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.
FourierTransform,
InverseFourierTransform — complex Fourier transforms (FT, IFT)
FourierSeries — truncated complex Fourier series to any order
FourierCoefficient — n
coefficient in a Fourier series
Fourier Sequence Transforms
FourierSequenceTransform — discrete-time Fourier transform (DTFT)
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
