# 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.

# 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:

# Definition of Vectors

### Introduction

In life there are objects that can be fully described by only one number. For example, if we want to know how much money we have in our pocket (liquidity), only one number is sufficient to inform us.

For other type of objects this is not enough. For example, if we want to describe the force that is applied to an object, we have to define the magnitude, as well as the direction of the force that it is applied. The packet containing magnitude and direction is called vector.

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