This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.
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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.
Fourier Transforms
FourierTransform, InverseFourierTransform complex Fourier transforms (FT, IFT)
Fourier Series
FourierSeries truncated complex Fourier series to any order
FourierCoefficient n coefficient in a Fourier series
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

Related Transforms
Related Functions