This is documentation for Mathematica 4, which was
based on an earlier version of the Wolfram Language.

InverseFourierTransform

InverseFourierTransform[expr, , t] gives the symbolic inverse Fourier transform of expr.

InverseFourierTransform[expr, , , ... , , , ... ] gives the multidimensional inverse Fourier transform of expr.

The inverse Fourier transform of a function is by default defined as .

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 inverse Fourier transform computed by InverseFourierTransform is .

Some common choices for a, b are {0, 1} (default; modern physics), {1, -1} (pure mathematics; systems engineering), {-1, 1} (classical physics), {0, -2 Pi} (signal processing).

Assumptions and other options to Integrate can also be given in InverseFourierTransform.

InverseFourierTransform[expr, , t] yields an expression depending on the continuous variable t that represents the symbolic inverse Fourier transform of expr with respect to the continuous variable . InverseFourier[list] takes a finite list of numbers as input, and yields as output a list representing the discrete inverse Fourier transform of the input.

In TraditionalForm, InverseFourierTransform is output using .

See The Mathematica Book: Section 1.5.11 and Section 3.5.11.