[sdiy] Walsh Functions/EN S-008

Tim Ressel timr at circuitabbey.com
Thu Sep 14 20:28:02 CEST 2017

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.

Bottom line: I think additive synthesis makes way more sense.


On 9/14/2017 10:46 AM, Bernard Arthur Hutchins Jr wrote:
>  Tom said:
> ------------------------------------------------------------------------
> " 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.
> Basing things on sine waves is so much simpler in many ways, despite 
> Walsh functions being much easier to generate.
> Tom "
> 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.
> At one point, (early 70's) Walsh 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 with Hal Chamberlin's heroic Fourier 
> series hardware of the time).  Microelectronics soon eclipsed the 
> hardware advantage.
> As for Electronotes supplement 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).  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.
> Bernie
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--Tim Ressel
Circuit Abbey
timr at circuitabbey.com

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