FourierSeries`
FourierSeries`

NInverseDTFourierTransform

NInverseDTFourierTransform[expr,ω,n]

gives a numerical approximation to the inverse discrete time Fourier transform of expr evaluated at the integer n, where expr is a periodic function of ω with period 1.

Details and Options

  • To use NInverseDTFourierTransform, you first need to load the Fourier Series Package using Needs["FourierSeries`"].
  • The numerical approximation to the inverse discrete time Fourier transform of expr is by default defined to be NIntegrate[expr nω,{ω,-π,π}].
  • Different choices for the definition of the inverse discrete time Fourier transform can be specified using the option FourierParameters.
  • With the setting FourierParameters->{a,b}, expr is assumed to have a period of , and the inverse discrete time Fourier transform computed by NInverseDTFourierTransform is NIntegrate[expr bnω,{ω,-,}].
  • The parameter b in the setting FourierParameters->{a,b} must be numeric.
  • In addition to the option FourierParameters, NInverseDTFourierTransform can also accept the options available to NIntegrate. These options are passed directly to NIntegrate.

Examples

Basic Examples  (1)

Numerical value for a sequence with a given discrete time Fourier transform:

Compare with the answer from symbolic evaluation: