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CHAPTER 1 Introduction1

1.1 What Is a Signal?1

1.2 What Is a System?2

1.3 Overview of Specific Systems2

1.4 Classification of Signals16

1.5 Basic Operations on Signals25

1.6 Elementary Signals34

1.7 Systems Viewed as Interconnections of Operations53

1.8 Properties of Systems55

1.9 Noise68

1.10 Theme Examples71

1.11 Exploring Concepts with MATLAB80

1.12 Summary86

Further Reading86

Additional Problems88

CHAPTER 2 Time-Domain Representations of Linear Time-Invariant Systems97

2.1 Introduction97

2.2 The Convolution Sum98

2.3 Convolution Sum Evaluation Procedure102

2.4 The Convolution Integral115

2.5 Convolution Integral Evaluation Procedure116

2.6 Interconnections of LTI Systems127

2.7 Relations between LTI System Properties and the Impulse Response133

2.8 Step Response139

2.9 Differential and Difference Equation Representations of LTI Systems141

2.10 Solving Differential and Difference Equations147

2.11 Characteristics of Systems Described by Differential and Difference Equations156

2.12 Block Diagram Representations161

2.13 State-Variable Descriptions of LTI Systems167

2.14 Exploring Concepts with MATLAB175

2.15 Summary181

Further Reading182

Additional Problems183

CHAPTER 3 Fourier Representations of Signals and Linear Time-Invariant Systems195

3.1 Introduction195

3.2 Complex Sinusoids and Frequency Response of LTI Systems196

3.3 Fourier Representations for Four Classes of Signals199

3.4 Discrete-Time Periodic Signals: The Discrete-Time Fourier Series202

3.5 Continuous-Time Periodic Signals: The Fourier Series215

3.6 Discrete-Time Nonperiodic Signals: The Discrete-Time Fourier Transform230

3.7 Continuous-Time Nonperiodic Signals: The Fourier Transform241

3.8 Properties of Fourier Representations253

3.9 Linearity and Symmetry Properties254

3.10 Convolution Property259

3.11 Differentiation and Integration Properties270

3.12 Time- and Frequency-Shift Properties280

3.13 Finding Inverse Fourier Transforms by Using Partial-Fraction Expansions286

3.14 Multiplication Property291

3.15 Scaling Properties299

3.16 Parseval Relationships303

3.17 Time-Bandwidth Product305

3.18 Duality307

3.19 Exploring Concepts with MATLAB312

3.20 Summary320

Further Reading321

Additional Problems322

CHAPTER 4 Applications of Fourier Representations to Mixed Signal Classes341

4.1 Introduction341

4.2 Fourier Transform Representations of Periodic Signals342

4.3 Convolution and Multiplication with Mixtures of Periodic and Nonperiodic Signals348

4.4 Fourier Transform Representation of Discrete-Time Signals358

4.5 Sampling362

4.6 Reconstruction of Continuous-Time Signals from Samples371

4.7 Discrete-Time Processing of Continuous-Time Signals382

4.8 Fourier Series Representations of Finite-Duration Nonperiodic Signals389

4.9 The Discrete-Time Fourier Series Approximation to the Fourier Transform396

4.10 Efficient Algorithms for Evaluating the DTFS404

4.11 Exploring Concepts with MATLAB408

4.12 Summary411

Further Reading412

Additional Problems413

CHAPTER 5 Application to Communication Systems425

5.1 Introduction425

5.2 Types of Modulation425

5.3 Benefits of Modulation429

5.4 Full Amplitude Modulation431

5.5 Double Sideband-Suppressed Carrier Modulation440

5.6 Quadrature-Carrier Multiplexing445

5.7 Other Variants of Amplitude Modulation446

5.8 Pulse-Amplitude Modulation451

5.9 Multiplexing455

5.10 Phase and Group Delays460

5.11 Exploring Concepts with MATLAB464

5.12 Summary474

Further Reading475

Additional Problems476

CHAPTER 6 Representing Signals by Using Continuous-Time Complex Exponentials: the Laplace Transform482

