Finite Z transform of a list: Sum of a_k z^(-k-n) with optional starting index n
ListZTransform[list, z]
ListZTransform[list, z, k]
ListZTransform[list, {z1, z2, …}, {k1, k2, …}]
H[z_] = ListZTransform[{(1/5), (1/5), (1/5), (1/5), (1/5)}, z]
→ 1/5 + 1/(5*z^4) + 1/(5*z^3) + 1/(5*z^2) + 1/(5*z)ListZTransform[{a, b, c}, z]
→ a + c/z^2 + b/zListZTransform[{a, b, c}, z, -1]
→ b + c/z + a*z