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Fourier transform

In mathematics, the Fourier transform (FT) is an integral transform that takes a function as input and outputs another function that describes the extent to which various frequencies are present in the original function. The output of the transform is a complex valued function of frequency. The term Fourier transform refers to both the mathematical…

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Overview

Definition

Background

Units

Properties

Complex domain

Fourier transform on Euclidean space

Fourier transform on function spaces

Generalizations

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Example

Applications

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Computation methods

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Fourier transform

Nodes291
Edges290
Triples351
Avg. degree1.99
Density0.006873
Components1

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Fourier transform

Top relations

see also · 25
Fourier transform → Analog, Change, Class, Computation, Decomposition, Deligne, Discrete, Discrete Fourier, Especially, Fourier, Fourier-related, Function, Integral, Lipson, Mapping, Mathematical, Mukai, NGC, Nonlocal, Periodicity
related to On other Lp · 16
Fourier transform → For, Fourier, Further, Hausdorff, However, Hölder, In, L1, L2, Lp, Lq, Riesz, Rn, The Fourier, Thorin, Young
related to Restriction problems · 16
Fourier transform → As, But, Consider, ER, For, Fourier, In, It, L2, Lp, One, Rn, Stein, The, The Fourier, Tomas
related to Fourier–Stieltjes transform on measurable spaces · 14
Fourier transform → Bochner's, Borel, Fourier, Fourier-Stieltjes, If, Lebesgue, Radon, Riemann, Riemann-Stieltjes, Rn, Stated, Stieltjes, That, The Fourier
related to Units · 12
Fourier transform → For, Fourier, Greek, If, In, Linear, See, That, The, Therefore, These, This
related to Fourier transform on Euclidean space · 11
Fourier transform → All, Alternatively, As, For, Fourier, Lebesgue, Parseval's, Plancherel's, Riemann, The Fourier, When
related to Gelfand transform · 11
Fourier transform → Banach, Gelfand, Given, Haar, Hausdorff, In, It, L1, Pontryagin, The Fourier, With
related to Lebesgue integrable functions · 11
Fourier transform → Eq, Fourier, Furthermore, Here, However, If, In, Lebesgue, Riemann, The, The Fourier
related to Locally compact abelian groups · 11
Fourier transform → For, Fourier, Haar, Hausdorff, If, L1, Lebesgue, Pontryagin, The Fourier, The Riemann, With
related to Quantum mechanics · 11
Fourier transform → Both, For, Fourier, Heisenberg, In, Nevertheless, The, The Fourier, Therefore, Thus, To

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Important terminology

fourier transform displaystyle function functions widehat xi pi frequency int infty integral mathbb right integrable left also one time group

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Fourier transformis aautomorphism of the space0.90text
Fourier transformis aDirac comb function whose teeth are multiplied by the Fourier series coefficients.Sampling the Fourier transformThe Fourier transform of an integrable function f0.90text
Fourier transformis aDirac comb function whose teeth are multiplied by the Fourier series coefficients0.90text
Fourier transformis alinear transform that has eigenfunctions obeying0.90text
Fourier transformis aunitary transform when using the right conventions0.90text
Fourier transformis aGaussian function with variance σ0.90text
Fourier transformis aautomorphism of the Schwartz space and0.90text
Fourier transformis aconstant function0.90text
particle physicsinstance ofIn some contexts0.80text
the same symbol finstance ofIn some contexts0.80text
Matlabinstance ofthis provides a transform for a continuum of frequency values.Many computer algebra systems0.80text
Mathematica that are capable of symbolic integration are capable of computing Fourier transforms symbolically. httpsinstance ofthis provides a transform for a continuum of frequency values.Many computer algebra systems0.80text

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