ListZTransform
ListZTransform[list,z]
gives the Z transform of list as a function of z.
ListZTransform[list,z,k]
places the first element of list at integer time k on the infinite time axis.
ListZTransform[list,{z1,z2,…},{k1,k2,…}]
gives the multidimensional Z transform.
Details
- The one-dimensional Z transform of a list of length is given by .
- ListZTransform[list,z] is equivalent to ListZTransform[list,z,0].
- ListZTransform[list,…] effectively computes the ZTransform of a sequence given by list.
- ListZTransform[list,z,k] effectively computes ZTransform[f[r],r,z] for a sequence f with f[r-1+k]=list[[r]] for 1<=r<=Length[list] and f[r]=0 otherwise.
Examples
open allclose allBasic Examples (2)
Properties & Relations (3)
ListZTransform of a list of numbers is equal to the ZTransform of a sum of shifted unit samples:
Inverse of the ListZTransform:
ListZTransform evaluated on a unit circle gives the Fourier transform of the list:
Text
Wolfram Research (2012), ListZTransform, Wolfram Language function, https://reference.wolfram.com/language/ref/ListZTransform.html.
CMS
Wolfram Language. 2012. "ListZTransform." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/ListZTransform.html.
APA
Wolfram Language. (2012). ListZTransform. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/ListZTransform.html