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.
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