Table of Contents

About the Author xv

Preface xvi

Acknowledgements xxi

About the Companion Website xxii

1 Practical MATLAB with Signals Theory 1

1.1 Introduction 1

1.2 Visualizing Functions 5

1.3 MATLAB M-Files 9

1.4 Numerical Integration 10

1.5 The for Loop 12

1.6 Conditional and Logical Expressions 12

1.7 Piecewise Continuous Signals 13

1.8 Complex Numbers in MATLAB 14

1.9 Conclusions 19

1.10 Worked Problems 19

1.11 End of Chapter Exercises 22

Bibliography 23

2 Introduction to Signals and Systems 25

2.1 Introduction 25

2.2 Introduction to Signal Manipulation 26

2.3 Basic Signals 32

2.4 The Sinusoidal Signal 40

2.5 Conclusions 44

2.6 Worked Problems 45

2.7 End of Chapter Exercises 47

Bibliography 51

3 Classification of Signals 53

3.1 Introduction 53

3.2 Odd and Even Signals 53

3.3 Periodic Signals 56

3.4 Energy and Power Signals 64

3.5 Complex Signals 69

3.6 Discrete Time Signals 71

3.7 Random Signals 72

3.8 Conclusions 73

3.9 Worked Problems 74

3.10 End of Chapter Exercises 76

4 Linear Systems 83

4.1 Introduction 83

4.2 Definition of a Linear System 83

4.3 LTI System Response Function h(t) 88

4.4 Convolution 88

4.5 Determining h(t) in an Unknown System 98

4.6 Causality 101

4.7 Combined Systems 102

4.8 Convolution and Random Numbers 103

4.9 Useful Hints and Help with MATLAB 105

4.10 Chapter Summary 106

4.11 Conclusions 106

4.12 Worked Problems 106

4.13 End of Chapter Exercises 109

Bibliography 113

5 The Fourier Series 115

5.1 Introduction 115

5.2 Expressing Signals by Components 116

5.3 Part One – Orthogonal Signals 119

5.4 Orthogonality 120

5.5 Part Two – The Fourier Series 127

5.6 Computing Fourier Series Components 132

5.7 Odd and Even Square Waves 136

5.8 Gibb’s Phenomenon 138

5.9 Setting-Up the Fourier Series Calculation 141

5.10 Some Common Fourier Series 143

5.11 Practical Harmonics 144

5.12 Part Three: The Complex Fourier Series 145

5.13 The Complex Fourier Series 147

5.14 Complex Fourier Series Components 151

5.15 Properties of the Complex Fourier Series 158

5.16 Analysis of a DC Power Supply 158

5.17 The Fourier Series with MATLAB 163

5.18 Conclusions 169

5.19 Worked Problems 169

5.20 End of Chapter Exercises 172

Bibliography 177

6 The Fourier Transform 179

6.1 Introduction 179

6.2 Properties of the Fourier Transform 185

6.3 The Rectangle Signal 188

6.4 The Sinc Function 189

6.5 Signal Manipulations: Time and Frequency 194

6.6 Fourier Transform Pairs 202

6.7 Rapid Changes vs. High Frequencies 203

6.8 Conclusions 206

6.9 Worked Problems 206

6.10 End of Chapter Exercises 207

Bibliography 211

7 Practical Fourier Transforms 213

7.1 Introduction 213

7.2 Convolution: Time and Frequency 213

7.3 Transfer Function of a Linear System 217

7.4 Energy in Signals: Parseval’s Theorem for the Fourier Transform 219

7.5 Data Smoothing and the Frequency Domain 220

7.6 Ideal Filters 221

7.7 A Real Low-Pass Filter 225

7.8 The Modulation Theorem 230

7.9 Periodic Signals and the Fourier Transform 234

7.10 The Analog Spectrum Analyzer 237

7.11 Conclusions 237

7.12 Worked Problems 238

7.13 End of Chapter Exercises 240

Bibliography 246

8 The Laplace Transform 247

8.1 Introduction 247

8.2 The Laplace Transform 248

8.3 Exploring the s-Domain 250

8.4 Visualizing the Laplace Transform 257

8.5 Properties of the Laplace Transform 270

8.6 Differential Equations 271

8.7 Laplace Transform Pairs 273

8.8 Circuit Analysis with the Laplace Transform 275

8.9 State Variable Analysis 285

8.10 Conclusions 294

8.11 Worked Problems 294

8.12 End of Chapter Exercises 297

Bibliography 303

9 Discrete Signals 305

9.1 Introduction 305

9.2 Discrete Time vs. Continuous Time Signals 305

9.3 A Discrete Time Signal 306

9.4 Data Collection and Sampling Rate 308

9.5 Introduction to Digital Filtering 320

9.6 Illustrative Examples 328

9.7 Filtering Application with MATLAB 336

9.8 Conclusions 339

9.9 Worked Problems 339

9.10 End of Chapter Exercises 343

Bibliography 347

10 The z-Transform 349

10.1 Introduction 349

10.2 The z-Transform 349

10.3 Calculating the z-Transform 352

10.4 A Discrete Time Laplace Transform 359

10.5 Properties of the z-Transform 360

10.6 z-Transform Pairs 361

10.7 Transfer Function of a Discrete Linear System 361

10.8 MATLAB Analysis with the z-Transform 362

10.9 Digital Filtering – FIR Filter 367

10.10 Digital Filtering – IIR Filter 373

10.11 Conclusions 377

10.12 Worked Problems 377

10.13 End of Chapter Exercises 378

11 Communication Systems 383

11.1 Introduction 383

11.2 Amplitude Modulation 386

11.3 Suppressed Carrier Transmission 394

11.4 Superheterodyne Receiver 396

11.5 Digital Communications 400

11.6 Phase Shift Keying 404

11.7 Spread Spectrum Systems 407

11.8 Conclusions 416

11.9 Worked Problems 417

11.10 End of Chapter Exercises 418

Bibliography 420

A Reference Tables 421

B The Illustrated Fourier Transform 425

C The Illustrated Laplace Transform 433

D The Illustrated z-Transform 439

E MATLAB Reference Guide 445

Index 453