Fourier transform

The Fourier transform, named after Joseph Fourier, is an integral transform that re-expresses a function in terms of sinusoidal basis functions, i.e. as a sum or integral of sinusoidal functions multiplied by some coefficients ("amplitudes"). There are many closely-related variations of this transform, summarized below, depending upon the type of function being transformed. See also: List of Fourier-related transforms.

Variants of the Fourier transform

Continuous Fourier transform

Most often, the unqualified term "Fourier transform" refers to the continuous Fourier transform, representing any square-integrable function f(t) as a sum of complex exponentials with angular frequencies ω and complex amplitudes F(ω):

Related Topics:
Continuous Fourier transform - Integrable - Complex

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f(t) = mathcal{F}^{-1}(F)(t)

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