NInverseFourierSinTransform
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 2
NIntegrate[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)
Needs["FourierSeries`"]Numerical approximation for an inverse Fourier sine transform:
NInverseFourierSinTransform[(ω ^ 2 + 1) E ^ (-ω), ω, 2.9]Compare with the answer from symbolic evaluation:
InverseFourierSinTransform[(ω ^ 2 + 1) E ^ (-ω), ω, t]% /. {t -> 2.9}