內容簡介
《信號與係統(第二版 英文版)》是美國麻省理工學院(MIT)的經典教材之一,討論瞭信號與係統分析的基本理論、基本分析方法及其應用。全書共分11章,主要講述瞭綫性係統的基本理論、信號與係統的基本概念、綫性時不變係統、連續與離散信號的傅裏葉錶示、傅裏葉變換以及時域和頻域係統的分析方法等內容。《信號與係統(第二版 英文版)》作者使用瞭大量在濾波、采樣、通信和反饋係統中的實例,並行討論瞭連續係統、離散係統、時域係統和頻域係統的分析方法,使讀者能透徹地理解各種信號係統的分析方法並比較其異同。
目錄
CONTENTS
1 SIGNALS AND SYSTEMS 1
1.0 Introduction 1
1.1 Continuous-Time and Discrete-Time Signals 1
1.1.1 Examples and Mathematical Representation 1
1.1.2 Signal Energy and Power 5
1.2 Transformations of the Independent Variable 7
1.2.1 Examples of Transformations of the Independent Variable 8
1.2.2 Periodic Signals 11
1.2.3 Even and Odd Signals 13
1.3 Exponential and Sinusoidal Signals 14
1.3.1 Continuous-Time Complex Exponential and Sinusoidal Signals 15
1.3.2 Discrete-Time Complex Exponential and Sinusoidal Signals 21
1.3.3 Periodicity Properties of Discrete-Time Complex Exponentials 25
1.4 The Unit Impulse and Unit Step Functions 30
1.4.1 The Discrete-Time Unit Impulse and Unit Step Sequences 30
1.4.2 The Continuous-Time Unit Step and Unit Impulse Functions 32
1.5 Continuous-Time and Discrete-Time Systems 38
1.5.1 Simple Examples of Systems 39
1.5.2 Interconnections of Systems 41
1.6 Basic System Properties 44
1.6.1 Systems with and without Memory 44
1.6.2 Invertibility and Inverse Systems 45
1.6.3 Causality 46
1.6.4 Stability 48
1.6.5 Time Invariance 50
1.6.6 Linearity 53
1.7 Summary 56
Problems 57
2 LINEAR TIME-INVARIANT SYSTEMS 74
2.0 Introduction 74
2.1 Discrete-Time LTI Systems: The Convolution Sum 75
2.1.1 The Representation of Discrete-Time Signals in Terms
of Impulses 75
2.1.2 The Discrete-Time Unit Impulse Response and the Convolution-Sum
Representation of LTI Systems 77
2.2 Continuous-Time LTI Systems: The Convolution Integral 90
2.2.1 The Representation of Continuous-Time Signals in Terms
of Impulses 90
2.2.2 The Continuous-Time Unit Impulse Response and the Convolution
Integral Representation of LTI Systems 94
2.3 Properties of Linear Time-invariant Systems 103
2.3.1 The Commutative Property 104
2.3.2 The Distributive Property 104
2.3.3 The Associative Property 107
2.3.4 LTI Systems with and without Memory 108
2.3.5 Invertibility of LTI Systems 109
2.3.6 Causality for LTI Systems 112
2.3.7 Stability for LTI Systems 113
2.3.8 The Unit Step Response of an LTI System 115
2.4 Causal LTI Systems Described by Differential and Difference
Equations 116
2.4.1 Linear Constant-Coefficient Differential Equations 117
2.4.2 Linear Constant-Coefficient Difference Equations 121
2.4.3 Block Diagram Representations of First-Order Systems Described
by Differential and Difference Equations 124
2.5 Singularity Functions 127
2.5.1 The Unit Impulse as an Idealized Short Pulse 128
2.5.2 Defining the Unit Impulse through Convolution 131
2.5.3 Unit Doublets and Other Singularity Functions 132
2.6 Summary 137
Problems 137
3 FOURIER SERIES REPRESENTATION OF PERIODIC SIGNALS 177
3.0 Introduction 177
3.1 A Historical Perspective 178
3.2 The Response of LTI Systems to Complex Exponentials 182
3.3 Fourier Series Representation of Continuous-Time
Periodic Signals 186
