NInverseFourierCosTransform
FourierSeries`
FourierSeries`
NInverseFourierCosTransform
NInverseFourierCosTransform[expr,ω,t]
gives a numerical approximation to the inverse Fourier cosine transform of expr evaluated at the numerical value t, where expr is a function of ω.
Details and Options
- To use NInverseFourierCosTransform, you first need to load the Fourier Series Package using Needs["FourierSeries`"].
- The numerical approximation to the inverse Fourier cosine transform of expr is by default defined to be
NIntegrate[expr Cos[ω t],{ω,0,∞}]. - Different choices for the definition of the inverse Fourier cosine transform can be specified using the option FourierParameters.
- With the setting FourierParameters->{a,b}, the inverse Fourier cosine transform computed by NInverseFourierCosTransform is 2
NIntegrate[expr Cos[b ω t],{ω,0,∞}]. - The parameter b in the setting FourierParameters->{a,b} must be numeric.
- In addition to the option FourierParameters, NInverseFourierCosTransform 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 cosine transform:
NInverseFourierCosTransform[E ^ (-6ω), ω, 1.4]Compare with the answer from symbolic evaluation:
InverseFourierCosTransform[E ^ (-6ω), ω, t]% /. {t -> 1.4}