Introduction

UNIT - V

Z-TRANSFORMS AND DIFFERENCE EQUATIONS

Z-transforms-Elementary properties- Inverse Z - transform (using partial fraction and residues) Convolution theorem Formation of difference equations - Solution of difference equations using Z-transform.

 Introduction

The Z-transform plays the same role for discrete systems as the Laplace transform does for continuous systems.

Applications of Z - transform

1. Communication is one of the fields whose development is based on discrete analysis. Difference equations are also based on discrete system and their solutions and analysis are carried out by Z - lo transform. 

2. In the system analysis area, the Z - transform converts convolutions to a product and difference equations to algebraic equations.

3. The stability of a discrete linear system can be determined by analyzing the transfer function ion H (z) given by the transform.

4.  Digital filters can be analyzed and designed using the Z- transform.

5. Digital control systems can be analyzed and designed using Z- transforms.