Fourier transform

This article specifically discusses Fourier transformation of functions on the real line; for other kinds of Fourier transformation, see Fourier analysis and list of Fourier-related transforms. In mathematics, the Fourier transform, named in honor of French mathematician Joseph Fourier, is a certain linear operator that maps functions to other functions. Loosely speaking, the Fourier transform decomposes a function into a continuous spectrum of its frequency components, and the inverse transform synthesizes a function from its spectrum of frequency components. A useful analogy is the relationship between a set of notes in musical notation (the frequency components) and the sound of the musical chord represented by these notes (the function/signal itself).
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<mathematics> A technique for expressing a waveform as a weighted sum of sines and cosines.
Computers generally rely on the version known as discrete Fourier transform.
Named after J. B. Joseph Fourier (1768 -- 1830).
See also wavelet, discrete cosine transform.
(1997-03-9)

Fourier transform
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