Engineering Mathematics

23

The z-transform

In Chapters 20–22, we studied the Laplace transform for continuous-time signals (input functions). The z-transform is the finite or discrete-time version of the Laplace transform. This transform is useful for solving initial-value problems whose continuous analogs are treated by Laplace transform. It has many properties in common with the Laplace transform. We know that continuous-time systems are described by differential equations whereas discrete-time systems are described by difference equations. So we use z-transform to solve difference equations that are approximations to the differential equations of the initial-value problems treated by Laplace transform. So, we shall consider discrete-time signals f [n] (also denoted ...