Signals, Systems, and Transforms, 5/e (GE-Paperback)
暫譯: 信號、系統與變換，第5版 (GE-平裝本)

描述

適用於電機與計算機工程系的二年級/三年級信號與系統課程。

本書提供了信號、系統及變換的理論與應用的清晰、全面的介紹。它介紹了信號與系統的數學背景，包括傅立葉變換、傅立葉級數、拉普拉斯變換、離散時間與離散傅立葉變換以及z變換。該書將MATLAB範例整合到信號與系統理論及應用的介紹中。

特色

伴隨網站增強學習 http://www.ee.washington.edu/class/SST_textbook/textbook.html

• 
  

  眾多互動範例和動畫演示，教授和學生均可使用以增強學習。

  
  

超過350道作業題目和150個範例

• 問題集的安排使得與共同概念相關的問題集被呈現。每組問題至少有一個問題的答案在附錄中提供。

系統與信號的數學理論 將數學理論與實際系統相關聯

• 
  

  使學生在可視化所呈現理論的應用時獲得動力。

  
  

MATLAB 整合於範例和問題中

• 
  

  通過實施MATLAB範例來加強學生對概念的理解。使學生學會使用MATLAB來協助解決章末問題。

  
  

關於雙邊拉普拉斯變換和z變換的短篇章節

• 
  

  允許教師向班級介紹這些主題。

  
  

重複引用的方程式

• 
  

  通過提供簡易參考來節省學生的時間。

  
  

結果驗證 為學生提供寶貴的問題解決練習

• 
  

  結果驗證要求幾乎所有問題的結果都需通過獨立程序進行驗證；這包括但不限於MATLAB。

  
  

選定答案的答案鍵使學生能檢查所選問題的作業

• 選定問題的答案在書末提供，以便學生能即時獲得對新概念理解的反饋。

所有問題的教師解答手冊

• 僅供教師使用。

本版新內容

•  第五章中傅立葉變換的性質的呈現已修訂和重新排列。


•  第六章新增有關主動濾波器設計與分析的小節。


• 連續時間信號的取樣和從樣本數據重建信號現在在第六章中合併。


• 第六章新增有關量化誤差的小節。


• 第七章新增使用拉普拉斯變換進行系統階躍響應計算與分析的小節。


• 第十一章新增使用z變換進行系統頻率響應計算與分析的小節。


•  第十二章新增範例，顯示使用離散時間傅立葉變換（DTFT）進行有限脈衝響應（FIR）濾波器的頻率響應分析。


• 第十二章新增範例，顯示使用離散傅立葉變換（DFT）實現FIR濾波器。


• 提供多個新範例和MATLAB® 應用。


• 所有章末問題集已修訂。每章的問題現在根據章節的適用部分進行分組。

Preface xvii
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 90
3.1 Impulse Representation of Continuous-Time Signals 91
3.2 Convolution for Continuous-Time LTI Systems 92
3.3 Properties of Convolution 105
3.4 Properties of Continuous-Time LTI Systems 108
Memoryless Systems, 109
Invertibility, 109
Causality, 110
Stability, 111
Unit Step Response, 112
3.5 Differential-Equation Models 113
Solution of Differential Equations, 115
General Case, 117
Relation to Physical Systems, 119
3.6 Terms in the Natural Response 120
Stability, 121
3.7 System Response for Complex-Exponential Inputs 124
Linearity, 124
Complex Inputs for LTI Systems, 125
Impulse Response, 129
3.8 Block Diagrams 130
Direct Form I, 134
Direct Form II, 134
nth-Order Realizations, 134
Practical Considerations, 136
Summary 139
Problems 149

4 Fourier Series 154
4.1 Approximating Periodic Functions 155
Periodic Functions, 155
Approximating Periodic Functions, 156
4.2 Fourier Series 160
Fourier Series, 161
Fourier Coefficients, 162
4.3 Fourier Series and Frequency Spectra 165
Frequency Spectra, 166
4.4 Properties of Fourier Series 175
4.5 System Analysis 178
4.6 Fourier Series Transformations 185
Amplitude Transformations, 186
Time Transformations, 188
Summary 190
Problems 191

