High Quality Content by WIKIPEDIA articles! In mathematical analysis, the set of Walsh functions form an orthogonal basis of the square-integrable functions on the unit interval. The functions take the values -1 and 1 only, on sub-intervals defined by dyadic fractions. They are useful in electronics, and other engineering applications. The orthogonal Walsh functions are used to perform the Hadamard transform, which is very similar to the way the orthogonal sinusoids are used to perform the Fourier transform. The Walsh functions are related to the Haar functions; both form a complete orthogonal system. The Haar function system may on the one hand be preferable because of its wavelet properties (e.g. localization), on the other hand the Walsh functions are bounded (in fact of modulus 1 everywhere).

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