BUILT-IN MATHEMATICA SYMBOL

# InverseFourier

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

InverseFourier[list, {p1, p2, ...}]
returns the specified positions of the discrete inverse Fourier transform.

## Details and OptionsDetails and Options

• 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 are (default), (data analysis), (signal processing).
• The setting effectively corresponds to conjugating both input and output lists.
• To ensure a unique discrete Fourier transform, Abs[b] 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.
• InverseFourier[list, {p1, p2, ...}] is equivalent to Extract[InverseFourier[list, {p1, p2, ...}] but may require less time and memory.
• If the elements of list are exact numbers, InverseFourier begins by applying N to them.

## ExamplesExamplesopen allclose all

### Basic Examples (2)Basic Examples (2)

Inverse Fourier transform of a real list:

 Out[1]=

Inverse Fourier transform of a complex list:

 Out[1]=