Difference equations are one of the few descriptions for linear time-invariant (LTI) systems that can incorporate the effects of stored energy - that is, describe systems which are not at rest when the input is applied. In this lesson you will learn how the output of a LTI system described by a difference equation can be expressed as the sum of a steady-state and a transient response. You will learn why the steady-state response takes the same form as the input and how the transient response reflects the impact of the stored energy in the system.

Difference equation descriptions for systems are widely used in signal processing to implement and model systems. Understanding how the output depends on the input and stored energy will provide you with very helpful insight for working with such systems.