ListZTransform
✖
ListZTransform
places the first element of list at integer time k on the infinite time axis.
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)Summary of the most common use cases
Z transform of a constant vector:

https://wolfram.com/xid/0en0n3gj2-hxcway

Plot the Z transform on the unit circle:

https://wolfram.com/xid/0en0n3gj2-0fsrfv


https://wolfram.com/xid/0en0n3gj2-d1f7mr


https://wolfram.com/xid/0en0n3gj2-j1c4z9

Scope (1)Survey of the scope of standard use cases
Properties & Relations (3)Properties of the function, and connections to other functions
ListZTransform of a list of numbers is equal to the ZTransform of a sum of shifted unit samples:

https://wolfram.com/xid/0en0n3gj2-8b6of

https://wolfram.com/xid/0en0n3gj2-dekd7k

Inverse of the ListZTransform:

https://wolfram.com/xid/0en0n3gj2-5b8f8c


https://wolfram.com/xid/0en0n3gj2-83e38

ListZTransform evaluated on a unit circle gives the Fourier transform of the list:

https://wolfram.com/xid/0en0n3gj2-os227


https://wolfram.com/xid/0en0n3gj2-bss4q6

Wolfram Research (2012), ListZTransform, Wolfram Language function, https://reference.wolfram.com/language/ref/ListZTransform.html.
Text
Wolfram Research (2012), ListZTransform, Wolfram Language function, https://reference.wolfram.com/language/ref/ListZTransform.html.
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.
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
Wolfram Language. (2012). ListZTransform. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/ListZTransform.html
BibTeX
@misc{reference.wolfram_2025_listztransform, author="Wolfram Research", title="{ListZTransform}", year="2012", howpublished="\url{https://reference.wolfram.com/language/ref/ListZTransform.html}", note=[Accessed: 05-June-2025
]}
BibLaTeX
@online{reference.wolfram_2025_listztransform, organization={Wolfram Research}, title={ListZTransform}, year={2012}, url={https://reference.wolfram.com/language/ref/ListZTransform.html}, note=[Accessed: 05-June-2025
]}