5 The Fourier Transform 201
5.1 Definition of the Fourier Transform 201
5.2 Properties of the Fourier Transform 210
Linearity, 211
Time Scaling, 212
Time Shifting, 214
Time Reversal, 215
Time Transformation, 216
Duality, 218
Convolution, 220
Frequency Shifting, 221
Time Integration, 224
Time Differentiation, 226
Frequency Differentiation, 231
Symmetry, 232
Summary, 233
5.3 Fourier Transforms of Time Functions 233
DC Level, 233
Unit Step Function, 233
Switched Cosine, 234
Pulsed Cosine, 234
Exponential Pulse, 236
Fourier Transforms of Periodic Functions, 236
Summary, 241
5.4 Application of the Fourier Transform 241
Frequency Response of Linear Systems, 241
Frequency Spectra of Signals, 250
Summary, 252
5.5 Energy and Power Density Spectra 253
Energy Density Spectrum, 253
Power Density Spectrum, 256
Power and Energy Transmission, 258
Summary, 260
Summary 262
Problems 263

6 Applications of the Fourier Transform 272
6.1 I deal Filters 272
6.2  Real Filters 279
RC Low-Pass Filter, 280
Butterworth Filter, 282
Bandpass Filters, 288
Active Filters, 289
Summary, 291
6.3 Bandwidth Relationships 291
6.4 Sampling Continuous-Time Signals 295
Impulse Sampling, 296
Shannon’s Sampling Theorem, 299
Practical Sampling, 299
6.5  Reconstruction of Signals from Sample Data 300
Interpolating Function, 302
Digital-to-Analog Conversion, 304
Quantization Error, 306
6.6 Sinusoidal Amplitude Modulation 308
Frequency-Division Multiplexing, 317
6.7 Pulse-Amplitude Modulation 319
Time-Division Multiplexing, 321
Flat-Top PAM, 323
Summary 326
Problems 326

7 The Laplace Transform 336
7.1 Definitions of Laplace Transforms 337
7.2 Examples 340
7.3 Laplace Transforms of Functions 345
7.4 Laplace Transform Properties 349
Real Shifting, 350
Differentiation, 354
Integration, 356
7.5 Additional Properties 357
Multiplication by t, 357
Initial Value, 358
Final Value, 359
Time Transformation, 360
7.6 Response of LTI Systems 363
Initial Conditions, 363
Transfer Functions, 364
Convolution, 369
Transforms with Complex Poles, 371
Functions with Repeated Poles, 374
7.7 LTI Systems Characteristics 375
Causality, 375
Stability, 376
Invertibility, 378
Frequency Response, 379
Step Response, 380
7.8 Bilateral Laplace Transform 382
Region of Convergence, 384
Bilateral Transform from Unilateral Tables, 386
Inverse Bilateral Laplace Transform, 389
7.9 Relationship of the Laplace Transform to the Fourier Transform 391
Summary 392
Problems 393

8 State Variables for Continuous-Time Systems 401
8.1 State-Variable Modeling 402
8.2 Simulation Diagrams 406
8.3 Solution of State Equations 412
Laplace-Transform Solution, 412
Convolution Solution, 417
Infinite Series Solution, 418
8.4 Properties of the State-Transition Matrix 421
8.5 Transfer Functions 423
Stability, 425
8.6 Similarity Transformations 427
Transformations, 427
Properties, 433
Summary 435
Problems 437

9 Discrete-Time Signals and Systems 446
9.1 Discrete-Time Signals and Systems 448
Unit Step and Unit Impulse Functions, 450
Equivalent Operations, 452
9.2 Transformations of Discrete-Time Signals 453
Time Transformations, 454
Amplitude Transformations, 459
9.3 Characteristics of Discrete-Time Signals 462
Even and Odd Signals, 462
Signals Periodic in n, 465
Signals Periodic in , 468
9.4 Common Discrete-Time Signals 469
9.5 Discrete-Time Systems 475
Interconnecting Systems, 476
9.6 Properties of Discrete-Time Systems 478
Systems with Memory, 478
Invertibility, 479
Inverse of a System, 480
Causality, 480
Stability, 481
Time Invariance, 481
Linearity, 482
Summary 484
Problems 486

10 Discrete-Time Linear Time-Invariant Systems 495
10.1 Impulse Representation of Discrete-Time Signals 496
10.2 Convolution for Discrete-Time Systems 497
Properties of Convolution, 506
10.3 Properties of Discrete-Time LTI Systems 509
Memory, 510
Invertibility, 510
Causality, 510
Stability, 511
Unit Step Response, 513
10.4 Difference-Equation Models 514
Difference-Equation Models, 514
Classical Method, 516
Solution by Iteration, 521
10.5 Terms in the Natural Response 522
Stability, 523
10.6 Block Diagrams 525
Two Standard Forms, 527
10.7 System Response for Complex-Exponential Inputs 531
Linearity, 532
Complex Inputs for LTI Systems, 532
Stability, 537
Sampled Signals, 537
Impulse Response, 537
Summary 539
Problems 540

