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Signals and Systems

ISBN: 9780138147570 | 0138147574
Edition: 2nd
Format: Hardcover
Publisher: Prentice Hall
Pub. Date: 8/6/1996

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SummaryTable of Contents
For undergraduate-level courses in Signals and Systems. This comprehensive exploration of signals and systems develops continuous-time and discrete-time concepts/methods in parallel -- highlighting the similarities and differences -- and features introductory treatments of the applications of these basic methods in such areas as filtering, communication, sampling, discrete-time processing of continuous-time signals, and feedback. Relatively self-contained, the text assumes no prior experience with system analysis, convolution, Fourier analysis,... MORE
PREFACEXVII(8)
ACKNOWLEDGMENTSXXV(2)
FOREWORDXXVII
1 SIGNALS AND SYSTEMS
1(73)
... MORE
1.0 Introduction
1(1)
1.1 Continuous-Time and Discrete-Time Signals
1(6)
1.1.1 Examples and Mathematical Representation
1(4)
1.1.2 Signal Energy and Power
5(2)
1.2 Transformations of the Independent Variable
7(7)
1.2.1 Examples of Transformations of the Independent Variable
8(3)
1.2.2 Periodic Signals
11(2)
1.2.3 Even and Odd Signals
13(1)
1.3 Exponential and Sinusoidal Signals
14(16)
1.3.1 Continuous-Time Complex Exponential and Sinusoidal Signals
15(6)
1.3.2 Discrete-Time Complex Exponential and Sinusoidal Signals
21(4)
1.3.3 Periodicity Properties of Discrete-Time Complex Exponentials
25(5)
1.4 The Unit Impulse and Unit Step Functions
30(8)
1.4.1 The Discrete-Time Unit Impulse and Unit Step Sequences
30(2)
1.4.2 The Continuous-Time Unit Step and Unit Impulse Functions
32(6)
1.5 Continuous-Time and Discrete-Time Systems
38(6)
1.5.1 Simple Examples of Systems
39(2)
1.5.2 Interconnections of Systems
41(3)
1.6 Basic System Properties
44(12)
1.6.1 Systems with and without Memory
44(1)
1.6.2 Invertibility and Inverse Systems
45(1)
1.6.3 Causality
46(2)
1.6.4 Stability
48(2)
1.6.5 Time Invariance
50(3)
1.6.6 Linearity
53(3)
1.7 Summary
56(1)
Problems
57(17)
2 LINEAR TIME-INVARIANT SYSTEMS
74(103)
2.0 Introduction
74(1)
2.1 Discrete-Time LTI Systems: The Convolution Sum
75(15)
2.1.1 The Representation of Discrete-Time Signals in Terms of Impulses
75(2)
2.1.2 The Discrete-Time Unit Impulse Response and the Convolution-Sum Representation of LTI Systems
77(13)
2.2 Continuous-Time LTI Systems: The Convolution Integral
90(13)
2.2.1 The Representation of Continuous-Time Signals in Terms of Impulses
90(4)
2.2.2 The Continuous-Time Unit Impulse Response and the Convolution Integral Representation of LTI Systems
94(9)
2.3 Properties of Linear Time-Invariant Systems
103(13)
2.3.1 The Commutative Property
104(1)
2.3.2 The Distributive Property
104(3)
2.3.3 The Associative Property
107(1)
2.3.4 LTI Systems with and without Memory
108(1)
2.3.5 Invertibility of LTI Systems
109(3)
2.3.6 Causality for LTI Systems
112(1)
2.3.7 Stability for LTI Systems
113(2)
2.3.8 The Unit Step Response of an LTI System
115(1)
