fwth.pd
The walsh-Hadamard transform is similar to fourier transform but works with square waves instead of sinewaves, which I find very interesting. I discovered it in Curtis Road's fantastic book "The Computer Music Tutorial" and since then got obsessed with it.
One big advantage of the Fast Walsh Hadamard Transform, is that it's much faster to compute than FFT since it only works with real numbers.

So I made this patch to demonstrate the idea with filtering. The core of it is based on a C code I found here: https://github.com/bvssvni/fwht/blob/master/fwht.c

This is just proof of concept. I'd love to make it real time but don't quite know how. Anybody?
I think this deserves a pair external that could be used like [rfft~] and [rifft~].
The C code for the algorithm is actually quite simple. I just don't know how to do all the wrapping.

@allister Are there any reference materials for Walsh synthesis other than the Roads' book?

@jancsika
for the theorem itself you there are good ressources here and there for example:
discrete walsh hadamard transform on Mathworks.com
Wikipedia page

I didn't find much on sound specific usage except for this old paper hutchins_paper_1.PDF from Hutchins in... 1975. He is cited in Roads book. Very interesting

@jancsika Take a look at this one:
hutchins_paper_2.PDF

Would be interesting to revisit the Walsh transform. I wrote code for it some 45 years ago, on punched cards by golly. At that time it was attractive because of needing less computing power.I recall contacting someone who was a guru for signal processing at the time (name lost in background noise) who advised it wouldn't be of much interest for music applications.

@paulspignon Wow that’s crazy ! What were you working on if I may ask ?

About music applications, do you know what the guy meant?
Seems to me you can acheive a lot of the same stuff as fft, but with different sounding artifacts ? That could be interesting.
Also, since you can acheive convolution, it could greatly improve performances of say partitionned convolution algorithm I don’t know

Anyway, I really hope we can prove this Signal Processing Guru wrong!