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

Examples

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Basic Examples  (2)

Z transform of a constant vector:

Plot the Z transform on the unit circle:

Two-dimensional Z transform:

Scope  (1)

Z transform of a symbolic sequence:

Specify an offset:

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:

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.

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

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: 26-July-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: 26-July-2025 ]}