Digital Filters Design for Signal and Image Processing

Table of Contents

Introduction

Chapter 1. Introduction to Signals and Systems

Yannick BERTHOUMIEU, Eric GRIVEL and Mohamed NAJIM

1.1. Introduction

1.2. Signals: categories, representations and characterizations

1.2.1. Definition of continuous-time and discrete-time signals

1.2.2. Deterministic and random signals

1.2.3. Periodic signals

1.2.4. Mean, energy and power

1.2.5. Autocorrelation function

1.3. Systems

1.4. Properties of discrete-time systems

1.4.1. Invariant linear systems

1.4.2. Impulse responses and convolution products

1.4.3. Causality

1.4.4. Interconnections of discrete-time systems

1.5. Bibliography

Chapter 2. Discrete System Analysis

Mohamed NAJIM and Eric GRIVEL

2.1. Introduction

2.2. The z-transform

2.2.1. Representations and summaries

2.2.2. Properties of the z-transform

2.2.2.1 Linearity

2.2.2.2 Advanced and delayed operators

2.2.2.3 Convolution

2.2.2.4 Changing the z-scale

2.2.2.5 Contrasted signal development

2.2.2.6 Derivation of the z-transform

2.2.2.7 The sum theorem

2.2.2.8 The final-value theorem

2.2.2.9 Complex conjugation

2.2.2.10 Parseval's theorem

2.2.3. Table of standard transform

2.3. The inverse z-transform

2.3.1. Introduction

2.3.2. Methods of determining inverse z-transforms

2.3.2.1 Cauchy's theorem: a case of complex variables

2.3.2.2 Development in rational fractions

2.3.2.3 Development by algebraic division of polynomials

2.4. Transfer functions and difference equations

2.4.1. The transfer function of a continuous system

2.4.2. Transfer functions ...