NFourierTransform

NFourierTransform[expr,t,ω]

gives a numerical approximation to the Fourier transform of expr evaluated at the numerical value ω, where expr is a function of t.

更多信息和选项

To use NFourierTransform, you first need to load the Fourier Series Package using Needs["FourierSeries`"].
The numerical approximation to the Fourier transform of expr is by default defined to be NIntegrate[expr ^ωt,{t,-∞,∞}].
Different choices for the definition of the Fourier transform can be specified using the option FourierParameters.
With the setting FourierParameters->{a,b}, the Fourier transform computed by NFourierTransform is NIntegrate[expr ^bωt,{t,-∞,∞}].
The parameter b in the setting FourierParameters->{a,b} must be numeric.
In addition to the option FourierParameters, NFourierTransform can also accept the options available to NIntegrate. These options are passed directly to NIntegrate.

Wolfram Language code: Needs["FourierSeries`"]

Numerical Fourier transform for a box function:

Wolfram Language code: f[t_] := UnitStep[1 - t] UnitStep[t + 1]

Wolfram Language code: Plot[NFourierTransform[f[t], t, ω], {ω, -20, 20}, PlotRange -> All]

Compare with the answer from symbolic evaluation:

Wolfram Language code: NFourierTransform[f[t], t, 0.7]

Wolfram Language code: FourierTransform[f[t], t, ω]

Wolfram Language code: % /. {ω -> 0.7}

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