NInverseFourierTransform
FourierSeries`
FourierSeries`
NInverseFourierTransform
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
- To use NInverseFourierTransform, you first need to load the Fourier Series Package using Needs["FourierSeries`"].
- The numerical approximation to the inverse Fourier transform of expr is by default defined to be
NIntegrate[expr -ωt,{ω,-∞,∞}]. - 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 NInverseFourierTransform is
NIntegrate[expr -bωt,{ω,-∞,∞}]. - The parameter b in the setting FourierParameters->{a,b} must be numeric.
- In addition to the option FourierParameters, NInverseFourierTransform can also accept the options available to NIntegrate. These options are passed directly to NIntegrate.
Examples
Basic Examples (1)
Needs["FourierSeries`"]Numerical inverse Fourier transform for a polynomial-exponential function:
NInverseFourierTransform[(ω ^ 2 + 3ω + 5) * E ^ (-ω ^ 2 + 1), ω, 3.7]Compare with the answer from symbolic evaluation:
InverseFourierTransform[(ω ^ 2 + 3ω + 5) * E ^ (-ω ^ 2 + 1), ω, t]% /. {t -> 3.7}