11 The z-Transform 552
11.1 Definitions of z-Transforms 552
11.2 Examples 555
Two z-Transforms, 555
Digital-Filter Example, 558
11.3 z-Transforms of Functions 560
Sinusoids, 561
11.4 z-Transform Properties 565
Real Shifting, 565
Initial and Final Values, 568
11.5 Additional Properties 570
Time Scaling, 570
Convolution in Time, 572
11.6 L TI System Applications 573
Transfer Functions, 573
Inverse z-Transform, 575
Complex Poles, 578
Causality, 580
Stability, 581
Invertibility, 584
Frequency Response, 585
11.7 Bilateral z-Transform 588
Bilateral Transforms, 592
Regions of Convergence, 594
Inverse Bilateral Transforms, 595
Summary 598
Problems 599

12 Fourier Transforms of Discrete-Time Signals 609
12.1 Discrete-Time Fourier Transform 610
z-Transform, 612
12.2 Properties of the Discrete-Time Fourier Transform 617
Periodicity, 618
Linearity, 619
Time Shift, 619
Frequency Shift, 620
Symmetry, 620
Time Reversal, 621
Convolution in Time, 621
Convolution in Frequency, 622
Multiplication by n, 623
Parseval’s Theorem, 623
12.3 Discrete-Time Fourier Transform of Periodic Sequences 624
12.4 Discrete Fourier Transform 630
Shorthand Notation for the DFT, 632
Frequency Resolution of the DFT, 632
Validity of the DFT, 634
Summary, 638
12.5 Fast Fourier Transform 638
Decomposition-in-Time Fast Fourier Transform Algorithm, 638
Decomposition-in-Frequency Fast Fourier Transform, 643
Summary, 646
12.6 Applications of the Discrete Fourier Transform 646
Calculation of Fourier Transforms, 646
Convolution, 654
Filtering, 663
Correlation, 671
Energy Spectral Density Estimation, 677
Summary, 678
12.7 The Discrete Cosine Transform, 678
Summary 683
Problems 684

13 State Variables for Discrete-Time Systems 692
13.1 State-Variable Modeling 693
13.2 Simulation Diagrams 697
13.3 Solution of State Equations 703
Recursive Solution, 703
z-Transform Solution, 705
13.4 Properties of the State Transition Matrix 710
13.5 Transfer Functions 712
Stability, 714
13.6 Similarity Transformations 715
Properties, 719
Summary 720
Problems 721

Appendices 718
A. Integrals and Trigonometric Identities 730
Integrals, 730
Trigonometric Identities, 731
B. Leibnitz’s and L’Hôpital’s Rules 732
Leibnitz’s Rule, 732
L’Hôpital’s Rule, 733
C. Summation Formulas for Geometric Series 734
D. Complex Numbers and Euler’s Relation 735
Complex-Number Arithmetic, 736
Euler’s Relation, 739
Conversion Between Forms, 740
E. Solution of Differential Equations 742
Complementary Function, 742
Particular Solution, 743
General Solution, 744
Repeated Roots, 744
F. Partial-Fraction Expansions 746
G.  Review of Matrices 749
Algebra of Matrices, 753
Other Relationships, 754
H. Answers to Selected Problems 756
I. Signals and Systems References 770
Index

