[sdiy] Walsh bank, was: Re: [sdiy] Micro as a Linear to Exponential converter?

[Tom Wiltshire]

On 15 Aug 2009, at 09:36, cheater cheater wrote:

> Ah, cool!
> Can those generate interesting waveforms without scaling (so, ak=+/-1
> for all k)?

Yes. It'll limit you a bit, but you'll still be able to produce a  
good variety of waveforms.

> How many terms do you need to get useful results?

Lots. You're building up waveforms out of 'square-wave' functions, so  
things will have crunchy digital edges until the number of functions  
gets pretty large. Yes, I *am* being deliberately vague, sorry. But  
it's partly a question of taste. Analogously, how many sine waves do  
you need to make an arbitrary waveform with standard fourier  
analysis? I've used 64 in my oscillator design, as a compromise  
between quality and feasibility. I'd say you need at least that many  
for Walsh synthesis, and probably more, since you're adding functions  
with sharp edges and that will make the results more crunchy. Double  
or quadruple this would be better.

The problem I see with Walsh synthesis is that it has the worst  
features of additive synthesis (How do we control all those  
coefficients effectively?) and it has added difficulties in that a  
given coefficient doesn't relate directly to a particular harmonic.  
This means you can't easily say "I'd like a little more sixth  
harmonic" and turn up a control for it - some maths has to be done to  
work out which coefficients need to alter and by how much. This makes  
it more obscure.

T.