[sdiy] Walsh Functions/EN S-008
Bernard Arthur Hutchins Jr
bah13 at cornell.edu
Fri Sep 15 03:25:34 CEST 2017
It is somewhat of a mystery WHY, of the infinite number of possible complete orthogonal function sets, Fourier gets to be boss. Indeed, at a seminar where Sebastian von Horner was convincingly explaining his notion that there might well be a "universal music", if there be other civilizations in space, someone quipped "What if they are Walsh function guys". Perhaps it is just that Newton got to be boss, and sinusoids are solution to second-order differential equations? This is a philosophical question (thusly deflected) unlikely to have a simple answer.
Another philosophical question for engineers to duck is "Why is there a well defined zero of frequency (DC) but not of time?" Don sent me an attractive write up of alternatives to a standard square-wave Fourier Series. By coincidence, I am working on EN#230 on related ideas. We know from the sampling theorem that if it is acceptable to sample at times n*T, it is equivalent to sample at (n+1/2)*T or (n+1/pi)*T, etc. Only a fast enough rate matters. Time and frequency being dual variables, is it acceptable to compute Fourier Series coefficients not at k*fo but at (k+1/2)*fo ? Lots of pretty plots to study.
Bernie
________________________________
From: ijfritz at comcast.net <ijfritz at comcast.net>
Sent: Thursday, September 14, 2017 5:58 PM
To: Donald Tillman; Bernard Arthur Hutchins Jr
Cc: synth-diy at synth-diy.org
Subject: Re: [sdiy] Walsh Functions/EN S-008
Well, neither are transistors. :-)
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------ Original Message ------
From: Donald Tillman
To: Bernard Arthur Hutchins Jr
Cc: synth-diy at synth-diy.org
Sent: September 14, 2017 at 2:26 PM
Subject: Re: [sdiy] Walsh Functions/EN S-008
> On Sep 14, 2017, at 10:46 AM, Bernard Arthur Hutchins Jr <bah13 at cornell.edu> wrote:
>
> The simplest Walsh function is already a square wave, far from mellow. The rest that make up a complete orthogonal set all have pulse-like autocorrelation functions and accordingly have a similar buzz. No real variability in the mix. You have to WORK to get familiar waveshapes.
And Walsh functions are not found in nature.
-- Don
--
Donald Tillman, Palo Alto, California
http://www.till.com
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