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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.
Reference
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
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
Related Functions
DiracDelta ▪ HeavisideTheta ▪ DiscreteDelta ▪ KroneckerDelta
SquareWave ▪ TriangleWave ▪ SawtoothWave
