[sdiy] Walsh Generators

[harrybissell]

inline... <snipp'd>

Glen wrote:

> I just visited Neil Johnson's web site and tried out his online Tcl Walsh
> Synthesizer. I entered the parameters he gave to yield a saw waveform, and
> it indeed yields a wave that resembles a sawtooth, but it has been
> quantized into 16 discrete steps. This would be akin to the quality of a
> 4-bit DAC, wouldn't it?

yes.

> How many Walsh functions would need to be summed together, in order to get
> a saw waveform that reaches a quality level comparable to a 16-bit DAC?
> Would it actually take 65,536 Walsh Functions? Would 24-bit audio quality
> need 16,777,216 functions?

The thing about the walsh functions is not the number of them you need... but
how easy it is to create large numbers of them.  You would use a very high
freqency
clock, and all digital means. Try that with sine waves.  Modulating the levels
is easy
as well... try THAT with sine waves.

Distortion of a sine wave is very obvious, much easier to make a walsh
funtion.

The problem imho, and why the walsh functions (and additive Fourier synthesis)
is
not popular is because of user interface.  There are no good 'global'
parameters to
move and make dramatic changes in the sound.  If "FM" programming is
daunting...
walsh programming is daunting on steriods  :^P

There were a number of experiments with using sliders to 'draw' waveforms
directly...
in effect sequencers run at audio rates.  A number of the waves sound exactly
the same  (picture all the ways to draw a square wave... they are just phase
shifted :^).
Moving one or more sliders does not affect the harmonic content in an easily
understood or controlled manner.  Thats why they are not used today.

Be the guy who figures out the walsh 'global' operator set and you will be
rich AND
famous :^P

H^) harry