信号系统和变换 英文版第4版PDF电子书下载

1 INTRODUCTION 1

1.1 Modeling　 1

1.2 Continuous-Time Physical Systems　 4

Electric Circuits,　 4

Operational Amplifier Circuits,　 6

Simple Pendulum,　 9

DC Power Supplies,　 10

Analogous Systems,　 12

1.3 Samplers and Discrete-Time Physical Systems　 14

Analog-to-Digital Converter,　 14

Numerical Integration,　 16

Picture in a Picture,　 17

Compact Disks,　 18

Sampling in Telephone Systems,　 19

Data-Acquisition System,　 21

1.4 MATLAB and SIMULINK　 22

2 CONTINUOUS-TIME SIGNALS AND SYSTEMS 23

2.1　Transformations of Continuous-Time Signals　 24

Time Transformations,　 24

Amplitude Transformations,　 30

2.2 Signal Characteristics　 32

Even and Odd Signals, 32

Periodic Signals,　 34

2.3 Common Signals in Engineering　 39

2.4 Singularity Functions　 45

Unit Step Function,　 45

Unit Impulse Function,　 49

2.5 Mathematical Functions for Signals　 54

2.6 Continuous-Time Systems　 59

Interconnecting Systems,　 61

Feedback System,　 64

2.7　Properties of Continuous-Time Systems　 65

Stability,　 69

Linearity,　 74

Summary 76

Problems　 78

3 CONTINUOUS-TIME LINEAR TIME-INVARIANT SYSTEMS 89

3.1 Impulse Representation of Continuous-Time Signals　 90

3.2 Convolution for Continuous-Time LTI Systems　 91

3.3　Properties of Convolution　 104

3.4　Properties of Continuous-Time LTI Systems　 107

Memoryless Systems,　 108

Invertibility,　 108

Causality,　 109

Stability,　 110

Unit Step Response,　 111

3.5　Differential-Equation Models　 112

Solution of Differential Equations,　 114

General Case,　 116

Relation to Physical Systems,　 118

3.6　Terms in the Natural Response　 119

Stability,　 120

3.7 System Response for Complex-Exponential Inputs　 123

Linearity, 123

Complex Inputs for LTI Systems,　 124

Impulse Response,　 128

3.8 Block Diagrams　 129

Direct Form Ⅰ，　 133

Direct Form Ⅱ，　 133

nth-Order Realizations,　 133

Practical Considerations, 135

Summary　 137

Problems　 139

4 FOURIER SERIES 150

4.1 Approximating Periodic Functions　 151

Periodic Functions,　 152

Approximating Periodic Functions,　 152

4.2 Fourier Series　 156

Fourier Series,　 157

Fourier Coefficients,　 158

4.3 Fourier Series and Frequency Spectra　 161

Frequency Spectra,　 162

4.4　Properties of Fourier Series　 171

4.5 System Analysis　 174

4.6 Fourier Series Transformations　 181

Amplitude Transformations,　 182

Time Transformations,　 184

Summary　 186

Problems 187

5　THE FOURIER TRANSFORM 197

5.1　Definition of the Fourier Transform　 197

5.2　Properties of the Fourier Transform　 206

Linearity,　 206

Time Scaling,　 208

Time Shifting,　 211

Time Transformation,　 212

Duality,　 213

Convolution,　 216

Frequency Shifting,　 217

Time Differentiation,　 219

Time Integration,　 224

Frequency Differentiation,　 227

Summary,　 227

5.3 Fourier Transforms of Time Functions　 228

DC Level,　 228

Unit Step Function,　 228

Switched Cosine,　 229

Pulsed Cosine,　 229

Exponential Pulse,　 231

Fourier Transforms of Periodic Functions,　 231

Summary,　 237

5.4 Sampling Continuous-Time Signals　 237

Impulse Sampling,　 238

Shannon's Sampling Theorem,　 240

Practical Sampling,　 242

5.5 Application of the Fourier Transform　 243

Frequency Response of Linear Systems,　 243

Frequency Spectra of Signals,　 252

Summary,　 255