3.3.1 Linear Combinations of Harmonically Related Complex
Exponentials 186
3.3.2 Determination of the Fourier Series Representation
of a Continuous-Time Periodic Signal 190
3.4 Convergence of the Fourier Series 195
3.5 Properties of Continuous-Time Fourier Series 202
3.5.1 Linearity 202
3.5.2 Time Shifting 202
3.5.3 Time Reversal 203
3.5.4 Time Scaling 204
3.5.5 Multiplication 204
3.5.6 Conjugation and Conjugate Symmetry 204
3.5.7 Parseval's Relation for Continuous-Time Periodic Signals 205
3.5.8 Summary of Properties of the Continuous-Time Fourier Series 205
3.5.9 Examples 205
3.6 Fourier Series Representation of Discrete-Time
Periodic Signals 211
3.6.1 Linear Combinations of Harmonically Related Complex
Exponentials 211
3.6.2 Determination of the Fourier Series Representation of a
Periodic Signal 212
3.7 Properties of Discrete-Time Fourier Series 221
3.7.1 Multiplication 222
3.7.2 First Difference 222
3.7.3 Parseval's Relation for Discrete-Time Periodic Signals 223
3.7.4 Examples 223
3.8 Fourier Series and LTI Systems 226
3.9 Filtering 231
3.9.1 Frequency-Shaping Filters 232
3.9.2 Frequency-Selective Filters 236
3.10 Examples of Continuous-Time Filters Described by
Differential Equations 239
3.10.1 A Simple RC Lowpass Filter 239
3.10.2 A Simple RC Highpass Filter 241
3.11 Examples of Discrete-Time Filters Described by
Difference Equations 244
3.11.1 First-Order Recursive Discrete-Time Filters 244
3.11.2 Nonrecursive Discrete-Time Filters 245
3.12 Summary 249
Problems 250
4 THE CONTINUOUS-TIME FOURIER TRANSFORM 2,84
4.0 Introduction 284
4.1 Representation of Aperiodic Signals: The Continuous-Time
Fourier Transform 285
4.1.1 Development of the Fourier Transform Representation
of an Aperiodic.Signal 285
4.1.2 Convergence of Fourier Transforms 289
4.1.3 Examples of Continuous-Time Fourier Transforms 290
4.2 The Fourier Transform for Periodic Signals 296
4.3 Properties of the Continuous-Time Fourier Transform 300
4.3.1 Linearity 301
4.3.2 Time Shifting 301
4.3.3 Conjugation and Conjugate Symmetry 303
4.3.4 Differentiation and Integration 306
4.3.5 Time and Frequency Scaling 308
4.3.6 Duality 309
4.3.7 Parseval's Relation 312
4.4 The Convolution Property 314
4.4.1 Examples 317
4.5 The Multiplication Property 322
4.5.1 Frequency-Selective Filtering with Variable Center Frequenc) 325
4.6 Tables of Fourier Properties and of Basic Fourier
Transform Pairs 328
4.7 Systems Characterized by Linear Constant-Coefficient
Differential Equations 330
4.8 Summary 333
Problems 334
5 THE DISCRETE-TIME FOURIER TRANSFORM 358
5.0 Introduction 358
5.1 Representation of Aperiodic Signals: The Discrete-Time
Fourier Transform 359
5.1.1 Development of the Discrete-Time Fourier Transform 359
5.1.2 Examples of Discrete-Time Fourier Transforms 362
5.1.3 Convergence Issues Associated with the Discrete-Time Fourier
Transform 366
5.2 The Fourier Transform for Periodic Signals 367
5.3 Properties of the Discrete-Time Fourier Transform 372
5.3.1 Periodicity of the Discrete-Time Fourier Transform 373
5,3.2 Linearity of the Fourier Transform 373
