Practical Signals Theory with MATLAB Applications (Hardcover, 2)

· 제목 : Practical Signals Theory with MATLAB Applications (Hardcover, 2) 
· 분류 : 외국도서 > 컴퓨터 > 컴퓨터 비전/패턴 인식
· ISBN : 9781394266555
· 쪽수 : 480쪽
· 출판일 : 2025-11-12

Preface………………………………………………………………. xxi

Pedagogy ……………………………………………………………xxi

Organization……………………………………………………….xxiv

Chapter 1. Practical MATLAB with Signals Theory ……………….. xxiv

Chapter 2. Introduction to Signals and Systems …………………..xxv

Chapter 3. Classi_cation of Signals ……………………………………xxv

Chapter 4. Linear Systems ………………………………………………..xxv

Chapter 5. The Fourier Series …………………………………………….xxv

Chapter 6. The Fourier Transform ………………………………………xxvi

Chapter 7. Practical Fourier Transforms ……………………………..xxvi

Chapter 8. The Laplace Transform ……………………………………..xxvi

Chapter 9. Discrete Signals ………………………………………………xxvi

Chapter 10. The z-Transform …………………………………………….xxvii

Chapter 11. Communications Systems……………………………… xxvii

0.1 Useful Information (inside cover / endpaper)………………… xxviii

0.1.1 Identities ……………………………………………… xxviii

0.1.2 De_nite Integrals …………………………………….xxviii

0.1.3 In_nite Series …………………………………………xxix

0.1.4 Orthogonality …………………………………………xxix

0.1.5 Signal Inner Product ………………………………..xxix

0.1.6 Convolution ……………………………………………xxix

0.1.7 Fourier Series ………………………………………….xxix

0.1.8 Complex Fourier Series……………………………..xxx

0.1.9 Fourier Transform …………………………………….xxx

0.1.10 Laplace Transform …………………………………xxx

0.1.11 z-Transform …………………………………………..xxx

0.2 List of Acronyms ………………………………………..xxxii

0.2.1 Communications Acronyms…………………… xxxiii

1 Practical MATLAB with Signals Theory 1

Learning Objectives ………………………………………………2

1.1 Introduction ……………………………………………………2

1.1.1 Accessing MATLAB ………………………………………..2

1.1.2 Learning MATLAB ………………………………………….4

1.1.3 The MATLAB Desktop……………………………………..4

1.1.4 Help with MATLAB …………………………………………5

1.1.5 Numeric Variables for Signals Theory ……………….6

1.1.6 MATLAB Arrays, Matrices, Vectors ……………………6

1.1.7 Recording a MATLAB session …………………………..9

1.2 Visualizing Functions ………………………………………..9

1.2.1 Making a Rough Sketch of a Function ……………….10

1.2.2 Plotting a Function by Hand ……………………………10

1.2.3 Plotting a Function with MATLAB ……………………..11

1.2.4 Enhanced Plotting Functions ………………………….13

1.3 MATLAB M-Files ……………………………………………….14

1.3.1 Creating a MATLAB Function ……………………………15

1.3.2 Anonymous Functions ……………………………………16

1.4 Numerical Integration ……………………………………….17

1.4.1 Generalized Numerical Integration …………………..19

1.5 The for loop ……………………………………………………..20

1.6 Conditional and Logical Expressions …………………..20

1.7 Piecewise Continuous Signals ……………………………22

1.8 Complex Numbers in MATLAB …………………………….24

1.8.1 Representation of Complex Numbers ………………..24

1.8.2 Euler's Formula ………………………………………………25

1.8.3 The Complex Plane …………………………………………26

Viewing a Function from Different Perspectives ………………28

1.9 Conclusions ………………………………………………………..29

1.10 Worked Problems ……………………………………………….30

1.11 End of Chapter Exercises ……………………………………..33

Bibliography ………………………………………………………………36

2 Introduction to Signals and Systems 37

Learning Objectives ……………………………………………………37

2.1 Introduction …………………………………………………………38

2.1.1 What is a Signal? ……………………………………………….39

2.1.2 What is a System? ……………………………………………..39

2.2 Introduction to Signal Manipulation ………………………...41

2.2.1 Amplification ……………………………………..42

2.2.2 Shifting ……………………………………………..42

2.2.3 Scaling ………………………………………………44

