# Definition of Z Transform

Introduction

Physical Meaning

Poles and Zeros

## Introduction

Z Transform is a very useful mathematical tool, mainly used to solve difference equations. It converts the difference equations into algebraic form, which are then easy to be solved and then the solution is inversely converted, using Inverse Z Transform, to the form it should initially be. It is the discrete equivalent of the Laplace Transform and a generalization of the Discrete Time Fourier Transform.

# Z Transform from the Definition

Example 4: Exponent

Example 5: Cosine

## Example 1: Causal Finite Duration Sequence # Z Transform using the Transformation Tables

Example 3: Convolution

Example 5: Transformation of Equation

## Example 1: Time Shifting  # Introduction

The Inverse Z Transform allows us to recover the discrete time sequence from the Z function: # Difference Equations

Example 1: Solving Difference Equation

Example 2: Solving Difference Equation

Difference Equations with Unilateral Z Transform

Example 4: Solving Difference Equation with Initial Conditions

## Introduction

Difference equations are called the equations of which the present value of the discrete output is function of the present and previous values of the discrete input and the previous values of the discrete output. For example a difference equation is: 