Wolfram Language & System 11.0 (2016)|Legacy Documentation

This is documentation for an earlier version of the Wolfram Language.View current documentation (Version 11.2)

Fourier Analysis

The Wolfram Language provides broad coverage of both numeric and symbolic Fourier analysis, supporting all standard forms of Fourier transforms on data, functions, and sequences, in any number of dimensions, and with uniform coverage of multiple conventions.


Fourier Transforms

FourierTransform, InverseFourierTransform complex Fourier transforms (FT, IFT)

FourierSinTransform  ▪  InverseFourierSinTransform

FourierCosTransform  ▪  InverseFourierCosTransform

Fourier Series

FourierSeries truncated complex Fourier series to any order

FourierSinSeries  ▪  FourierCosSeries  ▪  FourierTrigSeries

FourierCoefficient n^(th) coefficient in a Fourier series

FourierSinCoefficient  ▪  FourierCosCoefficient

Fourier Sequence Transforms

FourierSequenceTransform discrete-time Fourier transform (DTFT)

InverseFourierSequenceTransform inverse transform (IDTFT)

Discrete Fourier Transforms

Fourier, InverseFourier discrete transforms of lists of data in any dimension (DFT)

FourierDST, FourierDCT discrete sine, cosine transforms (DST, DCT, types I-IV)

FourierParameters select between Fourier analysis conventions


Convolve  ▪  DiscreteConvolve  ▪  ListConvolve

Related Transforms

LaplaceTransform  ▪  ZTransform

Related Functions

DiracDelta  ▪  HeavisideTheta  ▪  DiscreteDelta  ▪  KroneckerDelta

SquareWave  ▪  TriangleWave  ▪  SawtoothWave

Wavelet Analysis

DiscreteWaveletTransform  ▪  ContinuousWaveletTransform  ▪  ...