2.2.4 Linear Combination ……………………………..46

2.2.5 Addition and Multiplication of Signals ……………….4

2.2.6 Visualizing Signals - An Important Skill ……………..49

2.3 Basic Signals …………………………………………………..50

2.3.1 The Unit Rectangle : rect(t) ……………………………..50

2.3.2 The Unit Step u(t) ………………………………………….52

2.3.3 The Exponential e^kt ………………………………………..55

2.3.4 The Unit Impulse δ(t) ……………………………………..56

2.3.5 Plotting the Impulse Aδ(t-x) …………………………….60

2.4 The Sinusoidal Signal ……………………………………….61

2.4.1 The One-Sided Cosine Representation……………. 63

2.4.2 Phase Change - ……………………………………………65

Phase Change vs. Time Shift ………………………………….65

2.4.3 Sine vs. Cosine …………………………………………….68

2.5 Conclusions ………………………………………………………69

2.6 Worked Problems ……………………………………………….69

2.7 End of Chapter Exercises ……………………………………..72

Bibliography …………………………………………………………….76

3 Classification of Signals 79

Learning Objectives ………………………………………………79

3.1 Introduction ……………………………………………………80

3.2 Odd and Even Signals ………………………………………80

3.2.1 Combining Odd and Even signals …………………….82

3.2.2 The constant value s(t) = k ………………………………84

3.3 Periodic Signals ……………………………………………….85

3.3.1 DC Component in Periodic Signals …………………..86

3.3.2 Sinusoids and Rectifiers ………………………………….86

3.3.3 Square Wave …………………………………………89

3.3.4 Sawtooth Wave ……………………………………..89

3.3.5 Triangle wave …………………………………………89

3.3.6 Pulse Train ……………………………………………..91

3.3.7 Rectangular Pulse Train ……………………………91

3.3.8 Impulse Train ………………………………………….93

3.3.9 Trigonometric Identities …………………………93

3.3.10 Sinusoidal Multiplication …………………………95

Modulation Property …………………………95

Dial Tone Generator …………………………97

Squaring the Sinusoid …………………………99

3.4 Energy and Power Signals …………………………101

3.4.1 Periodic Signals = Power Signals ………………………… 104

V_rms is not always A/√2 …………………………105

3.4.2 Comparing Signal Power: The Decibel (dB) …………………………105

3.5 Complex Signals …………………………108

3.6 Discrete Time Signals …………………………111

3.7 Random Signals …………………………113

3.8 Conclusions …………………………115

3.9 Worked Problems …………………………115

3.10 End of Chapter Exercises …………………………118

Bibliography …………………………127

4 Linear Systems 129

Learning Objectives …………………………129

4.1 Introduction …………………………130

4.2 Definition of a Linear System …………………………130

4.2.1 Superposition …………………………131

4.2.2 Example 1: Zero-State Response …………………………132

4.2.3 Example 2: Operating in a linear region …………………………133

4.2.4 Example 3: Mixer …………………………135

4.2.5 Linear Time-Invariant (LTI) Systems …………………………136

4.2.6 Bounded Input, Bounded Output …………………………138

4.2.7 System Behavior as a Black Box …………………………139

4.3 LTI System Response Function h(t) …………………………139

4.4 Convolution …………………………140

4.4.1 The Convolution Integral …………………………141

4.4.2 Convolution is Commutative …………………………144

4.4.3 Convolution is Associative …………………………145

4.4.4 Convolution is Distributive over Addition …………………………147

4.4.5 Evaluation of the Convolution Integral …………………………147

Graphical Convolution 1: Rectangle with Itself …………………………148

4.4.6 Convolution Properties …………………………150

Graphical Convolution 2: Two Rectangles …………………………151

Graphical Convolution 3: Rectangle and Exponential Decay…………………………152

4.4.7 Convolution in MATLAB …………………………154

4.5 Determining h(t) in an Unknown System …………………………157

4.5.1 The Unit Impulse δ(t) Test Signal …………………………157

4.5.2 Convolution and Signal Decomposition …………………………158

Convolution and Periodic Signals …………………………160

4.5.3 An Ideal Distortionless System …………………………160

