This is documentation for Mathematica 4, which was
based on an earlier version of the Wolfram Language.

InverseFourier

InverseFourier[list] finds the discrete inverse Fourier transform of a list of complex numbers.

The inverse Fourier transform of a list of length is defined to be .

Note that the zero frequency term must appear at position 1 in the input 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 reversing both input and output lists.

To ensure a unique discrete Fourier transform, must be relatively prime to .

The list of data need not have a length equal to a power of two.

The list given in InverseFourier[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, InverseFourier begins by applying N to them.

See The Mathematica Book: Section 1.6.6 and Section 3.8.3.