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.
FourierSeries — truncated complex Fourier series to any order
FourierCoefficient — n coefficient in a Fourier series
FourierSequenceTransform — discrete-time Fourier transform (DTFT)
InverseFourierSequenceTransform — inverse transform (IDTFT)
FourierParameters — select between Fourier analysis conventions