BUILT-IN WOLFRAM LANGUAGE SYMBOL

InverseFourierTransform

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

InverseFourierTransform[expr,{ω1,ω2,},{t1,t2,}]
gives the multidimensional inverse Fourier transform of expr.

Details and OptionsDetails and Options

• 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), and {0,-2Pi} (signal processing).
• Assumptions and other options to Integrate can also be given in InverseFourierTransform. »
• InverseFourierTransform[expr,ω,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 ω. 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 .

ExamplesExamplesopen allclose all

Basic Examples  (2)Basic Examples  (2)

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TutorialsTutorials

Introduced in 1999
(4.0)