ListZTransform

gives the Z transform of list as a function of z.

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.

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Z transform of a constant vector:

Plot the Z transform on the unit circle:

Two-dimensional Z transform:

Z transform of a symbolic sequence:

Specify an offset:

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:

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