Deconvolution …………………………161

4.6 Causality …………………………162

4.6.1 Causality and Zero Input Response …………………………164

4.7 Combined Systems …………………………164

4.8 Convolution and Random Numbers …………………………166

4.9 Useful Hints and Help with MATLAB …………………………168

4.10 Chapter Summary …………………………169

4.11 Conclusions …………………………170

4.12 Worked Problems …………………………170

4.13 End of Chapter Exercises …………………………173

Bibliography ………………………… 180

5 The Fourier Series 181

Learning Objectives …………………………181

Chapter Overview …………………………182

5.1 Introduction …………………………182

5.2 Expressing Signals by Components …………………………182

5.2.1 The Spectrum Analyzer …………………………184

5.2.2 Approximating a Signal s(t) by Another …………………………184

5.2.3 Estimating One Signal by Another …………………………187

5.3 Part One - Orthogonal Signals …………………………189

5.4 Orthogonality ………………………… 190

5.4.1 An Orthogonal Signal Space …………………………191

5.4.2 The Signal Inner Product Formulation …………………………193

5.4.3 Complete Set of Orthogonal Signals …………………………195

5.4.4 What if a Complete Set is not Present? …………………………196

5.4.5 An Orthogonal Set of Signals …………………………196

5.5 Part Two - The Fourier Series …………………………204

5.5.1 The Orthogonal Signals {sin(2?m?_ot); cos(2?n?_ot)} …………………………204

5.5.2 The Fourier Series - An Orthogonal Set? …………………………205

5.6 Computing Fourier Series Components …………………………209

5.6.1 Fourier Series Approximation to an Odd Square Wave ……210

5.6.2 Zero-Frequency (DC) Component …………………………211

5.6.3 Fundamental Frequency Component …………………………212

5.6.4 Higher Order Components …………………………213

5.6.5 Frequency Spectrum of the Square Wave s(t) …………………………215

5.7 Odd and Even Square Waves …………………………217

5.7.1 The Fourier Series Components of an Even Square Wave…………………………219

5.8 Gibb's Phenomenon …………………………221

5.9 Setting-Up the Fourier Series Calculation …………………………224

5.9.1 Appearance of Pulse Train Frequency Components …………………………226

5.10 Some Common Fourier Series …………………………231

5.11 Practical Harmonics …………………………232

5.11.1 Audio Ampli_er Specs - Total Harmonic Distortion …………………………232

5.11.2 The CB Radio Booster …………………………233

5.12 Part Three: The Complex Fourier Series …………………………235

5.12.1 Not all Signals are Even or Odd…………………………235

5.13 The Complex Fourier Series …………………………237

5.13.1 Complex Fourier Series - The Frequency Domain …………………………238

5.13.2 Comparing the Real and Complex Fourier Series …………………………243

5.13.3 Magnitude and Phase …………………………244

5.14 Complex Fourier Series Components …………………………245

5.14.1 Real Signals and the Complex Fourier Series …………………………247

5.14.2 Stretching and Squeezing: Time vs. Frequency …………………………248

5.14.3 Shift in Time …………………………249

5.14.4 Change in Amplitude …………………………250

5.14.5 Power in Periodic Signals …………………………250

Find the Total Power in s(t) = Acos(t) + B sin(t) …………………………251

5.14.6 Parseval's Theorem for Periodic Signals …………………………252

5.15 Properties of the Complex Fourier Series …………………………258

5.16 Analysis of a DC Power Supply …………………………258

5.16.1 The DC Component …………………………259

5.16.2 An AC-DC Converter …………………………260

5.16.3 Vrms is always greater than or equal to V_dc …………………………261

5.16.4 Fourier Series: The Full-wave Rectifier …………………………261

5.16.5 Complex Fourier series components C_n …………………………264

Power in the Fundamental Frequency 120 Hz ………………………………267

5.17 The Fourier Series with MATLAB ……………………………………………268

5.17.1 Finding Fourier Series Components ………………………………………268

A full-wave rectified cosine (60 Hz) …………………………………………………..269

