NFourierCosTransform
FourierSeries`
FourierSeries`
NFourierCosTransform
NFourierCosTransform[expr,t,ω]
gives a numerical approximation to the Fourier cosine transform of expr evaluated at the numerical value ω, where expr is a function of n.
Details and Options
- To use NFourierCosTransform, you first need to load the Fourier Series Package using Needs["FourierSeries`"].
- The numerical approximation to the Fourier cosine transform of expr is by default defined to be
NIntegrate[expr Cos[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 NFourierCosTransform is 2
NIntegrate[expr Cos[b ω t],{t,0,∞}]. - The parameter b in the setting FourierParameters->{a,b} must be numeric.
- In addition to the option FourierParameters, NFourierCosTransform 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 cosine transform:
NFourierCosTransform[E ^ (-7 t), t, 0.4]Compare with the answer from symbolic evaluation:
FourierCosTransform[E ^ (-7t), t, ω]% /. {ω -> 0.4}