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
Details and Options
- ListFourierSequenceTransform gives the discrete-time Fourier transform (DTFT) of a numeric array, typically used to obtain the frequency response of an FIR filter.
- By default, the one-dimensional discrete-time Fourier transform of a list
of length 
is computed as 
. - ListFourierSequenceTransform[list,ω] is equivalent to ListFourierSequenceTransform[list,ω,0].
- ListFourierSequenceTransform takes FourierParameters option. Common settings for FourierParameters include:
-
{1,1} 
default settings {1,2Pi} 
period 1 {a,b} 
general setting - ListFourierSequenceTransform[list,ω,k] effectively computes FourierSequenceTransform[f[r],r,ω] for a sequence f with f[r-1+k]=list[[r]] for 1<=r<=Length[list] and f[r]=0 otherwise.
Examples
open all close allBasic Examples (2)
Scope (1)
Options (1)
Applications (1)
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:
Text
Wolfram Research (2012), ListFourierSequenceTransform, Wolfram Language function, https://reference.wolfram.com/language/ref/ListFourierSequenceTransform.html.
CMS
Wolfram Language. 2012. "ListFourierSequenceTransform." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/ListFourierSequenceTransform.html.
APA
Wolfram Language. (2012). ListFourierSequenceTransform. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/ListFourierSequenceTransform.html