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<p>Many moons ago I made a Walsh generator out of a CPLD. It quickly
became obvious that the coefficients bore no intuitive relation to
the resulting waveform. Add to that the requirement of bipolar
VCAs (apologies to Mr. Hutchens) and it quickly became a mess.
Even with tricks like digital inverters and diode VCAs, its still
a mess.<br>
</p>
<p><br>
</p>
<p>Bottom line: I think additive synthesis makes way more sense. <br>
</p>
<p><br>
</p>
<p>--Timbo<br>
</p>
<br>
<div class="moz-cite-prefix">On 9/14/2017 10:46 AM, Bernard Arthur
Hutchins Jr wrote:<br>
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<p><font size="2" face="arial"><span style="font-size: 14pt;"> Tom
said:</span></font></p>
<p><font size="2" face="arial"><br style="">
</font></p>
<hr style="font-family: "Times New Roman";"
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<font size="-1" face="Courier New"><span style="font-size:
14pt;">" Isn’t the trouble with Walsh function synthesis
that each coefficient controls a complex waveform with a
whole fistful of harmonics? While it’s possible to carefully
mix Walsh functions to get smooth-sounding waveforms by
cancelling out higher harmonics, any minor tweak to the
coefficient values is going to introduce large abrupt edges
and significant high frequencies. That makes waveform
morphing pretty much bound to go from A via buzziness to B.</span></font>
<p><font face="Courier New"><span style="font-size: 18.6667px;"><br>
</span><span style="font-size: 14pt;">Basing things on sine
waves is so much simpler in many ways, despite Walsh
functions being much easier to generate.</span><br>
<br>
<span style="font-size: 14pt;">Tom "</span></font></p>
<p><font face="Courier New"><span style="font-size: 18.6667px;"><br>
</span></font></p>
<p><font face="Courier New"><span style="font-size: 18.6667px;">Exactly
Tom. 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. </span></font></p>
<p><font face="Courier New"><span style="font-size: 18.6667px;"><br>
</span></font></p>
<p><font face="Courier New"><span style="font-size: 18.6667px;">At
one point, (early 70's)
</span><span style="font-size: 18.6667px;">W</span><span
style="font-size: 18.6667px;">alsh functions were going to
save the world. Lots of papers/conferences. My copies of
all these and much more was lost over the years at Cornell
- or somewhere in unopened boxes. It was true that they
WERE easier to generate. (Compare a board with a few
logic IC's</span><span style="font-size: 18.6667px;"> with
Hal Chamberlin's heroic Fourier series hardware of the
time). Microelectronics soon eclipsed the hardware
advantage. </span></font></p>
<p><font face="Courier New"><span style="font-size: 18.6667px;"><br>
</span></font></p>
<p><font face="Courier New"><span style="font-size: 18.6667px;">As
for Electronotes supplement </span><span style="font-size:
18.6667px;">S-008, a copy may surface. I seem to recall
it was a student report (one of which was me!). Anything
worth while is likely in the AES paper on the EN site.
Problem with promising to post it is I don't actually
have a PDF or hard copy (only a 221M ZIP which I am unable
to download)</span><span style="font-size: 18.6667px;">.
Then, if I did post it, people would ask about S-001
through S-006 and S-009 through S-013. Sometimes things
are discontinued to the advantage of all! So the S-008
issue is quite analogous to the larger issue of posting
old Electronotes. NOT easy and no serious offers of help.</span></font></p>
<p><font face="Courier New"><span style="font-size: 18.6667px;"><br>
</span></font></p>
<p><font face="Courier New"><span style="font-size: 18.6667px;">Bernie</span></font></p>
<p><font face="Courier New"><span style="font-size: 18.6667px;"><br>
</span></font></p>
<p><font face="Courier New"><span style="font-size: 18.6667px;"> </span><br>
</font><br>
</p>
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</blockquote>
<br>
<pre class="moz-signature" cols="72">--
--Tim Ressel
Circuit Abbey
<a class="moz-txt-link-abbreviated" href="mailto:timr@circuitabbey.com">timr@circuitabbey.com</a></pre>
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