] finds the discrete inverse Fourier transform of a list of complex numbers.
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.
The definition of the Fourier transform used is the one common in the physical sciences. The sign of the exponent must be reversed to obtain the definition common in electrical engineering.
The list of data need not have a length equal to a power of two.
The list given in InverseFourier[
] 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.
See the Mathematica book: Section 1.6.6, Section 3.8.3.
See also: Fourier.
Here is some data corresponding to a square pulse.
Here is the Fourier transform of the data. It involves complex numbers.
Here is the inverse Fourier transform.
After using Chop, this gives back exactly your original data.