5.17.2 Effective use of the Fast Fourier Transform………………..272

5.18 Conclusions …………………………………………………..276

5.19 Worked Problems …………………………………………………..277

5.20 End of Chapter Exercises …………………………………………………..281

Bibliography …………………………………………………..289

6 The Fourier Transform 291

Learning Objectives …………………………………………………..291

6.1 Introduction …………………………………………………..292

6.1.1 A Fresh Look at the Fourier Series …………………………………………………..292

Periodic and Non-Periodic Signals …………………………………………………..293

6.1.2 Approximating a Non-Periodic Signal Over All Time …………………………………295

6.1.3 Definition of the Fourier Transform …………………………………………………..299

6.1.4 Existence of the Fourier Transform …………………………………………………..300

6.1.5 The Inverse Fourier Transform …………………………………………………..301

6.2 Properties of the Fourier Transform …………………………………………………..302

6.2.1 Linearity of the Fourier Transform …………………………………………302

6.2.2 Value of the Fourier transform at the Origin …………………………304

6.2.3 Odd and Even Functions and the Fourier Transform ……………………305

6.3 The Rectangle Signal ………………………………………………….. 307

Alternate Solution …………………………………………………..308

6.4 The Sinc Function …………………………………………………..309

6.4.1 Expressing a Function in Terms of sinc(t) …………………………………………312

6.4.2 The Fourier Transform of a General Rectangle ………………………………313

6.5 Signal Manipulations: Time and Frequency ………………………………………318

6.5.1 Amplitude Variations …………………………………………………..318

6.5.2 Stretch and Squeeze: The Sinc Function …………………………………………………..318

6.5.3 The Scaling Theorem…………………………………………………..319

6.5.4 Testing the Limits …………………………………………………..321

6.5.5 A Shift in Time …………………………………………………..323

6.5.6 The Shifting Theorem …………………………………………………..324

6.5.7 The Fourier Transform of a Shifted Rectangle …………………………………326

Magnitude of G(?) …………………………………………………..326

Phase of G(?) …………………………………………………..326

6.5.8 Impulse Series - The Line Spectrum …………………………………………………..328

6.5.9 Shifted Impulse δ(? ? ?_o) …………………………………………………..328

6.5.10 Fourier Transform of a Periodic Signal …………………………………………………..329

6.6 Fourier Transform Pairs …………………………………………………..332

6.6.1 The Illustrated Fourier Transform …………………………………………………..334

6.7 Rapid Changes vs. High Frequencies …………………………………………………..335

6.7.1 Derivative Theorem …………………………………………………..336

6.7.2 Integration Theorem …………………………………………………..338

6.8 Conclusions …………………………………………………..339

6.9 Worked Problems …………………………………………………..340

6.10 End of Chapter Exercises …………………………………………………..342

Bibliography …………………………………………………..348

7 Practical Fourier Transforms 349

7.1 Introduction …………………………………………………..349

Learning Objectives …………………………………………………..349

7.2 Convolution: Time and Frequency …………………………………………………..350

The Logarithm Domain …………………………………………………..350

7.2.1 Simplifying the Convolution Integral ……………………………………351

7.3 Transfer Function of a Linear System ………………………………………356

7.3.1 Impulse Response: The Frequency Domain ……………………………357

7.3.2 Frequency Response Curve …………………………………………………..359

7.4 Energy in Signals: Parseval's Theorem for the Fourier Transform ………………360

7.4.1 Energy Spectral Density …………………………………………………..361

7.5 Data Smoothing and the Frequency Domain ………………………………363

7.6 Ideal Filters …………………………………………………..365

7.6.1 The Ideal Low-Pass Filter is not Causal …………………………………………………..368

7.7 A Real Low-Pass Filter …………………………………………………..370

MATLAB Example 1: First Order Filter ………………………………………………….. 376

7.8 The Modulation Theorem …………………………………………………..378

