For a discrete-time sequence x[n], the z-transform is defined as:
where Z{*} is the z-transform operator, transforming what appears between the brackets, with z being a complex variable. The square bracket notation used on the x[n] simply emphasizes the discrete nature of the sequence x.
The region of convergence (ROC) for a z-transform is defined as the values of z for which the summation X(z) is bounded.
 | Properties of the z-transform |
| Some common z-transform pairs |
| The inverse z-transform |
| The relationship between the z-transform and the Fourier transform |
Much of this discussion is derived from Oppenheim & Schafer, Discrete-Time Signal Processing, Prentice-Hall, 1989