2.4 Causal LTI Systems Described by Differential and Difference Equations
116(11)
2.4.1 Linear Constant-Coefficient Differential Equations
117(4)
2.4.2 Linear Constant-Coefficient Difference Equations
121(3)
2.4.3 Block Diagram Representations of First-Order Systems Described by Differential and Difference Equations
124(3)
2.5 Singularity Functions
127(10)
2.5.1 The Unit Impulse as an Idealized Short Pulse
128(3)
2.5.2 Defining the Unit Impulse through Convolution
131(1)
2.5.3 Unit Doublets and Other Singularity Functions
132(5)
2.6 Summary
137(1)
Problems
137(40)
3 FOURIER SERIES REPRESENTATION OF PERIODIC SIGNALS
177(107)
3.0 Introduction
177(1)
3.1 A Historical Perspective
178(4)
3.2 The Response of LTI Systems to Complex Exponentials
182(4)
3.3 Fourier Series Representation of Continuous-Time Periodic Signals
186(9)
3.3.1 Linear Combinations of Harmonically Related Complex Exponentials
186(4)
3.3.2 Determination of the Fourier Series Representation of a Continuous-Time Periodic Signal
190(5)
3.4 Convergence of the Fourier Series
195(7)
3.5 Properties of Continuous-Time Fourier Series
202(9)
3.5.1 Linearity
202(1)
3.5.2 Time Shifting
202(1)
3.5.3 Time Reversal
203(1)
3.5.4 Time Scaling
204(1)
3.5.5 Multiplication
204(1)
3.5.6 Conjugation and Conjugate Symmetry
204(1)
3.5.7 Parseval's Relation for Continuous-Time Periodic Signals
205(1)
3.5.8 Summary of Properties of the Continuous-Time Fourier Series
205(1)
3.5.9 Examples
205(6)
3.6 Fourier Series Representation of Discrete-Time Periodic Signals
211(10)
3.6.1 Linear Combinations of Harmonically Related Complex Exponentials
211(1)
3.6.2 Determination of the Fourier Series Representation of a Periodic Signal
212(9)
3.7 Properties of Discrete-Time Fourier Series
221(5)
3.7.1 Multiplication
222(1)
3.7.2 First Difference
222(1)
3.7.3 Parseval's Relation for Discrete-Time Periodic Signals
223(1)
3.7.4 Examples
223(3)
3.8 Fourier Series and LTI Systems
226(5)
3.9 Filtering
231(8)
3.9.1 Frequency-Shaping Filters
232(4)
3.9.2 Frequency-Selective Filters
236(3)
3.10 Examples of Continuous-Time Filters Described by Differential Equations
239(5)
3.10.1 A Simple RC Lowpass Filter
239(2)
3.10.2 A Simple RC Highpass Filter
241(3)
3.11 Examples of Discrete-Time Filters Described by Difference Equations
244(5)
3.11.1 First-Order Recursive Discrete-Time Filters
244(1)
3.11.2 Nonrecursive Discrete-Time Filters
245(4)
3.12 Summary
249(1)
Problems
250(34)
4 THE CONTINUOUS-TIME FOURIER TRANSFORM
284(74)
4.0 Introduction
284(1)
4.1 Representation of Aperiodic Signals: The Continuous-Time Fourier Transform
285(11)
4.1.1 Development of the Fourier Transform Representation of an Aperiodic Signal
285(4)
4.1.2 Convergence of Fourier Transforms
289(1)
4.1.3 Examples of Continuous-Time Fourier Transforms
290(6)
4.2 The Fourier Transform for Periodic Signals
296(4)
4.3 Properties of the Continuous-Time Fourier Transform
300(14)
4.3.1 Linearity
301(1)
4.3.2 Time Shifting
301(2)
4.3.3 Conjugation and Conjugate Symmetry
303(3)
4.3.4 Differentiation and Integration
306(2)
4.3.5 Time and Frequency Scaling
308(1)
4.3.6 Duality
