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BUILT-IN MATHEMATICA SYMBOL
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 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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