信号系统和变换 英文版第4版【2025|PDF|Epub|mobi|kindle电子书版本百度云盘下载】

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1 INTRODUCTION1

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 SYSTEMS23

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

Summary76

Problems　78

3 CONTINUOUS-TIME LINEAR TIME-INVARIANT SYSTEMS89

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 SERIES150

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

Problems187

5　THE FOURIER TRANSFORM197

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

Problems266

6 APPLICATIONS OF THE FOURIER TRANSFORM274

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 TRANSFORM335

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

Summary389

Problems390

8 STATE VARIABLES FOR CONTINUOUS-TIME SYSTEMS398

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 SIGNALS599

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 SYSTEMS681

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 Matrix699

13.5　Transfer Functions　701

Stability,　703

13.6 Similarity Transformations　704

Properties,　708

Summary　709

Problems　710

APPENDICES718

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

INDEX765