5.6 Energy and Power Density Spectra　 255

Energy Density Spectrum,　 255

Power Density Spectrum,　 258

Power and Energy Transmission,　 261

Summary,　 263

Summary　 264

Problems 266

6 APPLICATIONS OF THE FOURIER TRANSFORM 274

6.1 Ideal Filters　 274

6.2 Real Filters　 281

RC Low-Pass Filter,　 282

Butterworth Filter,　 284

Chebyschev and Elliptic Filters,　 290

Bandpass Filters,　 294

Summary,　 295

6.3 Bandwidth Relationships　 295

6.4 Reconstruction of Signals from Sample Data　 299

Interpolating Function,　 301

Digital-to-Analog Conversion,　 303

6.5 Sinusoidal Amplitude Modulation　 306

Frequency-Division Multiplexing,　 315

6.6　Pulse-Amplitude Modulation　 317

Time-Division Multiplexing,　 319

Flat-Top PAM,　 321

Summary　 324

Problems　 324

7　THE LAPLACE TRANSFORM 335

7.1　Definitions of Laplace Transforms　 336

7.2 Examples　 339

7.3　Laplace Transforms of Functions　 344

7.4　Laplace Transform Properties　 348

Real Shifting,　 349

Differentiation,　 353

Integration,　 355

7.5 Additional Properties　 356

Multiplication by t,　 356

Initial Value,　 357

Final Value,　 358

Time Transformation,　 359

7.6 Response of LTI Systems　 362

Initial Conditions,　 362

Transfer Functions,　 363

Convolution,　 368

Trausforms with Complex Poles,　 370

Functions with Repeated Poles,　 373

7.7　LTI Systems Characteristics　 374

Causality,　 374

Stability,　 375

Invertibility,　 377

Frequency Response,　 378

7.8 Bilateral Laplace Transform　 380

Region of Convergence,　 382

Bilateral Transform from Unilateral Tables,　 384

Inverse Bilateral Laplace Transform,　 386

7.9 Relationship of the Laplace Transform to the Fourier Transform　 388

Summary 389

Problems 390

8 STATE VARIABLES FOR CONTINUOUS-TIME SYSTEMS 398

8.1 State-Variable Modeling　 399

8.2 Simulation Diagrams　 403

8.3 Solution of State Equations　 408

Laplace-Transform Solution,　 409

Convolution Solution,　 414

Infinite Series Solution,　 415

8.4　Properties of the State-Transition Matrix　 418

8.5　Transfer Functions　 420

Stability,　 422

8.6 Similarity Transformations　 424

Transformations,　 424

Properties,　 430

Summary　 432

Prohlems　 434

9　DISCRETE-TIME SIGNALS AND SYSTEMS　 443

9.1　Discrete-Time Signals and Systems　 445

Unit Step and Unit Impulse Functions,　 447

Equivalent Operations,　 449

9.2　Transformations of Discrete-Time Signals　 450

Time Transformations,　 451

Amplitude Transformations,　 456

9.3 Characteristics of Discrete-Time Signals　 459

Even and Odd Signals,　 459

Signals Periodic in n,　 462

Signals Periodic in Ω，　 465

9.4 Common Discrete-Time Signals　 466

9.5　Discrete-Time Systems　 472

Interconnecting Systems,　 473

9.6　Properties of Discrete-Time Systems　 475

Systems with Memory,　 475

Invertibility,　 476

Inverse of a System,　 477

Causality,　 477

Stability,　 478

Time Invariance,　 478

Linearity,　 479

Summary　 481

Problems　 483

10　DISCRETE-TIME LINEAR TIME-INVARIANT SYSTEMS　 491

10.1 Impulse Representation of Discrete-Time Signals　 492

10.2 Convolution for Discrete-Time Systems　 493

Properties of Convolution,　 502

10.3　Properties of Discrete-Time LTI Systems　 505

Memory,　 506

Invertibility,　 506

Causality,　 506

Stability,　 507

Unit Step Response,　 509

10.4　Difference-Equation Models　 510

Difference-Equation Models,　 510

