Walsh Transform Resynthesis Synth

(96 Votes)
1.0 (Updated 13 years ago)
June 04, 2006
Reaktor 5 or lower


This ensemble implements resynthesis of either static 32-element waveforms or a dynamic signal provided by a sampler module. Resynthesis is done by use of a Walsh function (or Hadamard function) basis function expansion.

32 Walsh functions are used
(actually the 1st function, which is constant, is ignored, so really only 31 functions are used).

32 element sampled waveforms from either a sampler module or a wavetable are transformed using the Walsh transform to give 32 coefficients. The coefficients are then optionally modified by applying a spectral tilt, which attenuates either the low "sequency" coefficients, or the high sequency coefficients. The Walsh functions can be divided into two sets, each 90 degrees out of phase from each other. The relative level of these components can be adjusted, which I call the phase adjustment. Finally the order of the coefficients can be reversed, where the highest sequency component is swapped with the lowest, the next highest with the next lowest and so forth. This provides a scrambling of the spectrum and is a good way to get new sounds.

The processed walsh transform coefficients are multipled bu the 32 outputs of a Walsh function generator and summed to provide the re-synthesized waveform. This waveform is then passed through a more or less standard synthesizer, with a 4th order lowpass filter, ADSR envelopes on the filter cutoff and amplitude, and an AR envelope on the pitch.

There are two amplitude envelopes. The first envelope is triggered by the MIDI note gate, while the triggering of the second envelope is delayed with respect to the first.

There are 3 LFOs which can be combined, through a 3-way morph, to provide modulation signals to the spectral tilt, phase, and filter cutoff.

If your computer can handle it you should use the highest possible sampling rate, to reduce the level of aliasing noise. Of course, this is a rather digital sounding ensemble and some people might think that a little more aliasing noise makes it sound better! You can turn off the scope to save a little bit on the CPU usage. Also, if you are using the sampler, keep the sampler update rate low for low CPU usage. Also, if you are using the sampler you can probably get away with using a low system sampling rate, since the level of aliasing noise in the sampler is quite high and will swamp any aliasing caused by other parts of the ensemble at low sampling rates.


Jonathan Canupp
4 years ago
Really impressive ensemble - it's really inspiring to see such a novel function, and the undoubtedly staggering amount of work you've invested in implementing it (the Hadamard-Walsh function). I've been slogging through trying to implement matrices in Reaktor and this is just exponentially beyond what I've managed to accomplish. Beyond the math, it's capable of some very useful and equally novel sounds! Many tips of hats to you!
Pedro Eustache
8 years ago
Fantastic potential in the 'old school' digital sonic realm... Thanks for a great upload!
James McNalley
9 years ago
Amazing synth with incredible sound. The UI is clean and easy to use. Pleanty of great presets. wXform sounds like no other synth!
Simon Jarvis
9 years ago
I like it...superb graphics and well worth looking into further.
greg simpson
11 years ago
Great upload.
sameer uddin
11 years ago
David Bowes
12 years ago
I didn't get your email either Mr. stringer....
gabriel mulzer
13 years ago
interesting, looks like a lot of work I wonder why you didn't include a live input, I can imagine some people might have a use for it if you find the time to post a pure w-h demo, I would be interested, and maybe some other people too
James Duffett-Smith
13 years ago
Looks gorgeous, and has a certain distinct texture all of its own. Great if you are into the robotic kinda thing. Which sometimes I am. So thanks for sharing!
James Clark
13 years ago
Hi Donovan, great minds think alike, I guess! I didn't get your email. You can use jj.clark@sympatico.ca
Donovan Stringer
13 years ago
Yet again, we upload on the same night..This is becoming an embarassment; people will think we're in love.. Not sure if you ever recieved it, but I tried to send you an email about a month ago. I assumed it never arrived or you weren't interested in speaking to me. Either way, congrats on another smashing success for the UL; this is a very beautifully designed instrument.. cheers, D