[sdiy] Walsh Generators

[René Schmitz]

Glen wrote:

> Okay then, show me how you can input 16 higher-resolution values into
> Neil's Tcl Walsh Synthesizer, and end up with a saw wave having more than
> 16 discrete steps.  :)

Maybe that was a bit unclear...

Say after 16 steps you would change the 16 parameters, you could end up 
with a longer waveform that can have arbitrary shape. The finest 
amplitude step is only depending on the resolution of the multiplicative 
factors. Say you do this 16 times, you end up with 256 steps, and 16 * 
16 walsh coefficients (indexed by time and order of walsh function). You 
could of course do a transform of the length 256 directly, but still you 
have 256 coefficients.

And you could indeed just modulate W(0) at a rate of 16 times the 
clocking rate of the walsh generator, and you would merely use it as a 
DA converter...

Of course this applet doesn't allow you to do that.

The point I was trying to make is that the length of the transform 
doesn't impose a limit to the amplitude resolution. In the case of the 
modulated W(0) that is easy to see. You can move the line anywhere 
between -1 and +1, without steps. (Other than those implied by screen 
resolution :-P)

So there is no relation per se between the length of the transform and 
the "equivalent" resolution of a DA.

The implied assumption seems to be that you loop this tiny 16 step 
waveform, but this is infact a special case, "drawbars".

Walsh has the property that for N samples output, you need N Walsh 
coefficients, so there is no reduction in parameter space, there is no 
reduction in information, and as such I personally consider walsh 
synthesis as useful as drawing waveforms directly. :-)

Cheers,
  René

-- 
uzs159 at uni-bonn.de
http://www.uni-bonn.de/~uzs159