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Function Repository Resource:

NInverseFourierTransform

Source Notebook

Find a numerical approximation for the inverse Fourier transform

Contributed by: Wolfram Research

ResourceFunction["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

The numerical approximation to the inverse Fourier transform of expr is by default defined to be .
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 ResourceFunction["NInverseFourierTransform"] is .
The parameter b in the setting FourierParameters{a,b} must be numeric.
In addition to the option FourierParameters, ResourceFunction["NInverseFourierTransform"] can also accept the options available to NIntegrate. These options are passed directly to NIntegrate.

Examples

Basic Examples

Numerical inverse Fourier transform for a polynomial-exponential function:

In[1]:=
ResourceFunction[
 "NInverseFourierTransform"][(\[Omega]^2 + 3 \[Omega] + 5)*
  E^(-\[Omega]^2 + 1), \[Omega], 3.7]
Out[1]=

Compare with the answer from symbolic evaluation:

In[2]:=
InverseFourierTransform[(\[Omega]^2 + 3 \[Omega] + 5)*
  E^(-\[Omega]^2 + 1), \[Omega], t]
Out[2]=
In[3]:=
% /. {t -> 3.7}
Out[3]=

Requirements

Wolfram Language 11.3 (March 2018) or above

Resource History

See Also

License Information