309(3)
4.3.7 Parseval's Relation
312(2)
4.4 The Convolution Property
314(8)
4.4.1 Examples
317(5)
4.5 The Multiplication Property
322(6)
4.5.1 Frequency-Selective Filtering with Variable Center Frequency
325(3)
4.6 Tables of Fourier Properties and of Basic Fourier Transform Pairs
328(2)
4.7 Systems Characterized by Linear Constant-Coefficient Differential Equations
330(3)
4.8 Summary
333(1)
Problems
334(24)
5 THE DISCRETE-TIME FOURIER TRANSFORM
358(65)
5.0 Introduction
358(1)
5.1 Representation of Aperiodic Signals: The Discrete-Time Fourier Transform
359(8)
5.1.1 Development of the Discrete-Time Fourier Transform
359(3)
5.1.2 Examples of Discrete-Time Fourier Transforms
362(4)
5.1.3 Convergence Issues Associated with the Discrete-Time Fourier Transform
366(1)
5.2 The Fourier Transform for Periodic Signals
367(5)
5.3 Properties of the Discrete-Time Fourier Transform
372(10)
5.3.1 Periodicity of the Discrete-Time Fourier Transform
373(1)
5.3.2 Linearity of the Fourier Transform
373(1)
5.3.3 Time Shifting and Frequency Shifting
373(2)
5.3.4 Conjugation and Conjugate Symmetry
375(1)
5.3.5 Differencing and Accumulation
375(1)
5.3.6 Time Reversal
376(1)
5.3.7 Time Expansion
377(3)
5.3.8 Differentiation in Frequency
380(1)
5.3.9 Parseval's Relation
380(2)
5.4 The Convolution Property
382(6)
5.4.1 Examples
383(5)
5.5 The Multiplication Property
388(2)
5.6 Tables of Fourier Transform Properties and Basic Fourier Transform Pairs
390(1)
5.7 Duality
390(6)
5.7.1 Duality in the Discrete-Time Fourier Series
391(4)
5.7.2 Duality between the Discrete-Time Fourier Transform and the Continuous-Time Fourier Series
395(1)
5.8 Systems Characterized by Linear Constant-Coefficient Difference Equations
396(3)
5.9 Summary
399(1)
Problems
400(23)
6 TIME AND FREQUENCY CHARACTERIZATION OF SIGNALS AND SYSTEMS
423(91)
6.0 Introduction
423(1)
6.1 The Magnitude-Phase Representation of the Fourier Transform
423(4)
6.2 The Magnitude-Phase Representation of the Frequency Response of LTI Systems
427(12)
6.2.1 Linear and Nonlinear Phase
428(2)
6.2.2 Group Delay
430(6)
6.2.3 Log-Magnitude and Bode Plots
436(3)
6.3 Time-Domain Properties of Ideal Frequency-Selective Filters
439(5)
6.4 Time-Domain and Frequency-Domain Aspects of Nonideal Filters
444(4)
6.5 First-Order and Second-Order Continuous-Time Systems
448(13)
6.5.1 First-Order Continuous-Time Systems
448(3)
6.5.2 Second-Order Continuous-Time Systems
451(5)
6.5.3 Bode Plots for Rational Frequency Responses
456(5)
6.6 First-Order and Second-Order Discrete-Time Systems
461(11)
6.6.1 First-Order Discrete-Time Systems
461(4)
6.6.2 Second-Order Discrete-Time Systems
465(7)
6.7 Examples of Time- and Frequency-Domain Analysis of Systems
472(10)
6.7.1 Analysis of an Automobile Suspension System
473(3)
6.7.2 Examples of Discrete-Time Nonrecursive Filters
476(6)
6.8 Summary
482(1)
Problems
483(31)
7 SAMPLING
514(68)
7.0 Introduction
514(1)
7.1 Representation of a Continuous-Time Signal by Its Samples: The Sampling Theorem
515(7)
7.1.1 Impulse-Train Sampling
516(4)
7.1.2 Sampling with a Zero-Order Hold
