A method of analyzing and breaking down a given waveform into a set of simple waveforms, similar in concept to Fourier analysis. Where the Fourier transform breaks a waveform down into a set of sine waves of various frequencies, Walsh functions break down an arbitrary waveform into a set of pulse waves. The set of pulse waves that the analysis creates will differ in frequency, amplitude, and pulse width.
The theory of Walsh functions was developed in the mid-20th century by mathematician Joe Walsh, not related to the musician of the same name. Walsh functions have not seen many applications in electronic music to date (the Korg Poly-800 employed a very crude form to produce a triangle wave from a set of square waves), but are used extensively in signal analysis in radio.