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MJ.. I • '
ALAN V. OPPENHEIM
ALAN S. WILLSKV
WITH S. HAMID NAWAB
•
PRENTICE HALL SIGNAL PROCESSING SERIES .
ALAN V. OPPENHEIM, SERIES EDITOR ~ ~
SECOND EDITION
SIGNALS
&
SYSTEMS
v.
ALAN OPPENHEIM
s. w
ALAN ILLSKY
MAssACHUSETTS INsTITUTE OF TEcHNOLOGY
WITH
S.IIAMIDNAWAB
BosToN UNIVERSITY
PRENTICE-HALL INTERNATIONAL, INC.
CoNTENTS
PREFACE XVII
AcKNOWLEDGMENTS xxv
FoREWORD xxvii
1
1
SIGNALS AND SYSTEMS
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
74
LINEAR TIME-INVARIANT SYSTEMS
2.0 Introduction 74
2.1 Discrete-Time LTI Systems: The Convolution Sum 75
vii
viii Contents
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
177
PERIODIC SIGNALS
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
Contents ix
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 284
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
X Contents
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 Frequency 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
358
ThE DISCRETE-TIME FOURIER TRANSFORM
5.0 Introduction 358
5.1 Representation of Aperiodic Signals: The Discrete-Time
Fourier Transform 359
5.1.1 Development of the Discrete-~ime 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
Contents xi
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 and 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
423
OF SIGNALS AND SYSTEMS
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 Bode 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
514
SAMPLING
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
xii Contents
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 SYSTE.M S 582
8.0 Introduction 582
8.1 Complex Exponential and Sinusoidal Amplitude Modulation 583
8.1.1 Amplitude Modulation with a Complex Exponential Carrier 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 Digit~l 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
654
THE LAPLACE TRANSFORM
9.0 Introduction 654
9.1 The Laplace Transform 655
9.2 The Region of Convergence for Laplace Transforms 662
Contents xiii
9.3 The Inverse Laplace Transfonn 670
9.4 Geometric Evaluation of the Fourier Transfonn from the
Pole-Zero Plot 674
9.4.1 . First-Order Systems 676
9.4.2 Second-Order Systems 677
9.4.3 All-Pass Systems 681
9.5 Properties of the Laplace Transfonn 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 Scal1ng 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 6?1
9.6 Some Laplace Transfonn Pairs 692
9.7 Analysis and Characterization of LTI Systems Using the
Laplace Transfonn 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 Transfonn 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
741
THE Z-TRANSFORM
10.0 Introduction 741
10.1 The z-Transfonn 741
10.2 The Region of Convergence for the z-Transfonn. 748
xiv Contents
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
10.5.1 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 Unilateral z-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
816
UNEAR FEEDBACK SYSTEMS
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</p></div></div></div><div class="jsx-7d4e960818f559df modal-hidden"><div class="jsx-7d4e960818f559df modal-background"></div><div class="jsx-7d4e960818f559df modal-error-header"><div class="jsx-7d4e960818f559df modal-btn"><button class="jsx-7d4e960818f559df btn-close">×</button></div></div><div class="jsx-7d4e960818f559df modal-error-content"><div class="jsx-7d4e960818f559df modal-info"></div></div></div><div class="jsx-7d4e960818f559df ads1"></div><div class="jsx-7d4e960818f559df container"><div class="jsx-7d4e960818f559df detail-container"><div class="jsx-7d4e960818f559df detail-left"><div class="jsx-7d4e960818f559df ebook-frame"><div class="jsx-7d4e960818f559df ebook"><div class="jsx-7d4e960818f559df ebook-left"><img src="https://cdn.pdfdrive.to/media/content/thumbnails/e318dee9-d79b-418f-9800-045783c90f6e.webp" alt="ebook img" width="210" height="300" loading="lazy" title="ebook img" class="jsx-7d4e960818f559df ebook-img"></div><div class="jsx-7d4e960818f559df ebook-right"><h1 class="jsx-7d4e960818f559df ebook-title">Signals and System PDF</h1><div class="jsx-7d4e960818f559df file-info"><span class="jsx-7d4e960818f559df">967<!-- --> Pages</span><span class="jsx-7d4e960818f559df dot">·</span><span class="jsx-7d4e960818f559df">2013</span><span class="jsx-7d4e960818f559df dot">·</span><span class="jsx-7d4e960818f559df">292.34<!-- --> MB</span><span class="jsx-7d4e960818f559df dot">·</span><span class="jsx-7d4e960818f559df">english</span></div><div class="jsx-7d4e960818f559df author">by <span class="jsx-7d4e960818f559df"><a href="/author/alan-v-oppenheim" class="jsx-7d4e960818f559df author-name">Alan V. Oppenheim</a></span></div><div class="jsx-7d4e960818f559df tags"><span style="margin-right:5px" class="jsx-7d4e960818f559df"><a href="/top-technique-electronics-signal-processing-books" class="jsx-7d4e960818f559df">#<!-- -->Technique - Electronics: Signal Processing<!-- --> </a></span></div><div class="jsx-7d4e960818f559df btn-container"><div class="jsx-7d4e960818f559df hint-progress invisible"><i class="jsx-7d4e960818f559df">Checking for file health...</i></div><div class="jsx-7d4e960818f559df progress invisible"><div class="jsx-7d4e960818f559df progress-bar "></div></div><div class="jsx-27c21ff6cf33a438 download-content"><div class="jsx-27c21ff6cf33a438 download-group"><a href="/filedownload/signals-and-system" disabled="" class="jsx-27c21ff6cf33a438 btn-download">Download</a></div></div></div></div></div></div><div class="jsx-2ef0af5aad58e0f1 premium-container"><div class="jsx-563764575"><a href="/premium" rel="nofollow" class="jsx-563764575 premium-btn animated-button7"><span class="jsx-563764575"></span><span class="jsx-563764575"></span><span class="jsx-563764575"></span><span class="jsx-563764575"></span><svg id="icon-diamond" viewBox="0 0 32 32" fill="#fff" width="40" height="40" class="jsx-563764575"><path d="M2.103 12.052l13.398 16.629-5.373-16.629h-8.025zM11.584 12.052l4.745 16.663 4.083-16.663h-8.828zM17.051 28.681l12.898-16.629h-7.963l-4.935 16.629zM29.979 10.964l-3.867-6.612-3.869 6.612h7.736zM24.896 3.973h-7.736l3.867 6.839 3.869-6.839zM19.838 10.964l-3.867-6.612-3.868 6.612h7.735zM14.839 3.973h-7.735l3.868 6.839 3.867-6.839zM5.889 4.352l-3.867 6.612h7.735l-3.868-6.612z" class="jsx-563764575"></path></svg>Upgrade Premium</a></div><div class="jsx-2ef0af5aad58e0f1 limit-description-normal">Most books are stored in the elastic cloud where traffic is expensive. For this reason, we have a limit on daily download.</div></div><div class="jsx-7d4e960818f559df ads3"></div><div class="jsx-7d4e960818f559df mobile-ads"></div><h2 class="jsx-7d4e960818f559df summary-title">Preview <i class="jsx-7d4e960818f559df">Signals and System</i></h2><div class="jsx-7d4e960818f559df summary"><p class="jsx-7d4e960818f559df summary-content">l •.•
MJ.. I • '
ALAN V. OPPENHEIM
ALAN S. WILLSKV
WITH S. HAMID NAWAB
•
PRENTICE HALL SIGNAL PROCESSING SERIES .
ALAN V. OPPENHEIM, SERIES EDITOR ~ ~
SECOND EDITION
SIGNALS
&
SYSTEMS
v.
ALAN OPPENHEIM
s. w
ALAN ILLSKY
MAssACHUSETTS INsTITUTE OF TEcHNOLOGY
WITH
S.IIAMIDNAWAB
BosToN UNIVERSITY
PRENTICE-HALL INTERNATIONAL, INC.
