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

FourierTransform

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

FourierTransform[expr, , , ... , , , ... ] gives the multidimensional Fourier transform of expr.

The Fourier transform of a function is by default defined to be .

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 Fourier transform computed by FourierTransform 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 FourierTransform.

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

In TraditionalForm, FourierTransform is output using .

See The Mathematica Book: Section 1.5.11 and Section 3.5.11.