Introduction to Digital Signal Processing and Filter Design

CONTENTS

Preface

1 Introduction

1.1 Introduction

1.2 Applications of DSP

1.3 Discrete-Time Signals

1.3.1 Modeling and Properties of Discrete-Time Signals

1.3.2 Unit Pulse Function

1.3.3 Constant Sequence

1.3.4 Unit Step Function

1.3.5 Real Exponential Function

1.3.6 Complex Exponential Function

1.3.7 Properties of cos(ω₀n)

1.4 History of Filter Design

1.5 Analog and Digital Signal Processing

1.5.1 Operation of a Mobile Phone Network

1.6 Summary

Problems

References

2 Time-Domain Analysis and z Transform

2.1 A Linear, Time-Invariant System

2.1.1 Models of the Discrete-Time System

2.1.2 Recursive Algorithm

2.1.3 Convolution Sum

2.2 z Transform Theory

2.2.1 Definition

2.2.2 Zero Input and Zero State Response

2.2.3 Linearity of the System

2.2.4 Time-Invariant System

2.3 Using z Transform to Solve Difference Equations

2.3.1 More Applications of z Transform

2.3.2 Natural Response and Forced Response

2.4 Solving Difference Equations Using the Classical Method

2.4.1 Transient Response and Steady-State Response

2.5 z Transform Method Revisited

2.6 Convolution Revisited

2.7 A Model from Other Models

2.7.1 Review of Model Generation

2.8 Stability

2.8.1 Jury–Marden Test

2.9 Solution Using MATLAB Functions

2.10 Summary

Problems

References

3 Frequency-Domain Analysis

3.1 Introduction

3.2 Theory of Sampling

3.2.1 Sampling of Bandpass Signals

3.3 DTFT and IDTFT

3.3.1 Time-Domain Analysis of Noncausal Inputs

3.3.2 Time-Shifting Property

3.3.3 Frequency-Shifting Property

3.3.4 Time Reversal Property ...