Fourier transform

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.

“Fourier transform” is strongly related to:

Even and odd functions Dirac delta function Fractional Fourier transform Parseval's theorem Unitary operator Heaviside step function Linear canonical transformation Transform (mathematics) Plancherel theorem Rectangular function Convolution theorem Sinc function Eigenfunction Chebyshev polynomials Gaussian function Distribution (mathematics) Inner product space Laplace transform Fourier analysis Convolution Hilbert space Amplitude Hertz Second Eulers formula in complex analysis Sine and cosine transforms Integrability Self-dual Arg (mathematics) Triangular function Schwartz space Riesz-Thorin theorem DFT matrix Anticausal system Continuous linear extension Analog signal processing Hölder condition Phase angle Short-time Fourier transform Degeneracy (mathematics)

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