Classical Method,　 512

Solution by Iteration,　 517

10.5　Terms in the Natural Response　 518

Stability,　 519

10.6 Block Diagrams　 521

Two Standard Forms,　 523

10.7 System Response for Complex-Exponential Inputs　 527

Linearity,　 528

Complex Inputs for LTI Systems,　 528

Stability,　 533

Sampled Signals,　 533

Impulse Response,　 533

Summary　 535

Problems　 536

11　THE z-TRANSFORM　 546

11.1　Definitions of z-Transforms　 547

11.2 Examples　 549

Two z-Transforms,　 549

Digital-Filter Example,　 552

11.3 z-Transforms of Functions　 555

Sinusoids,　 556

11.4 z-Transform Properties　 559

Real Shifting,　 559

Initial and Final Values,　 562

11.5 Additional Properties　 564

Time Scaling,　 564

Convolution in Time,　 566

11.6　LTI System Applications　 568

Transfer Functions,　 568

Inverse z-Transform,　 570

Complex Poles,　 573

Causality,　 575

Stability,　 575

Invertibility,　 578

11.7 Bilateral z-Transform　 579

Bilateral Transforms,　 584

Regions of Convergence, 586

Inverse Bilateral Transforms,　 586

Summary　 589

Problems　 590

12　FOURIER TRANSFORMS OF DISCRETE-TIME SIGNALS 599

12.1　Discrete-Time Fourier Transform　 600

z-Transform,　 602

12.2　Properties of the Discrete-Time Fourier Transform　 605

Periodicity,　 605

Linearity,　 606

Time Shift,　 606

Frequency Shift,　 607

Symmetry,　 608

Time Reversal,　 608

Convolution in Time,　 609

Convolution in Frequency,　 609

Multiplication by n,　 610

Parseval's Theorem,　 610

12.3　Discrete-Time Fourier Transform of Periodic Sequences　 611

12.4　Discrete Fourier Transform　 617

Shorthand Notation for the DFT,　 620

Frequency Resolution of the DFT,　 621

Validity of the DFT,　 622

Summary,　 626

12.5 Fast Fourier Transform　 627

Decomposition-in-Time Fast Fourier Transform Algorithm,　 627

Decomposition-in-Frequency Fast Fourier Transform,　 632

Summary,　 635

12.6 Applications of the Discrete Fourier Transform　 635

Caleulation of Fourier Transforms,　 635

Convolution,　 646

Filtering,　 653

Correlation,　 660

Energy Spectral Density Estimation,　 666

Summary,　 667

12.7　The Discrete Cosine Transform,　 667

Summary　 672

Problems　 674

13　STATE VARIABLES FOR DISCRETE-TIME SYSTEMS 681

13.1 State-Variable Modeling　 682

13.2 Simulation Diagrams　 686

13.3 Solution of State Equations　 692

Recursive Solution,　 692

z-Transform Solution,　 694

13.4　Properties of the State Transition Matrix 699

13.5　Transfer Functions　 701

Stability,　 703

13.6 Similarity Transformations　 704

Properties,　 708

Summary　 709

Problems　 710

APPENDICES 718

A．Integrals and Trigonometric Identities　 718

Integrals,　 718

Trigonometric Identities,　 719

B．Leibnitz's and L'H？pital's Rules　 720

Leibnitz's Rule,　 720

L'H？pital's Rule,　 721

C．Summation Formulas for Geometric Series　 722

D．Complex Numbers and Euler's Relation　 723

Complex-Number Arithmetic,　 724

Euler's Relation,　 727

Conversion Between Forms,　 728

E．Solution of Differential Equations　 730

Complementary Function,　 730

Particular Solution,　 731

General Solution,　 732

Repeated Roots,　 732

F．Partial-Fraction Expansions　 734

G．Review of Matrices　 737

Algebra of Matrices,　 741

Other Relationships,　 742

H．Answers to Selected Problems　 744

I．Signals and Systems References　 760

INDEX 765