InverseFourier

• The inverse Fourier transform u_r of a list v_s of length n 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 b=-1 effectively corresponds to conjugating both input and output lists.

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

• 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.