Fourier
 Usage
• Fourier[list] finds the discrete Fourier transform of a list of complex numbers.
Notes
• The discrete Fourier transform  of a list  of length  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. • With the setting FourierParameters -> {a, b} the discrete Fourier transform computed by Fourier is  . • 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,  must be relatively prime to  . • 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 Version 1; modified in 4.
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