Fourier Analysis

Mathematica 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.

ReferenceReference

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

Convolutions

Convolve ▪ DiscreteConvolve ▪ ListConvolve

Related Transforms

LaplaceTransform ▪ ZTransform

Related Functions

DiracDelta ▪ HeavisideTheta ▪ DiscreteDelta ▪ KroneckerDelta

SquareWave ▪ TriangleWave ▪ SawtoothWave

Wavelet Analysis

DiscreteWaveletTransform ▪ ContinuousWaveletTransform ▪ ...

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