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Is there support for bilateral Z-transform in Mathematica, or a third-party package?

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1 Answer 1

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One of the nicest things about Mathematica is that one can often just implement the definitions as they are:

bilateralZTransform[c_, k_, z_, opts___] := Sum[c/z^k, {k, -∞, ∞}, opts]

Otherwise, one can exploit the relationship between GeneratingFunction[] and ZTransform[]:

bilateralZTransform[c_, k_, z_, opts___] :=
                    ZTransform[HeavisideTheta[k - 1] c, k, z, opts] +
                    GeneratingFunction[Function[k, c][-k], k, z, opts]
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