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<span style="font-size: 14pt;">It is somewhat of a mystery WHY, of the </span><span style="font-size: 18.6667px;">infinite</span><span style="font-size: 14pt;"> number of possible complete orthogonal function sets, Fourier gets to be boss. Indeed, at a seminar
</span><span style="font-size: 18.6667px;">where</span><span style="font-size: 14pt;"> </span><span style="font-size: 18.6667px;">Sebastian</span><span style="font-size: 14pt;"> von Horner was convincingly explaining his notion that there might well be a "</span><span style="font-size: 18.6667px;">universal</span><span style="font-size: 14pt;"> </span><span style="font-size: 18.6667px;">music</span><span style="font-size: 14pt;">",
if there be other </span><span style="font-size: 18.6667px;">civilizations</span><span style="font-size: 14pt;"> 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 </span><span style="font-size: 18.6667px;">question (thusly deflected)</span><span style="font-size: 14pt;"> unlikely to have a simple answer. </span>
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<div><span style="font-size: 18.6667px;">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.</span></div>
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<div><span style="font-size: 18.6667px;">Bernie<br>
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<div id="divRplyFwdMsg" dir="ltr"><font face="Calibri, sans-serif" color="#000000" style="font-size:11pt"><b>From:</b> ijfritz@comcast.net <ijfritz@comcast.net><br>
<b>Sent:</b> Thursday, September 14, 2017 5:58 PM<br>
<b>To:</b> Donald Tillman; Bernard Arthur Hutchins Jr<br>
<b>Cc:</b> synth-diy@synth-diy.org<br>
<b>Subject:</b> Re: [sdiy] Walsh Functions/EN S-008</font>
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<div><font face="Helvetica">Well, neither are transistors. :-)<br>
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Sent from XFINITY Connect Mobile App<br>
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------ Original Message ------<br>
<br>
From: Donald Tillman<br>
To: Bernard Arthur Hutchins Jr<br>
Cc: synth-diy@synth-diy.org<br>
Sent: September 14, 2017 at 2:26 PM<br>
Subject: Re: [sdiy] Walsh Functions/EN S-008<br>
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<br>
> On Sep 14, 2017, at 10:46 AM, Bernard Arthur Hutchins Jr <bah13@cornell.edu> wrote:<br>
> <br>
> 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.<br>
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And Walsh functions are not found in nature.<br>
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-- Don<br>
--<br>
Donald Tillman, Palo Alto, California<br>
http://www.till.com<br>
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