5.3.3 Time Shifting and Frequency Shifting 373
5.3.4 Conjugation and Conjugate Symmetry 375
5.3.5 Differencing and Accumulation 375
5.3.6 Time Reversal 376
5.3.7 Time Expansion 377
5.3.8 Differentiation in Frequency 380
5.3.9 Parseval's Relation 380
5.4 The Convolution Property 382
5.4.1 Examples 383
5.5 The Multiplication Property 388
5.6 Tables of Fourier Transform Properties and Basic Fourier
Transform Pairs 390
5.7 Duality 390
5.7.1 Duality in the Discrete-Time Fourier Series 391
5.7.2 Duality between the Discrete-Time Fourier Transform ~md the
Continuous-Time Fourier Series 395
5.8 Systems Characterized by Linear Constant-Coefficient
Difference Equations 396
5.9 Summary 399
Problems 400
6 TIME AND FREQUENCY CHARACTERIZATION
OF SIGNALS AND SYSTEMS 423
6.0 Introduction 423
6.1 The Magnitude-Phase Representation of the Fourier
Transform 423
6.2 The Magnitude-Phase Representation of the Frequency Response
of LTI Systems 427
6.2.1 Linear and Nonlinear Phase 428
6.2.2 Group Delay 430
6.2.3 Log-Magnitude and Phase Plots 436
6.3 Time-Domain Properties of Ideal Frequency-Selective
Filters 439
6.4 Time-Domain and Frequency-Domain Aspects of Nonideal
Filters 444
6.5 First-Order and Second-Order Continuous-Time Systems 448
6.5.1 First-Order Continuous-Time Systems 448
6.5.2 Second-Order Continuous-Time Systems 451
6.5.3 Bode Plots for Rational Frequency Responses 456
6.6 First-Order and Second-Order Discrete-Time Systems 461
6.6.1 First-Order Discrete-Time Systems 461
6.6.2 Second-Order Discrete-Time Systems 465
6.7 Examples of Time- and Frequency-Domain Analysis
of Systems 472
6.7.1 Analysis of an Automobile Suspension System 473
6.7.2 Examples of Discrete-Time Nonrecursive Filters 476
6.8 Summary 482
Problems 483
7 SAMPLING 514
7.0 Introduction 514
7.1 Representation of a Continuous-Time Signal by Its Samples:
The Sampling Theorem 515
7.1.1 Impulse-Train Sampling 516
7.1.2 Sampling with a Zero-Order Hold 520
7.2 Reconstruction of a Signal from Its Samples Using
Interpolation 522
7.3 The Effect of Undersampling: Aliasing 527
7.4 Discrete-Time Processing of Continuous-Time Signals 534
7.4.1 Digital Differentiator 541
7.4.2 Half-Sample Delay 543
7.5 Sampling of Discrete-Time Signals 545
7.5.1 Impulse-Train Sampling 545
7.5.2 Discrete-Time Decimation and Interpolation 549
7.6 Summary 555
Problems 556
8 COMMUNICATION SYSTEMS 582
8.0 Introduction 582
8.1 Complex Exponential and Sinusoidal Amplitude Modulation 583
8.1.1 Amplitude Modulation with a Complex Exponential Car~ier 583
8.1.2 Amplitude Modulation with a Sinusoidal Carrier 585
8.2 Demodulation for Sinusoidal AM 587
8.2.1 Synchronous Demodulation 587
8.2.2 Asynchronous Demodulation 590
8.3 Frequency-Division Multiplexing 594
8.4 Single-Sideband Sinusoidal Amplitude Modulation 597
8.5 Amplitude Modulation with a Pulse-Train Carrier 601
8.5.1 Modulation of a Pulse-Train Carrier 601
8.5.2 Time-Division Multiplexing 604
8.6 Pulse-Amplitude Modulation 604
8.6.1 Pulse-Amplitude Modulated Signals 604
8.6.2 Intersymbol Interference in PAM Systems 607
