gives the discrete-time Fourier transform (DTFT) of a list as a function of the parameter ω.


places the first element of list at integer time k on the infinite time axis.


gives the multidimensional discrete-time Fourier transform

Details and Options


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Basic Examples  (2)

Discrete-time Fourier transform of a constant vector:

Two-dimensional DTFT:

Applications  (1)

Create a lowpass filter:

Visualize the frequency response:

Apply to a noisy signal:

Properties & Relations  (4)

Discrete-time Fourier transform of a numeric list is equal to the Fourier sequence transform of a sum of shifted unit samples:

Inverse of a discrete-time Fourier transform of a list:

Fourier of a length- list returns samples of the ListFourierSequenceTransform at frequencies that are multiples of :

ListFourierSequenceTransform is equivalent to computing ListZTransform on the unit circle:

Introduced in 2012