AW: Walsh Function Primer

[Haible Juergen]

Thanks for the long description!

I know that walsh functions were the big deal in many EN issues,
at a time when "digital" was the new magic word.
*Everything* was suposed to be modelled with rectangular steps,
from VCO waveshapes to envelopes.
I have to admit that in retrospect (when I got these EN's many years
later) I haven't cared much for these Walsh functions. So maybe I
have missed something, but here are the reasons for a certain pejudice
of mine:

Don't we *have* (all too many) envelopes that are built from rectangular
steps, nowadays ? All these (bad) software envelopes in cheap
hybrid synthesizers are put together from rectangular steps.

The same for VCO waveforms. Unless you have a rather high resolution
(many, many rectangular "harmonics"), you always hear a certain hollow
character in your sounds. I think of the Korg Poly 800 (which also has
terrible
stairstep envelopes), or the "rectangular wave" drawbars on certain
organs
(maybe the SH-7 as well).

	>The quality of the final sound depends on how many Walsh
functions you 
	>     have available.  You could think of a Walsh synth as
mathematically 
	>     creating a set of sample points to create a waveform.
Obviously, the 
	>     more sample points you have, the finer the resolution and
the smoother 
	>     the sound will be.

Exactly. 

	>However, from a musical perspective I think Walsh functions are

>     > superior to sine waves.  With sine waves, you are literally
> starting 
>     > from the ground up when creating a sound.  Thus the result can
> sound a 
>     > bit dull, as you usually run out of functions for the higher 
>      >frequencies, making the sound "dull" like someone's turned the
> treble 
>      >down.
> 
And with rectangular base functions replace "dull" with "hollow".
Both side effects will decrease with increased number of base functions/
harmonics. Would be interesting to know if one method "converges" 
earlier than the other ...

JH.


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