Poles and Zeros of the $z$-Transform

In this lesson you will learn how to find the poles and zeros of a rational $z$-transform. Poles and zeros are important because they provide a very insightful characterization of systems described by linear constant coefficient difference equations. Such systems are widely used to implement filters and as mathematical models for signals. The poles and zeros indicate the stability and causality properties of a system as well as give insight into the frequency and impulse response, topics studied in subsequent lessons.