Preface xvii

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 90

3.1 Impulse Representation of Continuous-Time Signals 91

3.2 Convolution for Continuous-Time LTI Systems 92

3.3 Properties of Convolution 105

3.4 Properties of Continuous-Time LTI Systems 108

Memoryless Systems, 109

Invertibility, 109

Causality, 110

Stability, 111

Unit Step Response, 112

3.5 Differential-Equation Models 113

Solution of Differential Equations, 115

General Case, 117

Relation to Physical Systems, 119

3.6 Terms in the Natural Response 120

Stability, 121

3.7 System Response for Complex-Exponential Inputs 124

Linearity, 124

Complex Inputs for LTI Systems, 125

Impulse Response, 129

3.8 Block Diagrams 130

Direct Form I, 134

Direct Form II, 134

nth-Order Realizations, 134

Practical Considerations, 136

Summary 139

Problems 149



4 Fourier Series 154

4.1 Approximating Periodic Functions 155

Periodic Functions, 155

Approximating Periodic Functions, 156

4.2 Fourier Series 160

Fourier Series, 161

Fourier Coefficients, 162

4.3 Fourier Series and Frequency Spectra 165

Frequency Spectra, 166

4.4 Properties of Fourier Series 175

4.5 System Analysis 178

4.6 Fourier Series Transformations 185

Amplitude Transformations, 186

Time Transformations, 188

Summary 190

Problems 191



5 The Fourier Transform 201

5.1 Definition of the Fourier Transform 201

5.2 Properties of the Fourier Transform 210

Linearity, 211

Time Scaling, 212

Time Shifting, 214

Time Reversal, 215

Time Transformation, 216

Duality, 218

Convolution, 220

Frequency Shifting, 221

Time Integration, 224

Time Differentiation, 226

Frequency Differentiation, 231

Symmetry, 232

Summary, 233

5.3 Fourier Transforms of Time Functions 233

DC Level, 233

Unit Step Function, 233

Switched Cosine, 234

Pulsed Cosine, 234

Exponential Pulse, 236

Fourier Transforms of Periodic Functions, 236

Summary, 241

5.4 Application of the Fourier Transform 241

Frequency Response of Linear Systems, 241

Frequency Spectra of Signals, 250

Summary, 252

5.5 Energy and Power Density Spectra 253

Energy Density Spectrum, 253

Power Density Spectrum, 256

Power and Energy Transmission, 258

Summary, 260

Summary 262

Problems 263



6 Applications of the Fourier Transform 272

6.1 I deal Filters 272

6.2  Real Filters 279

RC Low-Pass Filter, 280

Butterworth Filter, 282

Bandpass Filters, 288

Active Filters, 289

Summary, 291

6.3 Bandwidth Relationships 291

6.4 Sampling Continuous-Time Signals 295

Impulse Sampling, 296

Shannon’s Sampling Theorem, 299

Practical Sampling, 299

6.5  Reconstruction of Signals from Sample Data 300

Interpolating Function, 302

Digital-to-Analog Conversion, 304

Quantization Error, 306

6.6 Sinusoidal Amplitude Modulation 308

Frequency-Division Multiplexing, 317

6.7 Pulse-Amplitude Modulation 319

Time-Division Multiplexing, 321

Flat-Top PAM, 323

Summary 326

Problems 326



7 The Laplace Transform 336

7.1 Definitions of Laplace Transforms 337

7.2 Examples 340

7.3 Laplace Transforms of Functions 345

7.4 Laplace Transform Properties 349

Real Shifting, 350

Differentiation, 354

Integration, 356

7.5 Additional Properties 357

Multiplication by t, 357

Initial Value, 358

Final Value, 359

Time Transformation, 360

7.6 Response of LTI Systems 363

Initial Conditions, 363

Transfer Functions, 364

Convolution, 369

Transforms with Complex Poles, 371

Functions with Repeated Poles, 374

7.7 LTI Systems Characteristics 375

Causality, 375

Stability, 376

Invertibility, 378

Frequency Response, 379

Step Response, 380

7.8 Bilateral Laplace Transform 382

Region of Convergence, 384

Bilateral Transform from Unilateral Tables, 386

Inverse Bilateral Laplace Transform, 389

7.9 Relationship of the Laplace Transform to the Fourier Transform 391

Summary 392

Problems 393



8 State Variables for Continuous-Time Systems 401

8.1 State-Variable Modeling 402

8.2 Simulation Diagrams 406

8.3 Solution of State Equations 412

Laplace-Transform Solution, 412

Convolution Solution, 417

Infinite Series Solution, 418

8.4 Properties of the State-Transition Matrix 421

8.5 Transfer Functions 423

Stability, 425

8.6 Similarity Transformations 427

Transformations, 427

Properties, 433

Summary 435

Problems 437