8.6.3 Digital Pulse-Amplitude and Pulse-Code Modulation 610
8.7 Sinusoidal Frequency Modulation 611
8.7.1 Narrowband Frequency Modulation 613
8.7.2 Wideband Frequency Modulation 615
8.7.3 Periodic Square-Wave Modulating Signal 617
8.8 Discrete-Time Modulation 619
8.8.1 Discrete-Time Sinusoidal Amplitude Modulation 619
8.8.2 Discrete-Time Transmodulation 623
8.9 Summary' 623
Problems 625
9 THE LAPLACE TRANSFORM 654
9.0 Introduction 654
9.1 The Laplace Transform 655
9.2 The Region of Convergence for Laplace Transforms 662
9.3 The Inverse Laplace Transform 670
9.4 Geometric Evaluation of the Fourier Transform from the
Pole-Zero Plot 674
9.4.1 First-Order Systems 676
9.4.2 Second-Order Systems 677
9.4.3 AU-Pass Systems 681
9.5 Properties of the Laplace Transform 682
9.5.1 Linearity of the Laplace Transform 683
9.5.2 Time Shifting 684
9.5.3 Shifting in the s-Domain 685
9.5.4 Time Scaling 685
9.5.5 Conjugation 687
9.5.6 Convolution Property 687
9.5.7 Differentiation in the Time Domain 688
9.5.8 Differentiation in the s-Domain 688
9.5.9 Integration in the Time Domain 690
9.5.10 The Initial- and Final-Value Theorems 690
9.5.11 Table of Properties 691
9.6 Some Laplace Transform Pairs 692
9.7 Analysis and Characterization of LTI Systems Using the
Laplace Transform 693
9.7.1 Causality 693
9.7.2 Stability 695
9.7.3 LTI Systems Characterized by Linear Constant-Coefficient
Differential Equations 698
9.7.4 Examples Relating System Behavior to the System Function 701
9.7.5 Butterworth Filters 703
9.8 System Function Algebra and Block Diagram
Representations 706
9.8.1 System Functions for Interconnections of LTI Systems 707
9.8.2 Block Diagram Representations for Causal LTI Systems Described
by Differential Equations and Rational System Functions 708
9.9 The Unilateral Laplace Transform 714
9.9.1 Examples of Unilateral Laplace Transforms 714
9.9.2 Properties of the Unilateral Laplace Transform 716
9.9.3 Solving Differential Equations Using the Unilateral Laplace
Transform 719
9.10 Summary 720
Problems 721
10 THE Z-TRANSFORM 741
10.0 Introduction 741
10.1 The z-Transform 741
10.2 The Region of Convergence for the z-Transform 748
10.3 The Inverse z-Transform 757
10.4 Geometric Evaluation of the Fourier Transform from the
Pole-Zero Plot 763
10.4.1 First-Order Systems 763
10.4.2 Second-Order Systems 765
10.5 Properties of the z-Transform 767
1.0.5.1 Linearity 767
10.5.2 Time Shifting 767
10.5.3 Scaling in the z-Domain 768
10.5.4 Time Reversal 769
10.5.5 Time Expansion 769
10.5.6 Conjugation 770
10.5.7 The Convolution Property 770
10.5.8 Differentiation in the z-Domain 772
10.5.9 The Initial-Value Theorem 773
10.5.10 Summary of Properties 774
10.6 Some Common z-Transform Pairs 774
10.7 Analysis and Characterization of LTI Systems Using
z-Transforms 774
10.7.1 Causality 776
10.7.2 Stability 777
10.7.3 LTI Systems Characterized by Linear Constant-Coefficient
Difference Equations 779
10.7.4 Examples Relating System Behavior to the System Function 781
10.8 System Function Algebra and Block Diagram
