DTFourierTransform

As of Version 7.0, DTFourierTransform has been renamed to FourierSequenceTransform and is part of the built-in Wolfram Language kernel.

DTFourierTransform[expr,n,ω]

gives the discrete time Fourier transform of expr as a function of ω, where expr is a function of n.

Details and Options

To use DTFourierTransform, you first need to load the Fourier Series Package using Needs["FourierSeries`"].
The discrete time Fourier transform of expr is by default defined to be expr ^2πω.
DTFourierTransform returns a periodic function of ω with default period 1.
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 DTFourierTransform is expr ^{2 πω}, a periodic function of ω with a default period of .

Use different definitions for calculating a discrete time Fourier transform:

Compare with the answer from a numerical approximation:

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