9 Discrete-Time Signals and Systems 446

9.1 Discrete-Time Signals and Systems 448

Unit Step and Unit Impulse Functions, 450

Equivalent Operations, 452

9.2 Transformations of Discrete-Time Signals 453

Time Transformations, 454

Amplitude Transformations, 459

9.3 Characteristics of Discrete-Time Signals 462

Even and Odd Signals, 462

Signals Periodic in n, 465

Signals Periodic in , 468

9.4 Common Discrete-Time Signals 469

9.5 Discrete-Time Systems 475

Interconnecting Systems, 476

9.6 Properties of Discrete-Time Systems 478

Systems with Memory, 478

Invertibility, 479

Inverse of a System, 480

Causality, 480

Stability, 481

Time Invariance, 481

Linearity, 482

Summary 484

Problems 486



10 Discrete-Time Linear Time-Invariant Systems 495

10.1 Impulse Representation of Discrete-Time Signals 496

10.2 Convolution for Discrete-Time Systems 497

Properties of Convolution, 506

10.3 Properties of Discrete-Time LTI Systems 509

Memory, 510

Invertibility, 510

Causality, 510

Stability, 511

Unit Step Response, 513

10.4 Difference-Equation Models 514

Difference-Equation Models, 514

Classical Method, 516

Solution by Iteration, 521

10.5 Terms in the Natural Response 522

Stability, 523

10.6 Block Diagrams 525

Two Standard Forms, 527

10.7 System Response for Complex-Exponential Inputs 531

Linearity, 532

Complex Inputs for LTI Systems, 532

Stability, 537

Sampled Signals, 537

Impulse Response, 537

Summary 539

Problems 540



11 The z-Transform 552

11.1 Definitions of z-Transforms 552

11.2 Examples 555

Two z-Transforms, 555

Digital-Filter Example, 558

11.3 z-Transforms of Functions 560

Sinusoids, 561

11.4 z-Transform Properties 565

Real Shifting, 565

Initial and Final Values, 568

11.5 Additional Properties 570

Time Scaling, 570

Convolution in Time, 572

11.6 L TI System Applications 573

Transfer Functions, 573

Inverse z-Transform, 575

Complex Poles, 578

Causality, 580

Stability, 581

Invertibility, 584

Frequency Response, 585

11.7 Bilateral z-Transform 588

Bilateral Transforms, 592

Regions of Convergence, 594

Inverse Bilateral Transforms, 595

Summary 598

Problems 599



12 Fourier Transforms of Discrete-Time Signals 609

12.1 Discrete-Time Fourier Transform 610

z-Transform, 612

12.2 Properties of the Discrete-Time Fourier Transform 617

Periodicity, 618

Linearity, 619

Time Shift, 619

Frequency Shift, 620

Symmetry, 620

Time Reversal, 621

Convolution in Time, 621

Convolution in Frequency, 622

Multiplication by n, 623

Parseval’s Theorem, 623

12.3 Discrete-Time Fourier Transform of Periodic Sequences 624

12.4 Discrete Fourier Transform 630

Shorthand Notation for the DFT, 632

Frequency Resolution of the DFT, 632

Validity of the DFT, 634

Summary, 638

12.5 Fast Fourier Transform 638

Decomposition-in-Time Fast Fourier Transform Algorithm, 638

Decomposition-in-Frequency Fast Fourier Transform, 643

Summary, 646

12.6 Applications of the Discrete Fourier Transform 646

Calculation of Fourier Transforms, 646

Convolution, 654

Filtering, 663

Correlation, 671

Energy Spectral Density Estimation, 677

Summary, 678

12.7 The Discrete Cosine Transform, 678

Summary 683

Problems 684



13 State Variables for Discrete-Time Systems 692

13.1 State-Variable Modeling 693

13.2 Simulation Diagrams 697

13.3 Solution of State Equations 703

Recursive Solution, 703

z-Transform Solution, 705

13.4 Properties of the State Transition Matrix 710

13.5 Transfer Functions 712

Stability, 714

13.6 Similarity Transformations 715

Properties, 719

Summary 720

Problems 721



Appendices 718

A. Integrals and Trigonometric Identities 730

Integrals, 730

Trigonometric Identities, 731

B. Leibnitz’s and L’Hôpital’s Rules 732

Leibnitz’s Rule, 732

L’Hôpital’s Rule, 733

C. Summation Formulas for Geometric Series 734

D. Complex Numbers and Euler’s Relation 735

Complex-Number Arithmetic, 736

Euler’s Relation, 739

Conversion Between Forms, 740

E. Solution of Differential Equations 742

Complementary Function, 742

Particular Solution, 743

General Solution, 744

Repeated Roots, 744

F. Partial-Fraction Expansions 746

G.  Review of Matrices 749

Algebra of Matrices, 753

Other Relationships, 754

H. Answers to Selected Problems 756

I. Signals and Systems References 770

Index