NFourierSinTransform
FourierSeries`
FourierSeries`
NFourierSinTransform
NFourierSinTransform[expr,t,ω]
gives a numerical approximation to the Fourier sine transform of expr evaluated at the numerical value ω, where expr is a function of n.
Details and Options
- To use NFourierSinTransform, you first need to load the Fourier Series Package using Needs["FourierSeries`"].
- The numerical approximation to the Fourier sine transform of expr is by default defined to be
NIntegrate[expr Sin[ω t],{t,0,∞}]. - Different choices for the definition of the Fourier cosine transform can be specified using the option FourierParameters.
- With the setting FourierParameters->{a,b}, the Fourier cosine transform computed by NFourierSinTransform is 2
NIntegrate[expr Sin[b ω t],{t,0,∞}]. - The parameter b in the setting FourierParameters->{a,b} must be numeric.
- In addition to the option FourierParameters, NFourierSinTransform can also accept the options available to NIntegrate. These options are passed directly to NIntegrate.
Examples
Basic Examples (1)
Needs["FourierSeries`"]Numerical approximation for a Fourier sine transform:
NFourierSinTransform[(t + 3) E ^ (-t), t, 0.9]Compare with the answer from symbolic evaluation:
FourierSinTransform[(t + 3) E ^ (-t), t, ω]% /. {ω -> 0.9}