6.1 Introduction482

6.2 The Laplace Transform482

6.3 The Unilateral Laplace Transform490

6.4 Properties of the Unilateral Laplace Transform491

6.5 Inversion of the Unilateral Laplace Transform496

6.6 Solving Differential Equations with Initial Conditions501

6.7 Laplace Transform Methods in Circuit Analysis506

6.8 Properties of the Bilateral Laplace Transform509

6.9 Properties of the Region of Convergence512

6.10 Inversion of the Bilateral Laplace Transform516

6.11 The Transfer Function520

6.12 Causality and Stability523

6.13 Determining the Frequency Response from Poles and Zeros528

6.14 Exploring Concepts with MATLAB541

6.15 Summary544

Further Reading546

Additional Problems546

CHAPTER 7 Representing Signals by Using Discrete-Time Complex Exponentials: the z-Transform553

7.1 Introduction553

7.2 The z-Transform553

7.3 Properties of the Region of Convergence561

7.4 Properties of the z-Transform566

7.5 Inversion of the z-Transform572

7.6 The Transfer Function579

7.7 Causality and Stability582

7.8 Determining the Frequency Response from Poles and Zeros588

7.9 Computational Structures for Implementing Discrete-Time LTI Systems594

7.10 The Unilateral z-Transform598

7.11 Exploring Concepts with MATLAB602

7.12 Summary606

Further Reading606

Additional Problems607

CHAPTER 8 Application to Filters and Equalizers614

8.1 Introduction614

8.2 Conditions for Distortionless Transmission614

8.3 Ideal Low-Pass Filters616

8.4 Design of Filters623

8.5 Approximating Functions624

8.6 Frequency Transformations630

8.7 Passive Filters633

8.8 Digital Filters634

8.9 FIR Digital Filters635

8.10 IIR Digital Filters645

8.11 Linear Distortion649

8.12 Equalization650

8.13 Exploring Concepts with MATLAB653

8.14 Summary658

Further Reading659

Additional Problems660

CHAPTER 9 Application to Linear Feedback Systems663

9.1 Introduction663

9.2 What Is Feedback?663

9.3 Basic Feedback Concepts666

9.4 Sensitivity Analysis668

9.5 Effect of Feedback on Disturbance or Noise670

9.6 Distortion Analysis671

9.7 Summarizing Remarks on Feedback673

9.8 Operational Amplifiers673

9.9 Control Systems679

9.10 Transient Response of Low-Order Systems682

9.11 The Stability Problem685

9.12 Routh-Hurwitz Criterion688

9.13 Root Locus Method692

9.14 Nyquist Stability Criterion700

9.15 Bode Diagram707

9.16 Sampled-Data Systems711

9.17 Exploring Concepts with MATLAB721

9.18 Summary725

Further Reading725

Additional Problems727

CHAPTER 10 Epilogue737

10.1 Introduction737

10.2 Speech Signals: An Example of Nonstationarity738

10.3 Time-Frequency Analysis739

10.4 Nonlinear Systems750

10.5 Adaptive Filters757

10.6 Concluding Remarks760

Further Reading760

APPENDIX A Selected Mathematical Identities763

A.l Trigonometry763

A.2 Complex Numbers764

A.3 Geometric Series765

A.4 Definite Integrals765

A.5 Matrices766

APPENDIX B Partial-Fraction Expansions767

B.l Partial-Fraction Expansions of Continuous-Time Representations767

B.2 Partial-Fraction Expansions of Discrete-Time Representation770

APPENDIX C Tables of Fourier Representations and Properties773

C.l Basic Discrete-Time Fourier Series Pairs773

C.2 Basic Fourier Series Pairs774

C.3 Basic Discrete-Time Fourier Transform Pairs774

C.4 Basic Fourier Transform Pairs775

C.5 Fourier Transform Pairs for Periodic Signals775

C.6 Discrete-Time Fourier Transform Pairs for Periodic Signals776

C.7 Properties of Fourier Representations777

C.8 Relating the Four Fourier Representations779

C.9 Sampling and Aliasing Relationships779

APPENDIX D Tables of Laplace Transforms and Properties781

D.l Basic Laplace Transforms781

D.2 Laplace Transform Properties782

APPENDIX E Tables of z-Tansforms and Properties784

E.l Basic z-Transforms784

E.2 z-Transform Properties785

APPENDIX F Introduction to MATLAB786

F.l Basic Arithmetic Rules786

F.2 Variables and Variable Names787

F.3 Vectors and Matrices787

F.4 Plotting in MATLAB789

F.5 M-files790

F.6 Additional Help791

INDEX793