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  • Fourier[ list ] finds the discrete Fourier transform of a list of complex numbers.
  • The Fourier transform of a list of length is defined to be .
  • Note that the zero frequency term appears at position 1 in the resulting list.
  • The definition of the Fourier transform used is the one common in the physical sciences. The sign of the exponent must be reversed to obtain the definition common in electrical engineering.
  • The list of data need not have a length equal to a power of two.
  • The list given in Fourier[ list ] can be nested to represent an array of data in any number of dimensions.
  • The array of data must be rectangular.
  • If the elements of list are exact numbers, Fourier begins by applying N to them.
  • See the Mathematica book: Section 1.6.6Section 3.8.3.
  • See also Implementation NotesA.9.44.25MainBookLinkOldButtonDataA.9.44.25.
  • See also: InverseFourier, Fit.