This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

# InverseFourierTransform

 InverseFourierTransformgives the symbolic inverse Fourier transform of expr. InverseFourierTransformgives 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.
• Some common choices for are (default; modern physics), (pure mathematics; systems engineering), (classical physics), and {0, -2Pi} (signal processing).
• InverseFourierTransform 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.
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 Scope   (4)
Elementary functions:
Special functions:
Piecewise functions and distributions:
Multidimensional inverse Fourier transform:
 Options   (3)
The inverse Fourier transform of BesselJ is a piecewise function:
Default modern physics convention:
Convention for pure mathematics and systems engineering:
Convention for classical physics:
Convention for signal processing:
Use GenerateConditions->True to get parameter conditions for when a result is valid:
InverseFourierTransform and FourierTransform are mutual inverses:
InverseFourierTransform and InverseFourierCosTransform are equal for even functions:
InverseFourierTransform and InverseFourierSinTransform differ by for odd functions:
The result from an inverse Fourier transform may not have the same form as the original:
The InverseFourierTransform of is a convolution of box functions:
New in 4