CoNTENTS
PREFACE XVII
AcKNOWLEDGMENTS xxv
FoREWORD xxvii
1
1
SIGNALS AND SYSTEMS
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
74
LINEAR TIME-INVARIANT SYSTEMS
2.0 Introduction 74
2.1 Discrete-Time LTI Systems: The Convolution Sum 75
vii
viii Contents
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
177
PERIODIC SIGNALS
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
Contents ix
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 284
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
X Contents
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 Frequency 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
358
ThE DISCRETE-TIME FOURIER TRANSFORM
5.0 Introduction 358
5.1 Representation of Aperiodic Signals: The Discrete-Time
Fourier Transform 359
5.1.1 Development of the Discrete-~ime 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
Contents xi
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 and 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
423
OF SIGNALS AND SYSTEMS
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 Bode 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
514
SAMPLING
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
xii Contents
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 SYSTE.M S 582
8.0 Introduction 582
8.1 Complex Exponential and Sinusoidal Amplitude Modulation 583
8.1.1 Amplitude Modulation with a Complex Exponential Carrier 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 Digit~l 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
654
THE LAPLACE TRANSFORM
9.0 Introduction 654
9.1 The Laplace Transform 655
9.2 The Region of Convergence for Laplace Transforms 662
Contents xiii
9.3 The Inverse Laplace Transfonn 670
9.4 Geometric Evaluation of the Fourier Transfonn from the
Pole-Zero Plot 674
9.4.1 . First-Order Systems 676
9.4.2 Second-Order Systems 677
9.4.3 All-Pass Systems 681
9.5 Properties of the Laplace Transfonn 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 Scal1ng 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 6?1
9.6 Some Laplace Transfonn Pairs 692
9.7 Analysis and Characterization of LTI Systems Using the
Laplace Transfonn 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 Transfonn 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
741
THE Z-TRANSFORM
10.0 Introduction 741
10.1 The z-Transfonn 741
10.2 The Region of Convergence for the z-Transfonn. 748
xiv Contents
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
10.5.1 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 Unilateral z-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
816
UNEAR FEEDBACK SYSTEMS
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</p><div class="jsx-7d4e960818f559df show-more"><span class="jsx-7d4e960818f559df"><i class="jsx-7d4e960818f559df">See more</i></span></div></div><div class="jsx-7d4e960818f559df title"><h2 class="jsx-7d4e960818f559df siminar">The list of books you might like</h2></div><div class="jsx-1ac4e25e396cc2e7 collection"><div class="jsx-1ac4e25e396cc2e7"><div class="jsx-1ac4e25e396cc2e7 collection-item"><img width="70" height="100" src="https://cdn.zlibrary.to/media/content/thumbnails/bdb6c691-c928-472f-b015-e0a09200eca3.webp" loading="lazy" alt="book image" title="The Silent Patient" class="jsx-1ac4e25e396cc2e7 collection-img"><div class="jsx-1ac4e25e396cc2e7 information"><h3 class="jsx-1ac4e25e396cc2e7 title-info"><a href="/dl/the-silent-patient-9" class="jsx-1ac4e25e396cc2e7 title-link">The Silent Patient</a></h3><div class="jsx-1ac4e25e396cc2e7 file-info"><span class="jsx-d61d22f45bf3720e">Alex Michaelides</span><div class="jsx-d61d22f45bf3720e"><span class="jsx-d61d22f45bf3720e dot">·</span><span class="jsx-d61d22f45bf3720e">0.52 MB</span></div></div><p class="jsx-1ac4e25e396cc2e7 desc"></p></div></div></div><div class="jsx-1ac4e25e396cc2e7"><div class="jsx-1ac4e25e396cc2e7 collection-item"><img width="70" height="100" src="https://cdn.zlibrary.to/media/content/thumbnails/efb033fd-8b2d-4ed1-8c99-d9414cac1fb5.webp" loading="lazy" alt="book image" title="Corrupt (Devil's Night #1)" class="jsx-1ac4e25e396cc2e7 collection-img"><div class="jsx-1ac4e25e396cc2e7 information"><h3 class="jsx-1ac4e25e396cc2e7 title-info"><a href="/dl/corrupt-devils-night-1-0" class="jsx-1ac4e25e396cc2e7 title-link">Corrupt (Devil's Night #1)</a></h3><div class="jsx-1ac4e25e396cc2e7 file-info"><span class="jsx-d61d22f45bf3720e">Penelope Douglas</span><div class="jsx-d61d22f45bf3720e"><span class="jsx-d61d22f45bf3720e dot">·</span><span class="jsx-d61d22f45bf3720e">518 Pages</span></div><div class="jsx-d61d22f45bf3720e"><span class="jsx-d61d22f45bf3720e dot">·</span><span class="jsx-d61d22f45bf3720e">2015</span></div><div class="jsx-d61d22f45bf3720e"><span class="jsx-d61d22f45bf3720e dot">·</span><span class="jsx-d61d22f45bf3720e">0.74 MB</span></div></div><p class="jsx-1ac4e25e396cc2e7 desc"></p></div></div></div><div class="jsx-1ac4e25e396cc2e7"><div class="jsx-1ac4e25e396cc2e7 collection-item"><img width="70" height="100" src="https://cdn.zlibrary.to/media/content/thumbnails/4b204c1d-d091-4ba5-8240-1aee408cc221.webp" loading="lazy" alt="book image" title="Credence" class="jsx-1ac4e25e396cc2e7 collection-img"><div class="jsx-1ac4e25e396cc2e7 information"><h3 class="jsx-1ac4e25e396cc2e7 title-info"><a href="/dl/credence-3" class="jsx-1ac4e25e396cc2e7 title-link">Credence</a></h3><div class="jsx-1ac4e25e396cc2e7 file-info"><span class="jsx-d61d22f45bf3720e">Penelope Douglas</span><div class="jsx-d61d22f45bf3720e"><span class="jsx-d61d22f45bf3720e dot">·</span><span class="jsx-d61d22f45bf3720e">487 Pages</span></div><div class="jsx-d61d22f45bf3720e"><span class="jsx-d61d22f45bf3720e dot">·</span><span class="jsx-d61d22f45bf3720e">2020</span></div><div class="jsx-d61d22f45bf3720e"><span class="jsx-d61d22f45bf3720e dot">·</span><span class="jsx-d61d22f45bf3720e">0.86 MB</span></div></div><p class="jsx-1ac4e25e396cc2e7 desc"></p></div></div></div><div class="jsx-1ac4e25e396cc2e7"><div class="ads4"></div><div class="jsx-1ac4e25e396cc2e7 collection-item"><img