520(2)
7.2 Reconstruction of a Signal from Its Samples Using Interpolation
522(5)
7.3 The Effect of Undersampling: Aliasing
527(7)
7.4 Discrete-Time Processing of Continuous-Time Signals
534(11)
7.4.1 Digital Differentiator
541(2)
7.4.2 Half-Sample Delay
543(2)
7.5 Sampling of Discrete-Time Signals
545(10)
7.5.1 Impulse-Train Sampling
545(4)
7.5.2 Discrete-Time Decimation and Interpolation
549(6)
7.6 Summary
555(1)
Problems
556(26)
8 COMMUNICATION SYSTEMS
582(72)
8.0 Introduction
582(1)
8.1 Complex Exponential and Sinusoidal Amplitude Modulation
583(4)
8.1.1 Amplitude Modulation with a Complex Exponential Carrier
583(2)
8.1.2 Amplitude Modulation with a Sinusoidal Carrier
585(2)
8.2 Demodulation for Sinusoidal AM
587(7)
8.2.1 Synchronous Demodulation
587(3)
8.2.2 Asynchronous Demodulation
590(4)
8.3 Frequency-Division Multiplexing
594(3)
8.4 Single-Sideband Sinusoidal Amplitude Modulation
597(4)
8.5 Amplitude Modulation with a Pulse-Train Carrier
601(3)
8.5.1 Modulation of a Pulse-Train Carrier
601(3)
8.5.2 Time-Division Multiplexing
604(1)
8.6 Pulse-Amplitude Modulation
604(7)
8.6.1 Pulse-Amplitude Modulated Signals
604(3)
8.6.2 Intersymbol Interference in PAM Systems
607(3)
8.6.3 Digital Pulse-Amplitude and Pulse-Code Modulation
610(1)
8.7 Sinusoidal Frequency Modulation
611(8)
8.7.1 Narrowband Frequency Modulation
613(2)
8.7.2 Wideband Frequency Modulation
615(2)
8.7.3 Periodic Square-Wave Modulating Signal
617(2)
8.8 Discrete-Time Modulation
619(4)
8.8.1 Discrete-Time Sinusoidal Amplitude Modulation
619(4)
8.8.2 Discrete-Time Transmodulation
623(1)
8.9 Summary
623(2)
Problems
625(29)
9 THE LAPLACE TRANSFORM
654(87)
9.0 Introduction
654(1)
9.1 The Laplace Transform
655(7)
9.2 The Region of Convergence for Laplace Transforms
662(8)
9.3 The Inverse Laplace Transform
670(4)
9.4 Geometric Evaluation of the Fourier Transform from the Pole-Zero Plot
674(8)
9.4.1 First-Order Systems
676(1)
9.4.2 Second-Order Systems
677(4)
9.4.3 All-Pass Systems
681(1)
9.5 Properties of the Laplace Transform
682(10)
9.5.1 Linearity of the Laplace Transform
683(1)
9.5.2 Time Shifting
684(1)
9.5.3 Shifting in the s-Domain
685(1)
9.5.4 Time Scaling
685(2)
9.5.5 Conjugation
687(1)
9.5.6 Convolution Property
687(1)
9.5.7 Differentiation in the Time Domain
688(1)
9.5.8 Differentiation in the s-Domain
688(2)
9.5.9 Integration in the Time Domain
690(1)
9.5.10 The Initial- and Final-Value Theorems
690(1)
9.5.11 Table of Properties
691(1)
9.6 Some Laplace Transform Pairs
692(1)
9.7 Analysis and Characterization of LTI Systems Using the Laplace Transform
693(13)
9.7.1 Causality
693(2)
9.7.2 Stability
695(3)
9.7.3 LTI Systems Characterized by Linear Constant-Coefficient Differential Equations
698(3)
9.7.4 Examples Relating System Behavior to the System Function
701(2)
9.7.5 Butterworth Filters
703(3)
9.8 System Function Algebra and Block Diagram Representations
706(8)
9.8.1 System Functions for Interconnections of LTI Systems
707(1)
9.8.2 Block Diagram Representations for Causal LTI Systems Described by Differential Equations and Rational System Functions
