Representation of LTI Systems by Differential and Difference Equations

Summary

This chapter models the continuous time and discrete time linear time‐invariant (LTI) systems by their dynamic nature using differential and difference equations. A differential equation basically links the rate of change of an input to that of the output in continuous time systems. Similarly, a difference equation relates the rate of change on the input–output pairs when the time variable is integer‐valued. Both the difference and differential equations can be used to represent the dynamic changes of the systems. In particular, a linear and constant coefficient differential (difference) equation, which satisfies the initial rest condition, uniquely describes a continuous (discrete) time LTI system. We also study solution methods for the differential and difference equations to investigate the relative rate of change between the input and output signals of an LTI system.