width="70" height="100" src="https://cdn.zlibrary.to/media/content/thumbnails/cf5ae923-f278-40f4-a88f-8d76be0c2a72.webp" loading="lazy" alt="book image" title="The Strength In Our Scars" class="jsx-1ac4e25e396cc2e7 collection-img"><div class="jsx-1ac4e25e396cc2e7 information"><h3 class="jsx-1ac4e25e396cc2e7 title-info"><a href="/dl/the-strength-in-our-scars-0" class="jsx-1ac4e25e396cc2e7 title-link">The Strength In Our Scars</a></h3><div class="jsx-1ac4e25e396cc2e7 file-info"><span class="jsx-d61d22f45bf3720e">Bianca Sparacino</span><div class="jsx-d61d22f45bf3720e"><span class="jsx-d61d22f45bf3720e dot">·</span><span class="jsx-d61d22f45bf3720e">2018</span></div><div class="jsx-d61d22f45bf3720e"><span class="jsx-d61d22f45bf3720e dot">·</span><span class="jsx-d61d22f45bf3720e">0.17 MB</span></div></div><p class="jsx-1ac4e25e396cc2e7 desc"></p></div></div></div><div class="jsx-1ac4e25e396cc2e7"><div class="mobile-ads"></div><div class="jsx-1ac4e25e396cc2e7 collection-item"><img width="70" height="100" src="https://cdn.pdfdrive.to/media/content/thumbnails/16dffc96-269d-4f80-89e9-1f2a821366d0.webp" loading="lazy" alt="book image" title="BELGIUM - Stamp Albums Web" class="jsx-1ac4e25e396cc2e7 collection-img"><div class="jsx-1ac4e25e396cc2e7 information"><h3 class="jsx-1ac4e25e396cc2e7 title-info"><a href="/dl/belgium-stamp-albums-web" class="jsx-1ac4e25e396cc2e7 title-link">BELGIUM - Stamp Albums Web</a></h3><div class="jsx-1ac4e25e396cc2e7 file-info"><span class="jsx-d61d22f45bf3720e">75 Pages</span><div class="jsx-d61d22f45bf3720e"><span class="jsx-d61d22f45bf3720e dot">·</span><span class="jsx-d61d22f45bf3720e">2015</span></div><div class="jsx-d61d22f45bf3720e"><span class="jsx-d61d22f45bf3720e dot">·</span><span class="jsx-d61d22f45bf3720e">0.12 MB</span></div></div><p class="jsx-1ac4e25e396cc2e7 desc"></p></div></div></div><div class="jsx-1ac4e25e396cc2e7"><div class="jsx-1ac4e25e396cc2e7 collection-item"><img width="70" height="100" src="https://cdn.pdfdrive.to/media/content/thumbnails/7968c211-0ae2-4604-9f5e-671708c5922d.webp" loading="lazy" alt="book image" title="DTIC ADA518756: Reforming Pentagon Decisionmaking" class="jsx-1ac4e25e396cc2e7 collection-img"><div class="jsx-1ac4e25e396cc2e7 information"><h3 class="jsx-1ac4e25e396cc2e7 title-info"><a href="/dl/dtic-ada518756-reforming-pentagon-decisionmaking" class="jsx-1ac4e25e396cc2e7 title-link">DTIC ADA518756: Reforming Pentagon Decisionmaking</a></h3><div class="jsx-1ac4e25e396cc2e7 file-info"><span class="jsx-d61d22f45bf3720e">Defense Technical Information Center</span><div class="jsx-d61d22f45bf3720e"><span class="jsx-d61d22f45bf3720e dot">·</span><span class="jsx-d61d22f45bf3720e">0.59 MB</span></div></div><p class="jsx-1ac4e25e396cc2e7 desc"></p></div></div></div><div class="jsx-1ac4e25e396cc2e7"><div class="jsx-1ac4e25e396cc2e7 collection-item"><img width="70" height="100" src="https://cdn-2.pdfdrive.to/media/content/thumbnails/1afe085f-7185-4433-9823-3b477746ca51.webp" loading="lazy" alt="book image" title="The Learning Leader: How to Focus School Improvement for Better Results" class="jsx-1ac4e25e396cc2e7 collection-img"><div class="jsx-1ac4e25e396cc2e7 information"><h3 class="jsx-1ac4e25e396cc2e7 title-info"><a href="/dl/the-learning-leader-how-to-focus-school-improvement-for-better-results" class="jsx-1ac4e25e396cc2e7 title-link">The Learning Leader: How to Focus School Improvement for Better Results</a></h3><div class="jsx-1ac4e25e396cc2e7 file-info"><span class="jsx-d61d22f45bf3720e">Douglas B. Reeves</span><div class="jsx-d61d22f45bf3720e"><span class="jsx-d61d22f45bf3720e dot">·</span><span class="jsx-d61d22f45bf3720e">250 Pages</span></div><div class="jsx-d61d22f45bf3720e"><span class="jsx-d61d22f45bf3720e dot">·</span><span class="jsx-d61d22f45bf3720e">2006</span></div><div class="jsx-d61d22f45bf3720e"><span class="jsx-d61d22f45bf3720e dot">·</span><span class="jsx-d61d22f45bf3720e">1.562 MB</span></div></div><p class="jsx-1ac4e25e396cc2e7 desc"></p></div></div></div><div class="jsx-1ac4e25e396cc2e7"><div class="jsx-1ac4e25e396cc2e7 collection-item"><img width="70" height="100" src="https://cdn.pdfdrive.to/media/content/thumbnails/29b8745a-3f5a-4b39-8477-967071d971a7.webp" loading="lazy" alt="book image" title="Boletín Oficial de la República Argentina. 2007 2da sección" class="jsx-1ac4e25e396cc2e7 collection-img"><div class="jsx-1ac4e25e396cc2e7 information"><h3 class="jsx-1ac4e25e396cc2e7 title-info"><a href="/dl/boletin-oficial-de-la-republica-argentina-2007-2da-seccion-3" class="jsx-1ac4e25e396cc2e7 title-link">Boletín Oficial de la República Argentina. 2007 2da sección</a></h3><div class="jsx-1ac4e25e396cc2e7 file-info"><span class="jsx-d61d22f45bf3720e">República Argentina</span><div class="jsx-d61d22f45bf3720e"><span class="jsx-d61d22f45bf3720e dot">·</span><span class="jsx-d61d22f45bf3720e">1.7 MB</span></div></div><p class="jsx-1ac4e25e396cc2e7 desc"></p></div></div></div><div class="jsx-1ac4e25e396cc2e7"><div class="jsx-1ac4e25e396cc2e7 collection-item"><img width="70" height="100" src="https://cdn.pdfdrive.to/media/content/thumbnails/eaf1e984-1706-46e7-ab24-e06c59d000d7.webp" loading="lazy" alt="book image" title="Exhibition - CMA@MOCA" class="jsx-1ac4e25e396cc2e7 collection-img"><div class="jsx-1ac4e25e396cc2e7 information"><h3 class="jsx-1ac4e25e396cc2e7 title-info"><a href="/dl/exhibition-cmamoca" class="jsx-1ac4e25e396cc2e7 title-link">Exhibition - CMA@MOCA</a></h3><div class="jsx-1ac4e25e396cc2e7 file-info"><span class="jsx-d61d22f45bf3720e">0.03 MB</span></div><p class="jsx-1ac4e25e396cc2e7 desc"></p></div></div></div><div class="jsx-1ac4e25e396cc2e7"><div class="mobile-ads"></div><div class="jsx-1ac4e25e396cc2e7 collection-item"><img width="70" height="100" src="https://cdn.pdfdrive.to/media/content/thumbnails/acc9d8c0-975f-40f7-8662-42be20b8f78c.webp" loading="lazy" alt="book image" title="IFRS 15 investment management companies" class="jsx-1ac4e25e396cc2e7 collection-img"><div class="jsx-1ac4e25e396cc2e7 information"><h3 class="jsx-1ac4e25e396cc2e7 title-info"><a href="/dl/ifrs-15-investment-management-companies-pdf" class="jsx-1ac4e25e396cc2e7 