Difference equations are often used to compute the output of a system from knowledge of the input. They are an important and widely used tool for representing the input-output relationship of linear time-invariant systems. In this lesson you will learn how the characteristics of the system are related to the coefficients in the difference equation. You will learn how stability, the nature of the system response to an input, and transient response time depend on the difference equation coefficients.

Understanding the relationship between difference equation coefficients and system characteristics will give you very useful insight for working with filters and other systems used in signal processing.