Unilateral Z-transform

Summary

The unilateral Z-transform of a sequence $(x_n)$ uses only its terms with $n \ge 0$: $X(z) = \sum_{n \ge 0} x_n z^{-n}$. It is the form of the Z-transform used for initial value problems. A forward shift of the sequence brings in its first terms, so initial values enter the transformed equation by themselves. It plays for difference equations the part that the one-sided Laplace transform plays for differential equations.