Walsh Transforms

[neil.johnson at camcon.co.uk]

Cripes!  Interest in Walsh functions gains momentum!!!!

In answer to Sean's email, a few words about the Walsh transform.

Basically, the Walsh transform (WT) is a tool very similar to the Fourier
transform (FT).  You can do the same sort of things with the WT that you can do
with the FT: analysis, synthesis, filtering, etc etc.  However, and this is a
big however, the WT is _much_ easier to compute than the FT.

Why?  Because Walsh functions (WF) are binary-valued and real.  All WFs look
like digital signals with the values -1 and +1.  So integration of a signal with
a WF can be done with adds and subtracts -  which can either be done with lots
of adds and negates if you use 2's complement maths, or directly with op-amps.

Result: no multiplication, no trig functions, no complex values, both analysis
and synthesis can be done in realtime directly in hardware.

Regarding music synthesis and large quantities of data: sure, there will be lots
of data.  You don't get to seriously play around with sound with just one "knob"
that does everything.  And as Tony has shown, the "data" can be CVs, allowing
for LOTS of fun in the privacy of your own studio.

For other information, check out my website
(http://members.xoom.com/Neil_Johnson) and look in the Interests section.

Neil
-----
+======================================================+
|     Neil Johnson  BEng(Hons) MSc CEng MIEE MIEEE     |
|         http://members.xoom.com/Neil_Johnson         |
|"I can hardly speak for myself, let alone my employer"|
+======================================================+