Walsh Functions can be used to generate individual Fourier sine harmonics. The intent is that these waveforms are going to be used in the context of classic Subtractive Synthesizer, like a square wave, and will got through a low pass filter. The tones generated here are unfiltered and will be on the bright side. And you wouldn't want an 8x square wave to fry your tweeters. I found it to be more intuitive this way. The Weighted Sliders button attenuates each slider by a factor of N.
The sliders are "attenuverter" style, both positive and negative, with the zero at the center.Ĭlick on the keyboard to play a note, or below to stop the note. ("SAL(1)" through "SAL(8)" in the above top diagram.) I tried the cosine versions also, but found no advantage to having both. These are the first 8 sine Walsh Functions. You need to enable JavaScript to run this app.
#Fourier series bipolar square wave software#
This is a software simulation of a potential oscillator that delivers a set of 8 Walsh functions, and lets you mix them down. Well, we have an opportunity to check them out. What is their timbre like? Can we apply them in a musically expressive way? They're certainly easy enough to generate. But I am intrigued about the possibility of other musical applications of Walsh Functions. I'm not interested in digital approximations of perfectly working analog functions. I don't believe such a thing was ever commercialized. The writings at the time (Electronotes, etc.) were geared toward using Walsh Functions to digitally implement the classic oscillator waveforms. (The nomenclature is a little weird that's a side effect of the math.) The illustration on the right is from Jacoby (references) and shows sine and cosine versions of the first 8 Walsh functions. What are Walsh Functions? They're sort of like a Fourier Series with square waves. Back some time ago, the use of Walsh Functions was suggested for electronic music.
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