FourierSeries`
FourierSeries`
NDTFourierTransform
NDTFourierTransform[expr,n,ω]
gives a numerical approximation to the discrete time Fourier transform of expr evaluated at the numerical value ω, where expr is a function of n.
Details and Options
- To use NDTFourierTransform, you first need to load the Fourier Series Package using Needs["FourierSeries`"].
- The numerical approximation to the discrete time Fourier transform of expr is by default defined to be NSum[expr -nω,{n,-∞,∞}].
- Different choices for the definition of the discrete time Fourier transform can be specified using the option FourierParameters.
- With the setting FourierParameters->{a,b}, the discrete time Fourier transform computed by NDTFourierTransform is
NSum[expr -bnω,{n,-∞,∞}]. - The parameter b in the setting FourierParameters->{a,b} must be numeric.
- In addition to the option FourierParameters, NDTFourierTransform can also accept the options available to NSum. These options are passed directly to NSum.
Examples
Basic Examples (1)
Different definitions for numerical approximation of a discrete time Fourier transform:
Compare with the answer from symbolic evaluation with FourierSequenceTransform: