Signals and Systems using MATLAB

Chapter 9

The Z-Transform

I was born not knowing and have had only a little time to change that here and there.

Richard P. Feynman, (1918–1988) Professor and Nobel Prize physicist

9.1 Introduction

Just as with the Laplace transform for continuous-time signals and systems, the Z-transform provides a way to represent discrete-time signals and systems, and to process discrete-time signals.

Although the Z-transform can be related to the Laplace transform, the relation is operationally not very useful. However, it can be used to show that the complex z-plane is in a polar form where the radius is a damping factor and the angle corresponds to the discrete frequency ω in radians. Thus, the unit circle in the z-plane is analogous to the jΩ axis in the ...