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BUILT-IN MATHEMATICA SYMBOL
FourierTransform
FourierTransform[expr, t, 
]
gives the symbolic Fourier transform of expr.
FourierTransform[expr, {t1, t2, ...}, {1, 2, ...}]
gives the multidimensional Fourier transform of expr.
Details and Options
- 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
are 
(default; modern physics), 
(pure mathematics; systems engineering), 
(classical physics), and {0, -2Pi} (signal processing). - The following options can be given:
-
Assumptions $Assumptions assumptions to make about parameters FourierParameters {0,1} parameters to define the Fourier transform GenerateConditions False whether to generate answers that involve conditions on parameters - 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
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