Z-transform, like the Laplace transform, is an indispensable mathematical

tool for the design, analysis and monitoring of systems. The z-transform is

the discrete-time counter-part of the Laplace transform and a generalization

of the Fourier transform of a sampled signal. Like Laplace transform the z-

transform allows insight into the transient behavior, the steady state

behavior, and the stability of discrete-time systems. A working knowledge

of the z-transform is essential to the study of digital filters and systems.