ListFourierSequenceTransform

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

• ListFourierSequenceTransform[list, ω, k] places the first element of list at integer time k on the infinite time axis.
• ListFourierSequenceTransform[list, {ω1, ω2, ...}, {k1, k2, ...}] gives the multidimensional discrete-time Fourier transform.

Examples

Compute the DTFT of a sequence:

ListFourierSequenceTransform[{1, 2, 3, 4}, ω]

Evaluate at a specific frequency:

ListFourierSequenceTransform[{1, 1, 1, 1}, ω] /. ω -> Pi/4

Please visit the official Wolfram Language Reference for more details.