FourierSeries`

NInverseFourierTransform

NInverseFourierTransform[expr,ω,t]

gives a numerical approximation to the inverse Fourier transform of expr evaluated at the numerical value t, where expr is a function of ω.

Details and Options

To use NInverseFourierTransform, you first need to load the Fourier Series Package using Needs["FourierSeries`"].
The numerical approximation to the inverse Fourier transform of expr is by default defined to be NIntegrate[expr ^-ωt,{ω,-∞,∞}].
Different choices for the definition of the inverse Fourier transform can be specified using the option FourierParameters.
With the setting FourierParameters->{a,b}, the inverse Fourier transform computed by NInverseFourierTransform is NIntegrate[expr ^-bωt,{ω,-∞,∞}].
The parameter b in the setting FourierParameters->{a,b} must be numeric.
In addition to the option FourierParameters, NInverseFourierTransform can also accept the options available to NIntegrate. These options are passed directly to NIntegrate.

Numerical inverse Fourier transform for a polynomial-exponential function:

Compare with the answer from symbolic evaluation:

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