[sdiy] Walsh Functions/EN S-008

Lanterman, Aaron D aaron.lanterman at ece.gatech.edu
Tue Oct 15 08:54:58 CEST 2019

> On Sep 14, 2017, at 9:25 PM, Bernard Arthur Hutchins Jr <bah13 at cornell.edu> wrote:
> 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 seminarwhere 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.  

I think it’s not just that sinusoids are solutions to 2nd-order differential equations — it’s that sinusoids are eigenfunctions of linear, time-invariant systems. Put a sinusoid in, you get a sinusoid out with a possibly different amplitude and phase, but the same frequency. Walsh functions, wavelets, etc. won’t operate the same way.

I make my students chant "Sinusoid in -> Sinusoid out."

Aaron Lanterman, Prof. of ECE, Georgia Tech
My blog on Education and Innovation: https://edupocalypsenow.wordpress.com
My blog on Electronics and Programming: https://lantertronics.blogspot.com

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