This lesson will introduce you to another very useful description for LTI systems: the system function and poles and zeros. You will learn that the system function is a generalization of the frequency response description when the input is an exponentially damped complex sinusoid. Also, the system function for systems described by difference equations is a ratio of polynomials. The roots of the denominator and numerator polynomials are called the poles and zeros of the system.
The system function is a powerful tool for the signal-processing practitioner. It is used to study the conditions under which a system is causal, stable, and can be inverted. It is also used in design of filters. The pole and zero locations provide a lot of insight into system characteristics, such as frequency response.