[sdiy] Walsh Functions/EN S-008

Bernard Arthur Hutchins Jr bah13 at cornell.edu
Thu Sep 14 19:46:05 CEST 2017

 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.


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