NDTFourierTransform
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)
Needs["FourierSeries`"]Different definitions for numerical approximation of a discrete time Fourier transform:
NDTFourierTransform[1 / (3n + 5) ^ 2, n, 0.7]NDTFourierTransform[1 / (3n + 5) ^ 2, n, 0.7, FourierParameters -> {1, -2π}]Compare with the answer from symbolic evaluation with FourierSequenceTransform:
NDTFourierTransform[1 / (3n + 5) ^ 2, n, 0.7]FourierSequenceTransform[1 / (3n + 5) ^ 2, n, ω]% /. {ω -> 0.7}