# 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

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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: