FourierTransform

Usage

• FourierTransform[expr, t, ] gives the symbolic Fourier transform of expr.
• FourierTransform[expr, {, , ... }, {, , ... }] gives the multidimensional Fourier transform of expr.

Notes

• 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 Section 1.5.12 and Section 3.5.12.

• New in Version 4.

Further Examples