title-link">IFRS 15 investment management companies</a></h3><div class="jsx-1ac4e25e396cc2e7 file-info"><span class="jsx-d61d22f45bf3720e">45 Pages</span><div class="jsx-d61d22f45bf3720e"><span class="jsx-d61d22f45bf3720e dot">·</span><span class="jsx-d61d22f45bf3720e">2017</span></div><div class="jsx-d61d22f45bf3720e"><span class="jsx-d61d22f45bf3720e dot">·</span><span class="jsx-d61d22f45bf3720e">0.28 MB</span></div></div><p class="jsx-1ac4e25e396cc2e7 desc"></p></div></div></div><div class="jsx-1ac4e25e396cc2e7"><div class="jsx-1ac4e25e396cc2e7 collection-item"><img width="70" height="100" src="https://cdn.pdfdrive.to/media/content/thumbnails/8b0b9da9-4de9-450d-9a90-52c75a837df3.webp" loading="lazy" alt="book image" title="Greek Government Gazette: Part 1, 2006 no. 244" class="jsx-1ac4e25e396cc2e7 collection-img"><div class="jsx-1ac4e25e396cc2e7 information"><h3 class="jsx-1ac4e25e396cc2e7 title-info"><a href="/dl/greek-government-gazette-part-1-2006-no-244" class="jsx-1ac4e25e396cc2e7 title-link">Greek Government Gazette: Part 1, 2006 no. 244</a></h3><div class="jsx-1ac4e25e396cc2e7 file-info"><span class="jsx-d61d22f45bf3720e">The Government of the Hellenic Republic</span><div class="jsx-d61d22f45bf3720e"><span class="jsx-d61d22f45bf3720e dot">·</span><span class="jsx-d61d22f45bf3720e">2006</span></div><div class="jsx-d61d22f45bf3720e"><span class="jsx-d61d22f45bf3720e dot">·</span><span class="jsx-d61d22f45bf3720e">0.35 MB</span></div></div><p class="jsx-1ac4e25e396cc2e7 desc"></p></div></div></div><div class="jsx-1ac4e25e396cc2e7"><div class="jsx-1ac4e25e396cc2e7 collection-item"><img width="70" height="100" src="https://cdn.pdfdrive.to/media/content/thumbnails/d2911ca2-937e-43ea-850e-85e6e7998e08.webp" loading="lazy" alt="book image" title="Capturing the Uncertainty in Adversary Attack Simulations" class="jsx-1ac4e25e396cc2e7 collection-img"><div class="jsx-1ac4e25e396cc2e7 information"><h3 class="jsx-1ac4e25e396cc2e7 title-info"><a href="/dl/capturing-the-uncertainty-in-adversary-attack-simulations" class="jsx-1ac4e25e396cc2e7 title-link">Capturing the Uncertainty in Adversary Attack Simulations</a></h3><div class="jsx-1ac4e25e396cc2e7 file-info"><span class="jsx-d61d22f45bf3720e">37 Pages</span><div class="jsx-d61d22f45bf3720e"><span class="jsx-d61d22f45bf3720e dot">·</span><span class="jsx-d61d22f45bf3720e">2008</span></div><div class="jsx-d61d22f45bf3720e"><span class="jsx-d61d22f45bf3720e dot">·</span><span class="jsx-d61d22f45bf3720e">0.24 MB</span></div></div><p class="jsx-1ac4e25e396cc2e7 desc"></p></div></div></div><div class="jsx-1ac4e25e396cc2e7"><div class="jsx-1ac4e25e396cc2e7 collection-item"><img width="70" height="100" src="https://cdn.pdfdrive.to/media/content/thumbnails/4c96d6d1-f255-4611-aaef-3621c1e14d06.webp" loading="lazy" alt="book image" title="ERIC EJ1069138: Taking a Closer Look at Reading Online" class="jsx-1ac4e25e396cc2e7 collection-img"><div class="jsx-1ac4e25e396cc2e7 information"><h3 class="jsx-1ac4e25e396cc2e7 title-info"><a href="/dl/eric-ej1069138-taking-a-closer-look-at-reading-online" class="jsx-1ac4e25e396cc2e7 title-link">ERIC EJ1069138: Taking a Closer Look at Reading Online</a></h3><div class="jsx-1ac4e25e396cc2e7 file-info"><span class="jsx-d61d22f45bf3720e">ERIC</span><div class="jsx-d61d22f45bf3720e"><span class="jsx-d61d22f45bf3720e dot">·</span><span class="jsx-d61d22f45bf3720e">2006</span></div><div class="jsx-d61d22f45bf3720e"><span class="jsx-d61d22f45bf3720e dot">·</span><span class="jsx-d61d22f45bf3720e">0.9 MB</span></div></div><p class="jsx-1ac4e25e396cc2e7 desc"></p></div></div></div><div class="jsx-1ac4e25e396cc2e7"><div class="jsx-1ac4e25e396cc2e7 collection-item"><img width="70" height="100" src="https://cdn.pdfdrive.to/media/content/thumbnails/5b5b5ebc-dbe6-4165-be4b-5c432d64edb2.webp" loading="lazy" alt="book image" title="Appalachian Regional Commission" class="jsx-1ac4e25e396cc2e7 collection-img"><div class="jsx-1ac4e25e396cc2e7 information"><h3 class="jsx-1ac4e25e396cc2e7 title-info"><a href="/dl/appalachian-regional-commission" class="jsx-1ac4e25e396cc2e7 title-link">Appalachian Regional Commission</a></h3><div class="jsx-1ac4e25e396cc2e7 file-info"><span class="jsx-d61d22f45bf3720e">60 Pages</span><div class="jsx-d61d22f45bf3720e"><span class="jsx-d61d22f45bf3720e dot">·</span><span class="jsx-d61d22f45bf3720e">2012</span></div><div class="jsx-d61d22f45bf3720e"><span class="jsx-d61d22f45bf3720e dot">·</span><span class="jsx-d61d22f45bf3720e">1.17 MB</span></div></div><p class="jsx-1ac4e25e396cc2e7 desc"></p></div></div></div><div class="jsx-1ac4e25e396cc2e7"><div class="mobile-ads"></div><div class="jsx-1ac4e25e396cc2e7 collection-item"><img width="70" height="100" src="https://cdn.pdfdrive.to/media/content/thumbnails/ea5ba8ff-da26-45a2-b729-45e883bf7a99.webp" loading="lazy" alt="book image" title="DTIC ADA458978: Valuing Programmed Depot Maintenance Speed: An Analysis of F-15 PDM" class="jsx-1ac4e25e396cc2e7 collection-img"><div class="jsx-1ac4e25e396cc2e7 information"><h3 class="jsx-1ac4e25e396cc2e7 title-info"><a href="/dl/dtic-ada458978-valuing-programmed-depot-maintenance-speed-an-analysis-of-f-15-pdm" class="jsx-1ac4e25e396cc2e7 title-link">DTIC ADA458978: Valuing Programmed Depot Maintenance Speed: An Analysis of F-15 PDM</a></h3><div class="jsx-1ac4e25e396cc2e7 file-info"><span class="jsx-d61d22f45bf3720e">Defense Technical Information Center</span><div class="jsx-d61d22f45bf3720e"><span class="jsx-d61d22f45bf3720e dot">·</span><span class="jsx-d61d22f45bf3720e">0.54 MB</span></div></div><p class="jsx-1ac4e25e396cc2e7 desc"></p></div></div></div><div class="jsx-1ac4e25e396cc2e7"><div class="jsx-1ac4e25e396cc2e7 collection-item"><img width="70" height="100" src="/default_image.png" loading="lazy" alt="book image" title="böbrek nakli alıcı adayı değerlendirmesi" class="jsx-1ac4e25e396cc2e7 collection-img"><div class="jsx-1ac4e25e396cc2e7 information"><h3 class="jsx-1ac4e25e396cc2e7 title-info"><a href="/dl/bobrek-nakli-alc-aday-degerlendirmesi" class="jsx-1ac4e25e396cc2e7 title-link">böbrek nakli alıcı adayı değerlendirmesi</a></h3><div class="jsx-1ac4e25e396cc2e7 file-info"><span class="jsx-d61d22f45bf3720e">112 Pages</span><div class="jsx-d61d22f45bf3720e"><span class="jsx-d61d22f45bf3720e dot">·</span><span class="jsx-d61d22f45bf3720e">2012</span></div><div class="jsx-d61d22f45bf3720e"><span class="jsx-d61d22f45bf3720e dot">·</span><span class="jsx-d61d22f45bf3720e">7.95 MB</span></div></div><p class="jsx-1ac4e25e396cc2e7 desc"></p></div></div></div><div class="jsx-1ac4e25e396cc2e7"><div class="jsx-1ac4e25e396cc2e7 collection-item"><img width="70" height="100" src="https://cdn.pdfdrive.to/media/content/thumbnails/29d56f7e-40f1-4bd9-8756-5463ecb03ec7.webp" loading="lazy" alt="book image" title="Socio-economic indicators in integrated coastal zone and community-based fisheries management [electronic resource] : case studies from the Caribbean" class="jsx-1ac4e25e396cc2e7 collection-img"><div class="jsx-1ac4e25e396cc2e7 information"><h3 class="jsx-1ac4e25e396cc2e7 title-info"><a href="/dl/socio-economic-indicators-in-integrated-coastal-zone-and-community-based-fisheries-management-electronic-resource-case-studies-from-the-caribbean" class="jsx-1ac4e25e396cc2e7 title-link">Socio-economic indicators in integrated coastal zone and community-based fisheries management [electronic resource] : case studies from the Caribbean</a></h3><div class="jsx-1ac4e25e396cc2e7 file-info"><span class="jsx-d61d22f45bf3720e">Tietze, Uwe, 1950-</span><div class="jsx-d61d22f45bf3720e"><span class="jsx-d61d22f45bf3720e dot">·</span><span class="jsx-d61d22f45bf3720e">2006</span></div><div class="jsx-d61d22f45bf3720e"><span class="jsx-d61d22f45bf3720e dot">·</span><span class="jsx-d61d22f45bf3720e">7.6 MB</span></div></div><p class="jsx-1ac4e25e396cc2e7 desc"></p></div></div></div><div class="jsx-1ac4e25e396cc2e7"><div class="jsx-1ac4e25e396cc2e7 collection-item"><img width="70" height="100" src="https://cdn.pdfdrive.to/media/content/thumbnails/904bf504-d27c-4a98-8fd8-22bb9f0c7a78.webp" loading="lazy" alt="book image" title="Greek Government Gazette: Part 7, 2006 no. 674" class="jsx-1ac4e25e396cc2e7 collection-img"><div class="jsx-1ac4e25e396cc2e7 information"><h3 class="jsx-1ac4e25e396cc2e7 title-info"><a href="/dl/greek-government-gazette-part-7-2006-no-674" class="jsx-1ac4e25e396cc2e7 title-link">Greek Government Gazette: Part 7, 2006 no. 674</a></h3><div class="jsx-1ac4e25e396cc2e7 file-info"><span class="jsx-d61d22f45bf3720e">The Government of the Hellenic Republic</span><div class="jsx-d61d22f45bf3720e"><span class="jsx-d61d22f45bf3720e dot">·</span><span class="jsx-d61d22f45bf3720e">2006</span></div><div class="jsx-d61d22f45bf3720e"><span class="jsx-d61d22f45bf3720e dot">·</span><span class="jsx-d61d22f45bf3720e">0.19 MB</span></div></div><p class="jsx-1ac4e25e396cc2e7 desc"></p></div></div></div><div class="jsx-1ac4e25e396cc2e7"><div class="jsx-1ac4e25e396cc2e7 collection-item"><img width="70" height="100" src="https://cdn.pdfdrive.to/media/content/thumbnails/90660cfd-6c74-4564-9b35-233a0fc41884.webp" loading="lazy" alt="book image" title="ERIC EJ1095001: FLAP: Personal Writing as a Tool for Physician Well-Being" class="jsx-1ac4e25e396cc2e7 collection-img"><div class="jsx-1ac4e25e396cc2e7 information"><h3 class="jsx-1ac4e25e396cc2e7 title-info"><a href="/dl/eric-ej1095001-flap-personal-writing-as-a-tool-for-physician-well-being" class="jsx-1ac4e25e396cc2e7 title-link">ERIC EJ1095001: FLAP: Personal Writing as a Tool for Physician Well-Being</a></h3><div class="jsx-1ac4e25e396cc2e7 file-info"><span class="jsx-d61d22f45bf3720e">ERIC</span><div class="jsx-d61d22f45bf3720e"><span class="jsx-d61d22f45bf3720e dot">·</span><span class="jsx-d61d22f45bf3720e">2006</span></div><div class="jsx-d61d22f45bf3720e"><span class="jsx-d61d22f45bf3720e dot">·</span><span class="jsx-d61d22f45bf3720e">0.18 MB</span></div></div><p class="jsx-1ac4e25e396cc2e7 desc"></p></div></div></div><div class="jsx-1ac4e25e396cc2e7"><div class="jsx-1ac4e25e396cc2e7 collection-item"><img width="70" height="100" src="https://cdn.pdfdrive.to/media/content/thumbnails/c874e669-7709-4c08-8737-55a818d3ef59.webp" loading="lazy" alt="book image" title="Canada Ancillary Restraints Article" class="jsx-1ac4e25e396cc2e7 collection-img"><div class="jsx-1ac4e25e396cc2e7 information"><h3 class="jsx-1ac4e25e396cc2e7 title-info"><a href="/dl/canada-ancillary-restraints-article" class="jsx-1ac4e25e396cc2e7 title-link">Canada Ancillary Restraints Article</a></h3><div class="jsx-1ac4e25e396cc2e7 file-info"><span class="jsx-d61d22f45bf3720e">Patrick English</span><div class="jsx-d61d22f45bf3720e"><span class="jsx-d61d22f45bf3720e dot">·</span><span class="jsx-d61d22f45bf3720e">21 Pages</span></div><div class="jsx-d61d22f45bf3720e"><span class="jsx-d61d22f45bf3720e dot">·</span><span class="jsx-d61d22f45bf3720e">2010</span></div><div class="jsx-d61d22f45bf3720e"><span class="jsx-d61d22f45bf3720e dot">·</span><span class="jsx-d61d22f45bf3720e">0.1 MB</span></div></div><p class="jsx-1ac4e25e396cc2e7 desc"></p></div></div></div><div class="jsx-1ac4e25e396cc2e7"><div class="jsx-1ac4e25e396cc2e7 collection-item"><img width="70" height="100" src="https://cdn.pdfdrive.to/media/content/thumbnails/a52b8214-9b71-41c6-88e7-3396c27bdb3b.webp" loading="lazy" alt="book image" title="Greek Government Gazette: Part 8, 2006 no. 118" class="jsx-1ac4e25e396cc2e7 collection-img"><div class="jsx-1ac4e25e396cc2e7 information"><h3 class="jsx-1ac4e25e396cc2e7 title-info"><a href="/dl/greek-government-gazette-part-8-2006-no-118" class="jsx-1ac4e25e396cc2e7 title-link">Greek Government Gazette: Part 8, 2006 no. 118</a></h3><div class="jsx-1ac4e25e396cc2e7 file-info"><span class="jsx-d61d22f45bf3720e">The Government of the Hellenic Republic</span><div class="jsx-d61d22f45bf3720e"><span class="jsx-d61d22f45bf3720e dot">·</span><span class="jsx-d61d22f45bf3720e">2006</span></div><div class="jsx-d61d22f45bf3720e"><span class="jsx-d61d22f45bf3720e dot">·</span><span class="jsx-d61d22f45bf3720e">0.28 MB</span></div></div><p class="jsx-1ac4e25e396cc2e7 desc"></p></div></div></div><div class="jsx-1ac4e25e396cc2e7"><div class="jsx-1ac4e25e396cc2e7 collection-item"><img width="70" height="100" src="https://cdn.pdfdrive.to/media/content/thumbnails/321fdb32-e610-4636-8863-a44be39285c0.webp" loading="lazy" alt="book image" title="Aydın Çalışma ve İş Kurumu İl Müdürlüğü Resmi Web Sitesi" class="jsx-1ac4e25e396cc2e7 collection-img"><div class="jsx-1ac4e25e396cc2e7 information"><h3 class="jsx-1ac4e25e396cc2e7 title-info"><a href="/dl/aydn-calsma-ve-is-kurumu-il-mudurlugu-resmi-web-sitesi" class="jsx-1ac4e25e396cc2e7 title-link">Aydın Çalışma ve İş Kurumu İl Müdürlüğü Resmi Web Sitesi</a></h3><div class="jsx-1ac4e25e396cc2e7 file-info"><span class="jsx-d61d22f45bf3720e">118 Pages</span><div class="jsx-d61d22f45bf3720e"><span class="jsx-d61d22f45bf3720e dot">·</span><span class="jsx-d61d22f45bf3720e">2013</span></div><div class="jsx-d61d22f45bf3720e"><span class="jsx-d61d22f45bf3720e dot">·</span><span class="jsx-d61d22f45bf3720e">3.73 MB</span></div></div><p class="jsx-1ac4e25e396cc2e7 desc"></p></div></div></div><div class="jsx-1ac4e25e396cc2e7"><div class="jsx-1ac4e25e396cc2e7 collection-item"><img width="70" height="100" src="https://cdn.pdfdrive.to/media/content/thumbnails/cdcec227-98e7-4082-b9aa-75ddf4292941.webp" loading="lazy" alt="book image" title="ERIC ED617122: Financial Literacy in Education Process: Literature Study" class="jsx-1ac4e25e396cc2e7 collection-img"><div class="jsx-1ac4e25e396cc2e7 information"><h3 class="jsx-1ac4e25e396cc2e7 title-info"><a href="/dl/eric-ed617122-financial-literacy-in-education-process-literature-study" class="jsx-1ac4e25e396cc2e7 title-link">ERIC ED617122: Financial Literacy in Education Process: Literature Study</a></h3><div class="jsx-1ac4e25e396cc2e7 file-info"><span class="jsx-d61d22f45bf3720e">ERIC</span><div class="jsx-d61d22f45bf3720e"><span class="jsx-d61d22f45bf3720e dot">·</span><span class="jsx-d61d22f45bf3720e">2022</span></div><div class="jsx-d61d22f45bf3720e"><span class="jsx-d61d22f45bf3720e dot">·</span><span class="jsx-d61d22f45bf3720e">0.51 MB</span></div></div><p class="jsx-1ac4e25e396cc2e7 desc"></p></div></div></div><div class="jsx-1ac4e25e396cc2e7"><div class="jsx-1ac4e25e396cc2e7 collection-item"><img width="70" height="100" src="https://cdn.pdfdrive.to/media/content/thumbnails/c6764255-df7a-4a69-a2b6-ee0acb6849f1.webp" loading="lazy" alt="book image" title="by Carmen Agra Deedy illustrated by Renato Alarcão The Frog Princess" class="jsx-1ac4e25e396cc2e7 collection-img"><div class="jsx-1ac4e25e396cc2e7 information"><h3 class="jsx-1ac4e25e396cc2e7 title-info"><a href="/dl/by-carmen-agra-deedy-illustrated-by-renato-alarcao-the-frog-princess" class="jsx-1ac4e25e396cc2e7 title-link">by Carmen Agra Deedy illustrated by Renato Alarcão The Frog Princess</a></h3><div class="jsx-1ac4e25e396cc2e7 file-info"><span class="jsx-d61d22f45bf3720e">30 Pages</span><div class="jsx-d61d22f45bf3720e"><span class="jsx-d61d22f45bf3720e dot">·</span><span class="jsx-d61d22f45bf3720e">2014</span></div><div class="jsx-d61d22f45bf3720e"><span class="jsx-d61d22f45bf3720e dot">·</span><span class="jsx-d61d22f45bf3720e">4.13 MB</span></div></div><p class="jsx-1ac4e25e396cc2e7 desc"></p></div></div></div></div><div class="jsx-7d4e960818f559df ads5"></div></div><div class="jsx-7d4e960818f559df detail-right"><div class="jsx-17865f972f87972f category-container"><div class="jsx-17865f972f87972f premium"><div class="jsx-563764575"><a href="/premium" rel="nofollow" class="jsx-563764575 premium-btn animated-button7"><span class="jsx-563764575"></span><span class="jsx-563764575"></span><span class="jsx-563764575"></span><span class="jsx-563764575"></span><svg id="icon-diamond" viewBox="0 0 32 32" fill="#fff" width="40" height="40" 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Oppenheim","description":null,"page":967,"release_year":2013,"file_size":292.34,"downloaded_count":1096,"language":"english","summary":"l •.• \nMJ.. I • ' \nALAN V. OPPENHEIM \nALAN S. WILLSKV \nWITH S. HAMID NAWAB \n• \nPRENTICE HALL SIGNAL PROCESSING SERIES . \nALAN V. OPPENHEIM, SERIES EDITOR ~ ~\nSECOND EDITION \nSIGNALS \n\u0026 \nSYSTEMS \nv. \nALAN OPPENHEIM \ns. w \nALAN ILLSKY \nMAssACHUSETTS INsTITUTE OF TEcHNOLOGY \nWITH \nS.IIAMIDNAWAB \nBosToN UNIVERSITY \nPRENTICE-HALL INTERNATIONAL, INC.\nCoNTENTS \nPREFACE XVII \nAcKNOWLEDGMENTS xxv \nFoREWORD xxvii \n1 \n1 \nSIGNALS AND SYSTEMS \n1.0 . Introduction 1 \n1.1 Continuous-Time and Discrete-Time Signals 1 \n1.1.1 Examples and Mathematical Representation 1 \n1.1.2 Signal Energy and Power 5 \n1.2 Transformations of the Independent Variable 7 \n1.2.1 Examples of Transformations of the Independent Variable 8 \n1.2.2 Periodic Signals 11 \n1.2.3 Even and Odd Signals 13 \n1.3 Exponential and Sinusoidal Signals 14 \n1.3.1 Continuous-Time Complex Exponential and Sinusoidal Signals 15 \n1.3.2 Discrete-Time Complex Exponential and Sinusoidal Signals 21 · \n1.3.3 Periodicity Properties of Discrete-Time Complex Exponentials 25 \n1.4 The Unit Impulse and Unit Step Functions 30 \n1.4.1 The Discrete-Time Unit Impulse and Unit Step Sequences 30 \n1.4.2 The Continuous-Time Unit Step and Unit Impulse Functions 32 \n1.5 Continuous-Time and Discrete-Time Systems 38 \n1.5.1 Simple Examples of Systems 39 \n1.5.2 Interconnections of Systems 41 \n1.6 Basic System Properties 44 \n1.6.1 Systems with and without Memory 44 \n1.6.2 Invertibility and Inverse Systems 45 \n1.6.3 Causality 46 \n1.6.4 Stability 48 \n1.6.5 Time Invariance 50 \n1.6.6 Linearity 53 \n1.7 Summary 56 \nProblems 57 \n2 \n74 \nLINEAR TIME-INVARIANT SYSTEMS \n2.0 Introduction 74 \n2.1 Discrete-Time LTI Systems: The Convolution Sum 75 \nvii\nviii Contents \n2.1.1 . The Representation of Discrete-Time Signals in Terms \nof Impulses 75 \n2.1.2 The Discrete-Time Unit Impulse Response and the Convolution-Sum \nRepresentation of LTI Systems 77 \n2.2 Continuous-Time LTI Systems: The Convolution Integral 90 \n2.2.1 The Representation of Continuous-Time Signals in Terms \nof Impulses 90 \n2.2.2 The Continuous-Time Unit Impulse Response and the Convolution \nIntegral Representation of LTI Systems 94 \n2.3 Properties of Linear Time-Invariant Systems 103 \n2.3.1 The Commutative Property 104 \n2.3.2 The Distributive Property 104 \n2.3.3 The Associative Property 107 \n2.3.4 LTI Systems with and without Memory 108 \n2.3.5 Invertibility of LTI Systems 109 \n2.3.6 Causality for LTI Systems 112 \n2.3.7 Stability for LTI Systems 113 \n2.3.8 • The Unit Step Response of an LTI System 115 \n2.4 Causal LTI Systems Described by Differential and Difference \n· Equations 116 \n2.4.1 Linear Constant -Coefficient Differential Equations 117 \n2.4.2 Linear Constant-Coefficient Difference Equations 121 \n2.4.3 Block Diagram Representations of First-Order Systems Described \nby Differential and Difference Equations 124 \n2.5 Singularity Functions 127 \n2.5.1 The Unit Impulse as an Idealized Short Pulse 128 \n2.5.2 Defining the Unit Impulse through Convolution 131 \n2.5.3 Unit Doublets and Other Singularity Functions 132 \n2.6 Summary 137 \nProblems 137 \n3 \nFoURIER SERIES REPRESENTATION OF \n177 \nPERIODIC SIGNALS \n3.0 Introduction 177 \n3.1 A Historical Perspective 178 \n3.2 The Response of LTI Systems to Complex Exponentials 182 \n3.3 Fourier Series Representation of Continuous-Time \nPeriodic Signals 186 \n3.3.1 Linear Combinations of Harmonically Related Complex \nExponentials 186 \n3.3.2 Determination of the Fourier Series Representation \nof a Continuous-Time Periodic Signal 190 \n3.4 Convergence of the Fourier Series 195\nContents ix \n3.5 Properties of Continuous-Time Fourier Series 202 \n3.5.1 Linearity 202 \n3.5.2 Time Shifting 202 \n3.5.3 Time Reversal 203 \n3.5.4 Time Scaling 204 \n3.5.5 Multiplication 204 \n3.5.6 Conjugation and Conjugate Symmetry 204 \n3.5.7 Parseval's Relation for Continuous-Time Periodic Signals 205 \n3.5.8 Summary of Properties of the Continuous-Time Fourier Series 205 \n3.5.9 Examples 205 \n3.6 Fourier Series Representation of Discrete-Time \nPeriodic Signals 211 \n3.6.1 Linear Combinations of Harmonically Related Complex \nExponentials 211 \n3.6.2 Determination of the Fourier Series Representation of a · \nPeriodic Signal 212 \n3.7 Properties of Discrete-Time Fourier Series 221 \n3.7.1 Multiplication 222 \n3.7.2 First Difference 222 \n3.7.3 Parseval's Relation for Discrete-Time Periodic Signals 223 \n3.7.4 Examples 223 \n3.8 Fourier Series and LTI Systems 226 \n3.9 Filtering 231 \n3.9.1 Frequency-Shaping Filters 232 \n3.9.2 Frequency-Selective Filters 236 \n3.10 Examples of Continuous-Time Filters Described by \nDifferential Equations 239 \n3.10.1 A Simple RC Lowpass Filter 239 \n3.10.2 A Simple RC Highpass Filter 241 \n3.11 Examples of Discrete-Time Filters Described by \nDifference Equations 244 \n3.11.1 First-Order Recursive Discrete-Time Filters 244 \n3.11.2 Nonrecursive Discrete-Time Filters 245 \n3.12 Summary 249 \nProblems 250 \n4 \nThE CONTINUOUS-TIME FOURIER TRANSFORM 284 \n4.0 Introduction 284 \n4.1 Representation of Aperiodic Signals: The Continuous-Time \nFourier Transform 285 \n4.1.1 Development of the Fourier Transform Representation \nof an Aperiodic Signal 285 \n4.1.2 Convergence of Fourier Transforms 289 \n4.1.3 Examples of Continuous-Time Fourier Transforms 290\nX Contents \n4.2 The Fourier Transform for Periodic Signals 296 \n4.3 Properties of the Continuous-Time Fourier Transform 300 \n4.3.1 Linearity 301 \n4.3.2 Time Shifting 301 \n4.3.3 Conjugation and Conjugate Symmetry 303 \n4.3.4 Differentiation and Integration 306 \n4.3.5 Time and Frequency Scaling 308 \n4.3.6 Duality 309 \n4.3.7 Parseval's Relation 312 \n4.4 The Convolution Property 314 \n4.4.1 Examples 317 \n4.5 The Multiplication Property 322 \n4.5.1 Frequency-Selective Filtering with Variable Center Frequency 325 \n4.6 Tables of Fourier Properties and of Basic Fourier \nTransform Pairs 328 · \n4.7 Systems Characterized by Linear Constant-Coefficient \nDifferential Equations 330 \n4.8 Summary 333 \nProblems 334 \n5 \n358 \nThE DISCRETE-TIME FOURIER TRANSFORM \n5.0 Introduction 358 \n5.1 Representation of Aperiodic Signals: The Discrete-Time \nFourier Transform 359 \n5.1.1 Development of the Discrete-~ime Fourier Transform 359 \n5.1.2 Examples of Discrete-Time Fourier Transforms 362 \n5 .1.3 Convergence Issues Associated with the Discrete-Time Fourier \nTransform 366 \n5.2 The Fourier Transform for Periodic Signals 367 \n5.3 Properties of the Discrete-Time Fourier Transform 372 \n5.3.1. Periodicity of the Discrete-Time Fourier Transform 373 \n5.3.2 Linearity of the Fourier Transform 373 \n5.3.3 Time Shifting and Frequency Shifting 373 \n5.3.4 Conjugation and Conjugate Symmetry 375 \n5.3.5 Differencing and Accumulation 375 \n5.3.6 Time Reversal 376 \n5.3.7 Time Expansion 377 \n5.3.8 Differentiation in Frequency 380 \n5.3.9 Parseval's Relation 380 \n5.4 The Convolution Property 382 \n5.4.1 Examples 383 \n5.5 The Multiplication Property 388 \n5.6 Tables of Fourier Transform Properties and Basic Fourier \nTransform Pairs 390\nContents xi \n5. 7 Duality 390 \n5.7.1 Duality in the Discrete-Time Fourier Series 391 \n5.7.2 Duality between the Discrete-Time Fourier Transform and the \nContinuous-Time Fourier Series 395 \n5.8 Systems Characterized by Linear Constant-Coefficient \nDifference Equations 396 \n5.9 Summary 399 \nProblems 400 \n6 \nTIME AND FREQUENCY CHARACTERIZATION \n423 \nOF SIGNALS AND SYSTEMS \n6.0 Introduction 423 \n6.1 The Magnitude-Phase 'Representation of. the Fourier \nTransform 423 \n6.2 The Magnitude-Phase Representation of the Frequency Response \nof LTI Systems 427 \n6.2.1 Linear and Nonlinear Phase 428 \n6.2.2 Group Delay 430 \n6.2.3 Log-Magnitude and Bode Plots 436 \n6.3 Time-Domain Properties of Ideal Frequency-Selective \nFilters 439 \n6.4 Time-Domain and Frequency-Domain Aspects of Nonideal \nFilters 444 \n6.5 First-Order and Second-Order Continuous-Time Systems 448 \n6.5 .1 First -Order Continuous-Time Systems 448 \n6.5 .2 Second-Order Continuous-Time Systems 451 \n6.5.3 Bode Plots for Rational Frequency Responses 456 \n6.6 First-Order and Second-Order Discrete-Time Systems 461 \n6.6.1 First-Order Discrete-Time Systems 461 \n6.6.2 Second-Order Discrete-Time Systems 465 \n6.7 