708(6)
9.9 The Unilateral Laplace Transform
714(6)
9.9.1 Examples of Unilateral Laplace Transforms
714(2)
9.9.2 Properties of the Unilateral Laplace Transform
716(3)
9.9.3 Solving Differential Equations Using the Unilateral Laplace Transform
719(1)
9.10 Summary
720(1)
Problems
721(20)
10 THE Z-TRANSFORM
741(75)
10.0 Introduction
741(1)
10.1 The z-Transform
741(7)
10.2 The Region of Convergence for the z-Transform
748(9)
10.3 The Inverse z-Transform
757(6)
10.4 Geometric Evaluation of the Fourier Transform from the Pole-Zero Plot
763(4)
10.4.1 First-Order Systems
763(2)
10.4.2 Second-Order Systems
765(2)
10.5 Properties of the z-Transform
767(7)
10.5.1 Linearity
767(1)
10.5.2 Time Shifting
767(1)
10.5.3 Scaling in the z-Domain
768(1)
10.5.4 Time Reversal
769(1)
10.5.5 Time Expansion
769(1)
10.5.6 Conjugation
770(1)
10.5.7 The Convolution Property
770(2)
10.5.8 Differentiation in the z-Domain
772(1)
10.5.9 The Initial-Value Theorem
773(1)
10.5.10 Summary of Properties
774(1)
10.6 Some Common z-Transform Pairs
774(1)
10.7 Analysis and Characterization of LTI Systems Using z-Transforms
774(9)
10.7.1 Causality
776(1)
10.7.2 Stability
777(2)
10.7.3 LTI Systems Characterized by Linear Constant-Coefficient Difference Equations
779(2)
10.7.4 Examples Relating System Behavior to the System Function
781(2)
10.8 System Function Algebra and Block Diagram Representations
783(6)
10.8.1 System Functions for Interconnections of LTI Systems
784(1)
10.8.2 Block Diagram Representations for Causal LTI Systems Described by Difference Equations and Rational System Functions
784(5)
10.9 The Unilateral z-Transform
789(7)
10.9.1 Examples of Unilateral z-Transforms and Inverse Transforms
790(2)
10.9.2 Properties of the Unilateral z-Transform
792(3)
10.9.3 Solving Difference Equations Using the Unilateral z-Transform
795(1)
10.10 Summary
796(1)
Problems
797(19)
11 LINEAR FEEDBACK SYSTEMS
816(93)
11.0 Introduction
816(3)
11.1 Linear Feedback Systems
819(1)
11.2 Some Applications and Consequences of Feedback
820(12)
11.2.1 Inverse System Design
820(1)
11.2.2 Compensation for Nonideal Elements
821(2)
11.2.3 Stabilization of Unstable Systems
823(3)
11.2.4 Sampled-Data Feedback Systems
826(2)
11.2.5 Tracking Systems
828(2)
11.2.6 Destabilization Caused by Feedback
830(2)
11.3 Root-Locus Analysis of Linear Feedback Systems
832(14)
11.3.1 An Introductory Example
833(1)
11.3.2 Equation for the Closed-Loop Poles
834(2)
11.3.3 The End Points of the Root Locus: The Closed-Loop Poles for K = 0 and ŠKŠ = +(XXX)
836(1)
11.3.4 The Angle Criterion
836(5)
11.3.5 Properties of the Root Locus
841(5)
11.4 The Nyquist Stability Criterion
846(12)
11.4.1 The Encirclement Property
847(3)
11.4.2 The Nyquist Criterion for Continuous-Time LTI Feedback Systems
850(6)
11.4.3 The Nyquist Criterion for Discrete-Time LTI Feedback Systems
856(2)
11.5 Gain and Phase Margins
858(8)
11.6 Summary
866(1)
Problems
867(42)
APPENDIX PARTIAL-FRACTION EXPANSION909(12)
BIBLIOGRAPHY921(10)
ANSWERS931(10)
INDEX941

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