFT-based techniques, in
that the amount of data needed to control the synthesis is enormous?
>From working with Csound, I have found that phase vocoder techniques
generate about 10 times as much data as a straight sample of the sound
at 44.1 kHz (!). I have come up with some useful synthesis techniques
using the phase vocoder (as well as some unique ideas I hope to flesh
out soon - I will be taking a class in the fall that will cover some
advanced phase vocoder techniques), but the sheer amount of data
generated turns me off - not very elegant, compared to the granular
techniques or Hilbert-based techniques that can generate similar
results. 

Can Walsh transforms be used in a useful form of synthesis, with easy
control parameters? Can they be easily used to generate such niceties as
constant-Q analysis/resynthesis of signals (which is difficult with
FFT-based techniques)? Could a hardware
analysis/modification/resynthesis engine be created, for useful
modifications of external signals, such as pitch shifting, frequency
warping, and so on? There are lots of cool FFT-based techniques detailed
in Trevor Wishart's "Audible Design" that involve altering the time base
and/or frequency of individual FFT "bins" in nonlinear ways, for
blurring of sounds, nonlinear alteration of the spectrum, and so on -
could Walsh techniques be used for this?

Thanks,

Sean Costello

P.S. Tony: The TB-3030 PC boards arrived today, and look BEAUTIFUL.