FourierSeries`
FourierSeries`

NInverseFourierSinTransform

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

  • To use NInverseFourierSinTransform, you first need to load the Fourier Series Package using Needs["FourierSeries`"].
  • The numerical approximation to the inverse Fourier sine transform of expr is by default defined to be NIntegrate[expr Sin[ω t],{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 NInverseFourierSinTransform is 2NIntegrate[expr Sin[b ω t],{ω,0,}].
  • The parameter b in the setting FourierParameters->{a,b} must be numeric.
  • In addition to the option FourierParameters, NInverseFourierSinTransform can also accept the options available to NIntegrate. These options are passed directly to NIntegrate.

Examples

Basic Examples  (1)

Numerical approximation for an inverse Fourier sine transform:

Compare with the answer from symbolic evaluation: