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, involutional, linear operation on real numbers (or complex 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 . It decomposes an arbitrary input vector into a superposition of Walsh functions.
The transform is named for the French mathematician Jacques Hadamard, the German-American mathematician Hans Rademacher, and the American mathematician Joseph Leonard Walsh.
Read more about Hadamard Transform: Definition, Quantum Computing Applications, Computational Complexity, Other Applications
Famous quotes containing the word transform:
“It is necessary to turn political crisis into armed crisis by performing violent actions that will force those in power to transform the military situation into a political situation. That will alienate the masses, who, from then on, will revolt against the army and the police and blame them for this state of things.”
—Carlos Marighella (d. 1969)