This is documentation for Mathematica 6, which was
based on an earlier version of the Wolfram Language.

# 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 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.
Find a discrete Fourier transform:
 Out[1]=

Find a power spectrum:
 Out[1]=
 Scope   (4)
 Options   (2)
 Applications   (9)