InverseFourier

Usage

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

Notes

• 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.

• New in Version 1; modified in 4.