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

[Scott Nordlund]

> 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.

In my (brief) experimentation with Walsh functions (I just hacked 
together a simple patch in Pd), I didn't really find a lot to get 
excited about. I only got endless buzzy, uninteresting waveforms with
no intuitive relationship between the coefficients and the resulting
waveform or sound.  I'd say you'd be better off defining the values of 
a 32 step waveform directly (like an analog sequencer clocked at a high
high rate).  It's still an orthogonal set, and still capable of 
generating any arbitrary waveform or spectrum (limited by the number of
steps), but here there is at least a one-to-one correspondence between 
the coefficients and the resulting waveform.

Incidentally, while contemplating the obscure Beilfuss synthesizer
(and reading the patents), it occurred to me that analog voltages and 
multiplexers (such as you'd find in an analog sequencer) can be used 
a sort of "ROM" that supports an infinite number of simultaneous 
reads.   So you can (relatively) easily have a number of oscillators 
generating the same waveform (or with some low-level fiddling, 
different portions of the same waveform).  In some cases, this could 
be considerably simpler than direct digital synthesis, plus it's also
not subject to aliasing, though it still has a sort of Rube Goldberg 
feel to it.



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