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Function Repository Resource:

NInverseFourierSinTransform

Source Notebook

Find a numerical approximation for an inverse Fourier sine transform

Contributed by: Wolfram Research

ResourceFunction["NInverseFourierSinTransform"][expr,ω,t]

gives a numerical approximation to the inverse Fourier sine 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 sine transform of expr is by default defined to be NIntegrate[expr Sin [ωt],{ω,0,}].
Different choices for the definition of the inverse Fourier sine transform can be specified using the option FourierParameters.
With the setting FourierParameters{a,b}, the inverse Fourier sine transform computed by ResourceFunction["NInverseFourierSinTransform"] is NIntegrate[expr Sin [bωt],{ω,0,}].
The parameter b in the setting FourierParameters{a,b} must be numeric.
In addition to the option FourierParameters, ResourceFunction["NInverseFourierSinTransform"] can also accept the options available to NIntegrate. These options are passed directly to NIntegrate.

Examples

Basic Examples

Numerical approximation for an inverse Fourier sine transform:

In[1]:=
ResourceFunction[
 "NInverseFourierSinTransform"][(\[Omega]^2 + 1) E^(-\[Omega]), \[Omega], 2.9]
Out[1]=

Compare with the answer from symbolic evaluation:

In[2]:=
InverseFourierSinTransform[(\[Omega]^2 + 1) E^(-\[Omega]), \[Omega],
  t]
Out[2]=
In[3]:=
% /. {t -> 2.9}
Out[3]=

Requirements

Wolfram Language 11.3 (March 2018) or above

Resource History

See Also

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