7.8.1 A Voice Privacy System …………………………………………………..379

Spectral Inversion …………………………………………………..380

7.9 Periodic Signals and the Fourier Transform ……………………384

7.9.1 The Impulse Train …………………………………………………..385

7.9.2 General Appearance of Periodic Signals …………………………………………………..387

7.9.3 The Fourier Transform of a Square wave ………………………………387

Changing the Pulse Train Appearance …………………………………………389

7.9.4 Other Periodic Waveforms …………………………………………………..390

7.10 The Analog Spectrum Analyzer …………………………………………………..390

7.11 Conclusions …………………………………………………..392

7.12 Worked Problems …………………………………………………..392

7.13 End of Chapter Exercises …………………………………………………..397

Bibliography …………………………………………………..406

8 The Laplace Transform 407

Learning Objectives …………………………………………………..408

8.1 Introduction …………………………………………………..408

8.2 The Laplace Transform …………………………………………………..409

8.2.1 The Frequency Term e^jwt …………………………………………………..411

8.2.2 The Exponential Term e^σt …………………………………………………..412

8.2.3 The s-domain …………………………………………………..412

8.3 Exploring the s-domain …………………………………………………..413

8.3.1 Poles and Zeros …………………………………………………..414

8.3.2 A Pole at the origin …………………………………………………..414

8.3.3 Decaying Exponential …………………………………………………..417

8.3.4 A Sinusoid …………………………………………………..420

8.3.5 A Decaying Sinusoid …………………………………………………..422

8.3.6 An Unstable System …………………………………………………..424

8.4 Visualizing the Laplace Transform ……………………………………………424

8.4.1 First Order Low-pass Filter …………………………………………………..425

8.4.2 Pole Position Determines Frequency Response ………………………428

8.4.3 Second Order Low-pass Filter …………………………………………………..431

8.4.4 Two-Sided Laplace Transform …………………………………………………..435

8.4.5 The Bode Diagram …………………………………………………..437

8.4.6 Calculating the Laplace Transform …………………………………………………..442

8.4.7 System Analysis in MATLAB …………………………………………………..443

8.5 Properties of the Laplace Transform …………………………………………………..447

8.6 Differential Equations …………………………………………………..448

8.6.1 Solving a Differential Equation …………………………………………………..449

8.6.2 Transfer Function as Differential Equations ……………………………………………452

8.7 Laplace Transform Pairs …………………………………………………..452

8.7.1 The Illustrated Laplace Transform …………………………………………………..454

8.8 Circuit Analysis with the Laplace Transform ………………………………………455

8.8.1 Voltage Divider …………………………………………………..457

8.8.2 A First-Order Low-pass Filter ………………………………………………….. 458

8.8.3 A First-Order High-pass Filter …………………………………………………..462

8.8.4 A Second Order Filter …………………………………………………..464

8.9 State Variable Analysis …………………………………………………..475

8.9.1 State Variable Analysis - First Order System ………………………………475

8.9.2 First Order State Space Analysis with MATLAB …………………………….478

8.9.3 State Variable Analysis - Second Order System ……………………………480

8.9.4 Matrix Form of the State Space Equations ……………………………………482

8.9.5 Second Order State Space Analysis with MATLAB …………………………484

8.9.6 Differential Equation …………………………………………………..485

8.9.7 State Space and Transfer Functions with MATLAB …………………………487

8.10 Conclusions …………………………………………………..489

8.11 Worked Problems …………………………………………………..490

8.12 End of Chapter Exercises …………………………………………………..495

Bibliography …………………………………………………..505

9 Discrete Signals 507

9.1 Introduction …………………………………………………..507

Learning Objectives …………………………………………………..507

9.2 Discrete Time vs. Continuous Time Signals …………………………………508

9.3 A Discrete Time Signal …………………………………………………..509