Representations 783
10.8.1 System Functions for Interconnections of LTI Systems 784
10.8.2 Block Diagram Representations for Causal LTI Systems Described
by Difference Equations and Rational System Functions 784
10.9 The Unilateralz-Transform 789
10.9.1 Examples of Unilateral z-Transforms and Inverse Transforms 790
10.9.2 Properties of the Unilateral z-Transform 792
10.9.3 Solving Difference Equations Using the Unilateral
z-Transform 795
10.10 Summary 796
Problems 797
11 LINEAR FEEDBACK SYSTEMS 816
11.0 Introduction 816
11.1 Linear Feedback Systems 819
11.2 Some Applications and Consequences of Feedback 820
11.2.1 Inverse System Design 820
11.2.2 Compensation for Nonideal Elements 821
11.2.3 Stabilization of Unstable Systems 823
11.2.4 Sampled-Data Feedback Systems 826
11.2.5 Tracking Systems 828
11.2.6 Destabilization Caused by Feedback 830
11.3 Root-Locus Analysis of Linear Feedback Systems 832
11.3.1 An Introductory Example 833
11.3.2 Equation for the Closed-Loop Poles 834
11.3.3 The End Points of the Root Locus: The Closed-Loop Poles for
K = 0 and I|K|=+ 836
11.3.4 The Angle Criterion 836
11.3.5 Properties of the Root Locus 841
11.4 The Nyquist Stability Criterion 846
11.4.1 The Encirclement Property 847
11.4.2 The Nyquist Criterion for Continuous-Time LTI
Feedback Systems 850
11.4.3 The Nyquist Criterion for Discrete-Time LTI
Feedback Systems 856
11.5 Gain and Phase Margins 858
11.6 Summary 866
Problems 867
APPENDIX PARTIAL-FRACTION EXPANSION 909
BIBLIOGRAPHY 921
ANSWERS 931
INDEX 941
前言/序言
《信號與係統(第二版)》 本書深入探討瞭信號與係統分析的核心概念和理論,為理解和處理各種工程與科學領域中的動態行為提供瞭堅實的基礎。全書內容嚴謹,邏輯清晰,旨在幫助讀者掌握分析連續時間和離散時間信號,以及綫性時不變(LTI)係統的方法。 主要內容概覽: 信號的錶示與性質: 本書從對信號的深入理解入手,詳細介紹瞭信號的各種分類,包括周期信號、非周期信號、能量信號、功率信號、偶信號、奇信號等。通過對信號基本性質的闡述,如振幅、頻率、相位、能量和功率,為後續的係統分析奠定基礎。此外,傅裏葉級數和傅裏葉變換作為信號的頻譜分析工具,也被詳細介紹,揭示瞭信號在頻域的特性,為信號的濾波、調製等處理提供瞭理論依據。 係統的模型與分類: 係統的概念是本書的另一個核心。作者清晰地定義瞭係統,並對不同類型的係統進行瞭分類,包括記憶係統與無記憶係統、因果係統與非因果係統、穩定係統與不穩定係統,以及綫性係統與非綫性係統。特彆地,綫性時不變(LTI)係統作為工程中最常見也最重要的係統模型,得到瞭重點關注。對於LTI係統的分析,本書引入瞭捲積這一基本運算,詳細闡述瞭其在時間和頻率域中的應用,以及如何通過捲積來預測係統的輸齣。 時域分析: 在時域中,本書詳細講解瞭如何利用捲積積分(對於連續時間LTI係統)和捲積和(對於離散時間LTI係統)來計算係統的輸齣。通過大量的例題和練習,讀者可以熟練掌握如何求解不同輸入信號作用下的係統響應,包括階躍響應、衝激響應等。這些時域分析方法對於理解係統的動態行為至關重要。 頻域分析: 頻域分析是理解係統頻率特性的關鍵。本書引入瞭傅裏葉變換和拉普拉斯變換(對於連續時間係統)以及離散時間傅裏葉變換(DTFT)和Z變換(對於離散時間係統)。這些變換工具能夠將信號和係統從時域轉換到頻域,使得復雜的時域運算轉化為簡單的代數運算。通過頻域分析,讀者可以清晰地瞭解係統的頻率響應,例如濾波器的通帶、阻帶特性,以及係統在高頻和低頻下的行為。 係統的性質與穩定性: 本書對LTI係統的各種重要性質進行瞭深入分析,包括可加性、齊次性、時不變性等。特彆地,係統的穩定性是係統分析中至關重要的概念。本書詳細闡述瞭判斷係統穩定性的各種方法,包括時域中的零輸入響應和零狀態響應,以及頻域中的根軌跡和奈奎斯特判據等(雖然可能不會直接使用這些術語,但會介紹其內在原理)。理解係統的穩定性對於設計可靠的係統至關重要。 狀態空間方法: 除瞭傳統的時域和頻域分析方法,本書還可能引入更現代的狀態空間方法。狀態空間方法提供瞭一種描述和分析多輸入多輸齣(MIMO)係統的統一框架。通過引入狀態嚮量,可以將高階係統錶示為一組一階微分方程或差分方程組,從而更容易地進行數值計算和控製設計。 應用與實例: 為瞭更好地說明理論的實際應用,本書會穿插大量的實際工程案例,例如通信係統中的信號傳輸與處理、控製係統中的係統設計與穩定性分析、電路分析中的信號響應等。這些實例能夠幫助讀者將所學的理論知識與實際問題聯係起來,加深對信號與係統概念的理解。 本書特點: 《信號與係統(第二版)》以其嚴謹的數學推導、清晰的邏輯結構和豐富的例題練習而著稱。作者在講解抽象概念的同時,注重與實際工程應用的結閤,使得讀者不僅能掌握理論知識,更能培養解決實際工程問題的能力。第二版可能在原有基礎上對內容進行瞭更新和完善,例如增加瞭更現代的分析工具或案例,使其更加貼閤當前工程實踐的需求。本書適閤作為高等院校電子工程、通信工程、自動化、計算機科學等相關專業本科生和研究生的教材,也是相關領域工程師的必備參考書。通過研讀本書,讀者將能建立起紮實的信號與係統分析功底,為進一步學習更高級的課程或進行相關領域的研究打下堅實的基礎。