Signals, Systems, and Transforms, 5/e (GE-Paperback)

描述

適用於電機與電腦工程系的大二/大三級信號與系統課程。本教材清晰而全面地介紹了信號、系統和轉換的理論和應用。它提供了信號和系統的數學背景，包括傅立葉變換、傅立葉級數、拉普拉斯變換、離散時間和離散傅立葉變換以及z變換。本教材將MATLAB示例融入信號和系統理論和應用的介紹中。

特點

配套網站增強學習體驗：http://www.ee.washington.edu/class/SST_textbook/textbook.html

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  大量互動示例和動畫演示，教授和學生都可以使用以增強學習效果。

  
  

超過350個作業問題和150個示例

• 問題集按照相關概念分組，附錄中提供了每組問題中至少一個問題的答案。

系統和信號的數學理論將數學理論與實際系統相關聯

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  讓學生能夠輕鬆地將所學理論應用於實際應用中，激發學生的學習動機。

  
  

MATLAB集成到示例和問題中

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  通過實施MATLAB示例來加深學生對概念的理解，使學生學會使用MATLAB來解決章末問題。

  
  

關於雙邊拉普拉斯和z變換的簡短部分

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  讓教師能夠向學生介紹這些主題。

  
  

重複引用的方程式

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  通過提供方便的參考，節省學生的時間。

  
  

結果驗證為學生提供寶貴的問題解決實踐

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  結果驗證要求幾乎所有問題的結果都通過獨立的程序驗證，包括但不限於MATLAB。

  
  

選定答案的答案鍵允許學生檢查所選問題的答案

• 在教材末尾提供了選定問題的答案，使學生能夠立即獲得對新概念的理解反饋。

所有問題的教師解答手冊

• 僅供教師使用。

本版新增內容

•  修訂並重新排列了傅立葉變換的性質介紹，放在第5章。


•  在第6章新增了關於主動濾波器設計和分析的新小節。


• 將連續時間信號的取樣和從樣本數據重建信號的內容移到第6章。


• 在第6章新增了關於量化誤差的新小節。


• 在第7章新增了使用拉普拉斯變換計算和分析系統階跃響應的新小節。


• 在第11章新增了使用z變換計算和分析系統頻率響應的新小節。


•  在第12章新增了一個新示例，展示了使用離散時間傅立葉變換（DTFT）對有限脈衝響應（FIR）濾波器進行頻率響應分析。


• 在第12章新增了一個新示例，展示了使用離散傅立葉變換（DFT）實現FIR濾波器。


• 提供了多個新示例和MATLAB應用。


• 修訂了所有章末問題集。

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

前言 xvii
1 引言 1
1.1 建模 1
1.2 連續時間物理系統 4
電路, 4
運算放大器電路, 6
簡單擺錘, 9
直流電源, 10
類比系統, 12
1.3 取樣器和離散時間物理系統 14
模數轉換器, 14
數值積分, 16
畫中畫, 17
光碟, 18
電話系統中的取樣, 19
數據采集系統, 21
1.4 MATLAB 和 Simulink 22

2 連續時間信號和系統 23
2.1 連續時間信號的轉換 24
時間轉換, 24
幅度轉換, 30
2.2 信號特性 32
奇偶信號, 32
周期信號, 34
2.3 工程中常見的信號 39
2.4 奇異函數 45
單位階躍函數, 45
單位脈沖函數, 49
2.5 信號的數學函數 54
2.6 連續時間系統 59
系統互連, 61
反饋系統, 64
2.7 連續時間系統的特性 65
穩定性, 69
線性性, 74
摘要 76
問題 78
3 連續時間線性時不變系統 90
3.1 連續時間信號的脈沖表示 91
3.2 連續時間 LTI 系統的卷積 92
3.3 卷積的特性 105
3.4 連續時間 LTI 系統的特性 108
無記憶系統, 109
可逆性, 109
因果性, 110
穩定性, 111
單位階躍響應, 112
3.5 微分方程模型 113
微分方程的解, 115
一般情況, 117
與物理系統的關係, 119
3.6 自然響應中的項 120
穩定性, 121
3.7 複指數輸入的系統響應 124
線性性, 124
LTI 系統的複指數輸入, 125
脈沖響應, 129
3.8 方塊圖 130
直接形式 I, 134
直接形式 II, 134
n 階實現, 134
實際考慮, 136
摘要 139
問題 149

4 傅立葉級數 154
4.1 逼近周期函數 155
周期函數, 155
逼近周期函數, 156
4.2 傅立葉級數 160
傅立葉級數, 161
傅立葉系數, 162
4.3 傅立葉級數和頻譜 165
頻譜, 166
4.4 傅立葉級數的特性 175
4.5 系統分析 178
4.6 傅立葉級數變換 185
幅度變換, 186
時間變換, 188
摘要 190
問題 191

5 傅立葉變換 201
5.1 傅立葉變換的定義 201
5.2 傅立葉變換的特性 210
線性性, 211
時間縮放, 212
時間平移, 214
時間反轉, 215
時間變換, 216
對偶性, 218
卷積, 220
頻率平移, 221
時間積分, 224
時間微分, 226
頻率微分, 231
對稱性, 232
摘要, 233
5.3 時間函數的傅立葉變換 233
直流水平, 233
單位階躍函數, 233
開關餘弦, 234
脈沖餘弦, 234
指數脈沖, 236
周期函數的傅立葉變換, 236
摘要, 241
5.4 傅立葉變換的應用 241
線性系統的頻率響應, 241
信號的頻譜, 250
摘要, 252
5.5 能量和功率密度譜 253
能量密度譜, 253
功率密度譜, 256
功率和能量傳輸, 258
摘要, 260
摘要 262
問題 263

6 傅立葉變換的應用 272