9.3.1 Digital Signal Processing …………………………………………………..510

9.3.2 A Periodic Discrete Time Signal …………………………………………………..513

9.4 Data Collection and Sampling Rate …………………………………………………..513

9.4.1 The Selection of a Sampling Rate …………………………………………………..513

9.4.2 Bandlimited Signal …………………………………………………..515

9.4.3 Theory of Sampling …………………………………………………..516

9.4.4 The Sampling Function …………………………………………………..516

9.4.5 Recovering a Waveform from Samples ……………………………………518

9.4.6 A Practical Sampling Signal ……………………………………………519

9.4.7 Minimum Sampling Rate …………………………………………………..519

9.4.8 Nyquist Sampling Rate …………………………………………………..521

9.4.9 The Nyquist Sampling Rate is a Theoretical Minimum ……………………………523

9.4.10 Sampling Rate and Alias Frequency …………………………………………………..525

9.4.11 Practical Aliasing …………………………………………………..528

9.4.12 Analysis of Aliasing ………………………………………………….. 531

9.4.13 Anti-Alias Filter …………………………………………………533

9.5 Introduction to Digital Filtering …………………………………………534

9.5.1 Impulse Response Function …………………………………………535

9.5.2 A Discrete Response Function ……………………………………… 535

9.5.3 Delay Blocks are a Natural Consequence of Sampling ………..539

9.5.4 General Digital Filtering …………………………………………………540

9.5.5 The Fourier Transform of Sampled Signals …………………………..542

9.5.6 The Discrete Fourier Transform (DFT) …………………………………543

9.5.7 A Discrete Fourier Series …………………………………………………..546

9.5.8 Computing the Discrete Fourier Transform (DFT) ………548

9.5.9 The Fast Fourier Transform (FFT) ……………………548

9.6 Illustrative Examples ………………………………………550

The FFT (fft) and Inverse FFT (ifft) ……………………………553

9.6.1 FFT and Sample Rate ……………………………………556

9.6.2 Practical DFT Issues ……………………………………556

9.7 Filtering Application with MATLAB ……………………563

9.7.1 Fourier Analysis ……………………………………………563

9.7.2 System Response …………………………………………564

9.7.3 Check Calculation ……………………………………… 565

9.8 Conclusions …………………………………………...566

9.9 Worked Problems ……………………………………567

9.10 End of Chapter Exercises …………………………572

Bibliography …………………………………………………..579

10 The z-Transform 581

10.1 Introduction ……………………………………………581

Learning Objectives …………………………………………581

10.2 The z-Transform …………………………………………………..582

10.2.1 Fourier Transform, Laplace Transform, z-transform ………………582

10.2.2 Defnition of the z-Transform ………………………………………585

10.2.3 The z-Plane and the Fourier Transform ………………………………………587

10.3 Calculating the z-Transform ……………………………………588

10.3.1 Unit Step u[n] …………………………………………………..590

10.3.2 Exponential aⁿ u[n] …………………………………………………592

10.3.3 Sinusoid cos(nω_o) u[n] and sin(nω_o) u[n] ………………………594

10.3.4 Differentiation …………………………………………………..596

10.3.5 The Effect of Sampling Rate …………………………………………………..597

10.4 A Discrete Time Laplace Transform ………………………………598

10.5 Properties of the z-Transform ………………………………………602

10.6 z-Transform Pairs …………………………………………………..602

10.7 Transfer Function of a Discrete Linear System ……………………603

10.8 MATLAB Analysis with the z-transform ………………………………603

10.8.1 First Order Low-pass Filter …………………………………604

10.8.2 Pole-zero Plot …………………………………………………..606

10.8.3 Bode diagram …………………………………………………..608

10.8.4 Impulse Response …………………………………………………..609

10.8.5 Calculating Frequency Response ………………………………..610

10.8.6 Pole Position Determines Frequency Response …………….611

10.9 Digital Filtering - FIR Filter ……………………………………………612

10.9.1 A One Pole FIR Filter …………………………………………………..614

10.9.2 A Two Pole FIR Filter …………………………………………………..615