Examples of Time- and Frequency-Domain Analysis \nof Systems 472 \n6.7.1 Analysis of an Automobile Suspension System 473 \n6.7.2 Examples of Discrete-Time Nonrecursive Filters 476 \n6.8 Summary 482 \nProblems 483 \n7 \n514 \nSAMPLING \n7.0 Introduction 514 \n7.1 Representation of a Continuous-Time Signal by Its Samples: \nThe Sampling Theorem 515 \n7.1.1 Impulse-Train Sampling 516 \n7 .1.2 Sampling with a Zero-Order Hold 520\nxii Contents \n7.2 Reconstruction of a Signal from Its Samples Using \nInterpolation 522 \n7.3 The Effect of Undersampling: Aliasing 527 \n7.4 Discrete-Time Processing of Continuous-Time Signals 534 \n7.4.1 Digital Differentiator 541 \n7.4.2 Half-Sample Delay 543 \n7.5 Sampling of Discrete-Time Signals 545 \n7.5.1 Impulse-Train Sampling 545 \n7.5 .2 Discrete-Time Decimation and Interpolation 549 \n7.6 Summary 555 \nProblems 556 \n8 \nCoMMUNICATION SYSTE.M S 582 \n8.0 Introduction 582 \n8.1 Complex Exponential and Sinusoidal Amplitude Modulation 583 \n8.1.1 Amplitude Modulation with a Complex Exponential Carrier 583 \n8.1.2 Amplitude Modulation with a Sinusoidal Carrier 585 \n8.2 Demodulation for Sinusoidal AM 587 \n8.2.1 Synchronous Demodulation 587 \n8.2.2 Asynchronous Demodulation 590 \n8.3 Frequency-Division Multiplexing 594 \n8.4 Single-Sideband Sinusoidal Amplitude Modulation 597 \n8.5 Amplitude Modulation with a Pulse-Train Carrier 601 \n8.5.1 Modulation of a Pulse-Train Carrier 601 \n8.5.2 Time-Division Multiplexing 604 \n8.6 Pulse-Amplitude Modulation 604 \n8.6.1 Pulse-Amplitude Modulated Signals 604 \n8.6.2 Intersymbol Interference in PAM Systems 607 \n8.6.3 Digit~l Pulse-Amplitude and Pulse-Code Modulation 610 \n8.7 Sinusoidal Frequency Modulation 611 \n8.7.1 Narrowband Frequency Modulation 613 \n8.7.2 Wideband Frequency Modulation 615 \n8.7.3 Periodic Square-Wave Modulating Signal 617 \n8.8 Discrete-Time Modulation 619 \n8.8.1 Discrete-Time Sinusoidal Amplitude Modulation 619 \n8.8.2 Discrete-Time Transmodulation 623 \n8.9 Summary 623 \nProblems 625 \n9 \n654 \nTHE LAPLACE TRANSFORM \n9.0 Introduction 654 \n9.1 The Laplace Transform 655 \n9.2 The Region of Convergence for Laplace Transforms 662\nContents xiii \n9.3 The Inverse Laplace Transfonn 670 \n9.4 Geometric Evaluation of the Fourier Transfonn from the \nPole-Zero Plot 674 \n9.4.1 . First-Order Systems 676 \n9.4.2 Second-Order Systems 677 \n9.4.3 All-Pass Systems 681 \n9.5 Properties of the Laplace Transfonn 682 \n9.5.1 Linearity of the Laplace Transform 683 \n9.5.2 Time Shifting 684 \n9.5.3 Shifting in the s-Domain 685 \n9.5 .4 Time Scal1ng 685 \n9.5.5 Conjugation 687 \n9.5.6 Convolution Property 687 \n9.5.7 Differentiation in the Time Domain 688 \n9.5.8 Differentiation in the s-Domain 688 \n9.5.9 Integration in the Time Domain 690 \n9.5.10 The Initial- and Final-Value Theorems 690 \n9.5.11 Table of Properties 6?1 \n9.6 Some Laplace Transfonn Pairs 692 \n9.7 Analysis and Characterization of LTI Systems Using the \nLaplace Transfonn 693 \n9.7 .1 Causality 693 \n9.7.2 Stability 695 \n9.7.3 LTI Systems Characterized by Linear Constant-Coefficient \nDifferential Equations 698 \n9.7.4 Examples Relating System Behavior to the System Function 701 \n9.7.5 Butterworth Filters 703 \n9.8 System Function Algebra and Block Diagram \nRepresentations 706 \n9.8.1 System Functions for Interconnections of LTI Systems 707 \n9.8.2 Block Diagram Representations for Causal LTI Systems Described \nby Differential Equations and Rational System Functions 708 \n9.9 The Unilateral Laplace Transfonn 714 \n9.9.1 Examples of Unilateral Laplace Transforms 714 \n9.9.2 Properties of the Unilateral Laplace Transform 716 \n9.9.3 Solving Differential Equations Using the Unilateral Laplace \nTransform 719 \n9.10 Summary 720 \nProblems 721 \n10 \n741 \nTHE Z-TRANSFORM \n10.0 Introduction 741 \n10.1 The z-Transfonn 741 \n10.2 The Region of Convergence for the z-Transfonn. 748\nxiv Contents \n10.3 The Inverse z-Transform 757 \n10.4 Geometric Evaluation of the Fourier Transform from the \nPole-Zero Plot 763 \n10.4.1 First-Order Systems 763 \n10.4.2 Second-Order Systems 765 \n10.5 Properties of the z-Transform 767 \n10.5.1 Linearity 767 \n10.5.2 Time Shifting 767 \n10.5.3 Scaling in the z-Domain 768 \n10.5.4 Time Reversal 769 \n10.5.5 Time Expansion 769 \n10.5.6 Conjugation 770 \n10.5.7 The Convolution Property 770 \n10.5.8 Differentiation in the z-Domain 772 \n10.5.9 The Initial-Value Theorem 773 \n10.5.10 Summary of Properties 774 \n10.6 Some Common z-Transform Pairs 774 \n10.7 Analysis and Characterization of LTI Systems Using \nz-Transforms 774 \n10.7.1 Causality 776 \n10.7.2 Stability 777 \n10.7.3 LTI Systems Characterized by Linear Constant-Coefficient \nDifference Equations 779 \n10.7.4 Examples Relating System Behavior to the System Function 781 \n10.8 System Function Algebra and Block Diagram \nRepresentations 783 \n10.8.1 System Functions for Interconnections of LTI Systems 784 \n10.8.2 Block Diagram Representations for Causal LTI Systems Described \nby Difference Equations and Rational System Functions 784 \n10.9 The Unilateral z-Transform 789 \n10.9.1 Examples of Unilateral z-Transforms and Inverse Transforms 790 \n10.9.2 Properties of the Unilateral z-Transform 792 \n10.9.3 Solving Difference Equations Using the Unilateral \nz-Transform 795 \n10.10 Summary 796 \nProblems 797 \n11 \n816 \nUNEAR FEEDBACK SYSTEMS \n11.0 Introduction 816 \n11.1 Linear Feedback Systems 819 \n11.2 Some Applications and Consequences of Feedback 820 \n11.2.1 Inverse System Design 820 \n11.2.2 Compensation for Nonideal Elements 821 \n11.2.3 Stabilization of Unstable Systems 823","status":1,"price":null,"rent_price":null,"isbn":null,"redirect_url":"book"},"myLikesProps":null,"myDriveProps":null,"requestedBooksProps":null,"user":null},"__N_SSP":true},"page":"/book/[detail]","query":{"detail":"signals-and-system"},"buildId":"0yngpp-mRDH7Bzgj1Hnuf","isFallback":false,"gssp":true,"scriptLoader":[]}</script><next-route-announcer><p aria-live="assertive" id="__next-route-announcer__" role="alert" style="border: 0px; 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