This is documentation for Mathematica 6, which was
based on an earlier version of the Wolfram Language.
View current documentation (Version 11.2)

Fourier

Fourier[list]
finds the discrete Fourier transform of a list of complex numbers.
  • The discrete Fourier transform vs of a list ur of length n is by default defined to be .  »
  • Note that the zero frequency term appears at position 1 in the resulting list.
  • Other definitions are used in some scientific and technical fields.
  • Different choices of definitions can be specified using the option FourierParameters.
  • Some common choices for {a, b} are {0, 1} (default), {-1, 1} (data analysis), {1, -1} (signal processing).
  • The setting b=-1 effectively corresponds to conjugating both input and output lists.
  • To ensure a unique inverse discrete Fourier transform, b must be relatively prime to n.  »
  • The list of data supplied to Fourier 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.
New in 1 | Last modified in 4