10.9.3 Higher Order FIR Filters …………………………………………………..616

10.10Digital Filtering - IIR Filter …………………………………………………..621

10.10.1A One Pole IIR Filter …………………………………………………..621

10.10.2 IIR vs. FIR …………………………………………………..624

10.10.3 Higher Order IIR Filters …………………………………………………..626

10.10.4 Combining FIR and IIR Filters …………………………………………627

10.11Conclusions …………………………………………………..627

10.12Worked Problems …………………………………………………..628

10.13End of Chapter Exercises …………………………………………………..631

11 Communication Systems 637

Learning Objectives …………………………………………………..637

11.1 Introduction …………………………………………………..638

11.1.1 A Baseband Signal m(t) …………………………………………………..638

11.1.2 The need for a Carrier Signal …………………………………………………..639

11.1.3 A Carrier Signal c(t) …………………………………………………..640

11.1.4 Modulation Techniques …………………………………………………..640

11.1.5 The Radio Spectrum …………………………………………………..642

11.2 Amplitude Modulation …………………………………………………..644

11.2.1 Double Sideband Transmitted Carrier - (DSB-TC) …………………………645

11.2.2 Demodulation of AM DSB-TC Signals …………………………………650

11.2.3 Graphical Analysis …………………………………………………..651

11.2.4 AM Demodulation - Diode Detector …………………………………………654

11.2.5 Examples of Diode Detection …………………………………………………657

11.3 Suppressed Carrier Transmission …………………………………………………658

11.3.1 Demodulation of Single Sideband Signals ……………………………………659

11.3.2 Percent Modulation and Overmodulation ……………………………………662

11.4 Superheterodyne Receiver …………………………………………………..662

11.4.1 An Experiment with Intermediate Frequency ………………………666

11.4.2 When Receivers become Transmitters …………………………….668

11.4.3 Image Frequency …………………………………………………..668

11.4.4 Beat Frequency Oscillator ……………………………………….670

11.5 Digital Communications …………………………………………………..670

11.5.1 Modulation Methods …………………………………………………..672

11.5.2 Morse Code …………………………………………………..672

11.5.3 Amplitude Shift Keying (ASK) …………………………………………………..676

11.5.4 Frequency Shift Keying (FSK) …………………………………………………..677

11.6 Phase Shift Keying (PSK) …………………………………………………..678

11.6.1 Differential Coding …………………………………………………..679

11.6.2 Quadrature Amplitude Modulation (QAM) …………………………………………681

11.7 Spread Spectrum Systems …………………………………………………..683

11.7.1 Introduction …………………………………………………..683

11.7.2 Pseudorandom Noise …………………………………………………..686

11.7.3 Encoding Bits in DSSS …………………………………………693

11.7.4 Spectral Properties of a Pseudo-Random Sequence …693

11.7.5 Code Division Multiple Access (CDMA) …………695

11.8 Conclusions …………………………………………………..700

11.9 Worked Problems ……………………………………700

11.10End of Chapter Exercises …………………………703

Bibliography …………………………………………………..706

A Reference Tables 707

A.1 Fourier Transform …………………………………………707

A.1.1 Fourier Transform Theorems …………………………707

A.2 Laplace Transform …………………………………………709

A.2.1 Laplace Transform Theorems ………………………..709

A.3 z-Transform …………………………………………………..711

A.3.1 z-Transform Theorems ………………………………….711

B The Illustrated Fourier Transform 713

C The Illustrated Laplace Transform 725

D The Illustrated z-Transform 735

E MATLAB Reference Guide 743

E.1 De_ning Signals ………………………………………………743

E.1.1 MATLAB Variables ………………………………………..743

E.1.2 The Time Axis ……………………………………………..744

E.1.3 Common Signals…………………………………………. 745

E.2 Complex Numbers ………………………………………….745

E.3 Plot Commands ………………………………………………747

E.4 Signal Operations …………………………………………… 748

E.5 Defining Systems ………………………………………………. 749

E.5.1 System Definition …………………………………….750

E.5.2 System Analysis ……………………………………...752