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Walsh transform - translation to russian
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![[[Fast Walsh–Hadamard transform]], a faster way to calculate the Walsh spectrum of (1, 0, 1, 0, 0, 1, 1, 0).](https://commons.wikimedia.org/wiki/Special:FilePath/1010 0110 Walsh spectrum (fast WHT).svg?width=200 "[[Fast Walsh–Hadamard transform]], a faster way to calculate the Walsh spectrum of (1, 0, 1, 0, 0, 1, 1, 0).")
.svg?width=200 "The original function can be expressed by means of its Walsh spectrum as an arithmetical polynomial.")
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Definition
Wikipedia
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The Hadamard transform (also known as the Walsh–Hadamard transform, Hadamard–Rademacher–Walsh transform, Walsh transform, or Walsh–Fourier transform) is an example of a generalized class of Fourier transforms. It performs an orthogonal, symmetric, involutive, linear operation on 2m real numbers (or complex, or hypercomplex numbers, although the Hadamard matrices themselves are purely real).
The Hadamard transform can be regarded as being built out of size-2 discrete Fourier transforms (DFTs), and is in fact equivalent to a multidimensional DFT of size 2 × 2 × ⋯ × 2 × 2. It decomposes an arbitrary input vector into a superposition of Walsh functions.
The transform is named for the French mathematician Jacques Hadamard (French: [adamaʁ]), the German-American mathematician Hans Rademacher, and the American mathematician Joseph L. Walsh.
