[sdiy] Walsh Generators

[ASSI]

On Donnerstag, 17. März 2005 05:39, Glen wrote:
> Are Walsh generators viable candidates for additive synthesis in
> software, or are they primarily an idea that appeals to hardware
> implementations?

That depends a lot on the instruction set of the processor: Walsh 
synthesis could really fly on VLIW with predicates (notably, IA64 and 
quite a few embedded DSP have these). In other words, the appeal is 
much the same as it is in hardware: if you can make use of the more or 
less unlimited parallelism and simple scaling/sign-flipping operation 
of approximation with Walsh functions, then they are a really viable 
alternative to Fourier synthesis.

> Why don't we hear more about the technique? Is there some big
> drawback?

It is certainly much less known than any other technique, so you have to 
work your way through the requisite math mostly by yourself (at least 
Neil Johnson has typed in the original paper in LaTeX so we can read it 
properly formatted). I'm still chewing on some of these questions 
myself, for instance it should in principle be possible to derive the 
(Fourier) spectrum directly from the Walsh coefficients, but I have yet 
to find a way to do this more efficiently than doing it via the 
time-domain waveform.

>From a more practical standpoint it is much more difficult to ensure 
that a given Walsh approximation is band-limited to the extent this is 
possible - you will get the typical "staircase noise" especially in the 
bass range unless you go to extremely large coefficient tables. If 
you're trying to use interpolation, then you lose much or all of the 
advantages that Walsh approximation initially gave you. For audio 
signal synthesis you might very well take the artefacts (not unlike the 
ones that the first wavetable synthesizers produce) as character rather 
than as a nuisance.


Achim.
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