Linear Systems and Signals,9780195158335

Linear Systems and Signals

by
Edition: 2nd
ISBN13: 9780195158335
ISBN10: 0195158334
Format: Hardcover
Pub. Date: 2004-07-01
Publisher(s): Oxford University Press
Upgraded Edition: Click here!
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Summary

Incorporating new problems and examples, the second edition of Linear Systems and Signals features MATLABRG material in each chapter and at the back of the book. It gives clear descriptions of linear systems and uses mathematics not only to prove axiomatic theory, but also to enhance physicaland intuitive understanding.

Author Biography


B. P. Lathi is Professor Emeritus of Electrical Engineering at California State University, Sacramento. He is the author of Signal Processing and Linear Systems (OUP, 2000) and Modern Digital and Analog Communications Systems, 3/e (OUP, 1998).

Table of Contents

PREFACE xiii
B BACKGROUND
B.1 Complex Numbers
B.1-1 A Historical Note
1(4)
B.1-2 Algebra of Complex Numbers
5(11)
B.2 Sinusoids
16(6)
B.2-1 Addition of Sinusoids
18(3)
B.2-2 Sinusoids in Terms of Exponentials: Euler's Formula
21(1)
B.3 Sketching Signals
22(2)
B.3-1 Monotonic Exponentials
22(1)
B.3-2 The Exponentially Varying Sinusoid
23(1)
B.4 Cramer's Rule
24(2)
B.5 Partial Fraction Expansion
26(11)
B.5-1 Method of Clearing Fractions
27(1)
B.5-2 The Heaviside "Cover-Up" Method
28(4)
B.5-3 Repeated Factors of Q(x)
32(2)
B.5-4 Mixture of the Heaviside "Cover-Up" and Clearing Fractions
34(1)
B.5-5 Improper F(x) with m = n
35(1)
B.5-6 Modified Partial Fractions
36(1)
B.6 Vectors and Matrices
37(11)
B.6-1 Some Definitions and Properties
38(1)
B.6-2 Matrix Algebra
39(4)
B.6-3 Derivatives and Integrals of a Matrix
43(2)
B.6-4 The Characteristic Equation of a Matrix: The Cayley-Hamilton Theorem
45(2)
B.6-5 Computation of an Exponential and a Power of a Matrix
47(1)
B.7 Miscellaneous
48(20)
B.7-1 L'Hôpital's Rule
48(1)
B.7-2 The Taylor and Maclaurin Series
48(1)
B.7-3 Power Series
48(1)
B.7-4 Sums
49(1)
B.7-5 Complex Numbers
49(1)
B.7-6 Trigonometric Identities
49(1)
B.7-7 Indefinite Integrals
50(1)
B.7-8 Common Derivative Formulas
51(1)
B.7-9 Some Useful Constants
52(1)
B.7-10 Solution of Quadratic and Cubic Equations
52(1)
References
53(1)
MATLAB Session B: Elementary Operations
53(11)
Problems
64(4)
1 SIGNALS AND SYSTEMS
1.1 Size of a Signal
68(83)
1.1-1 Signal Energy
69(1)
1.1-2 Signal Power
69(6)
1.2 Some Useful Signal Operations
75(7)
1.2-1 Time Shifting
75(2)
1.2-2 Time Scaling
77(3)
1.2-3 Time Reversal
80(1)
1.2-4 Combined Operations
81(1)
1.3 Classification of Signals
82(4)
1.3-1 Continuous-Time and Discrete-Time Signals
82(1)
1.3-2 Analog and Digital Signals
82(1)
1.3-3 Periodic and Aperiodic Signals
83(3)
1.3-4 Energy and Power Signals
86(1)
1.3-5 Deterministic and Random Signals
86(1)
1.4 Some Useful Signal Models
86(10)
1.4-1 Unit Step Function u(t)
87(3)
1.4-2 The Unit Impulse Function δ(t)
90(4)
1.4-3 The Exponential Function est
94(2)
1.5 Even and Odd Functions
96(3)
1.5-1 Some Properties of Even and Odd Functions
96(1)
1.5-2 Even and Odd Components of a Signal
97(2)
1.6 Systems
99(2)
1.7 Classification of Systems
101(12)
1.7-1 Linear and Nonlinear Systems
101(5)
1.7-2 Time-Invariant and Time-Varying Systems
106(1)
1.7-3 Instantaneous and Dynamic Systems
107(1)
1.7-4 Causal and Noncausal Systems
108(2)
1.7-5 Continuous-Time and Discrete-Time Systems
110(1)
1.7-6 Analog and Digital Systems
111(1)
1.7-7 Invertible and Noninvertible Systems
112(1)
1.7-8 Stable and Unstable Systems
112(1)
1.8 System Model: Input Output Description
113(9)
1.8-1 Electrical Systems
113(4)
1.8-2 Mechanical Systems
117(4)
1.8-3 Electromechanical Systems
121(1)
1.9 Internal and External Description of a System
122(2)
1.10 Internal Description: The State-Space Description
124(5)
1.11 Summary
129(2)
References
131(1)
MATLAB Session I: Working with Functions
131(7)
Problems
138(13)
2 TIME-DOMAIN ANALYSIS OF CONTINUOUS-TIME SYSTEMS
2.1 Introduction
151(1)
2.2 System Response to Internal Conditions: The Zero-Input Response
152(12)
2.2-1 Some Insights into the Zero-Input Behavior of a System
163(1)
2.3 The Unit Impulse Response h(t)
164(5)
2.4 System Response to External Input: Zero-State Response
169(29)
2.4-1 The Convolution Integral
171(8)
2.4-2 Graphical Understanding of Convolution Operation
179(13)
2.4-3 Interconnected Systems
192(3)
2.4-4 A Very Special Function for LTIC Systems: The Everlasting Exponential est
195(2)
2.4-5 Total Response
197(1)
2.5 Classical Solution of Differential Equations
198(9)
2.5-1 Forced Response: The Method of Undetermined Coefficients
199(8)
2.6 System Stability
207(8)
2.6-1 Internal (Asymptotic) Stability
209(2)
2.6-2 Relationship Between BIBO and Asymptotic Stability
211(4)
2.7 Intuitive Insights into System Behavior
215(8)
2.7-1 Dependence of System Behavior on Characteristic Modes
215(1)
2.7-2 Response Time of a System: The System Time Constant
216(2)
2.7-3 Time Constant and Rise Time of a System
218(1)
2.7-4 Time Constant and Filtering
218(2)
2.7-5 Time Constant and Pulse Dispersion (Spreading)
220(1)
2.7-6 Time Constant and Rate of Information Transmission
220(1)
2.7-7 The Resonance Phenomenon
221(2)
2.8 Appendix 2.1: Determining the Impulse Response
223(2)
2.9 Summary
225(1)
References
226(1)
MATLAB Session 2: M-Files
227(8)
Problems
235(10)
3 TIME-DOMAIN ANALYSIS OF DISCRETE-TIME SYSTEMS
3.1 Introduction
245(3)
3.1-1 Size of a Discrete-Time Signal
246(2)
3.2 Useful Signal Operations
248(4)
3.3 Some Useful Discrete-Time Signal Models
252(7)
3.3-1 Discrete-Time Impulse Function σ[η]
252(1)
3.3-2 Discrete-Time Unit Step Function u[η]
253(1)
3.3-3 Discrete-Time Exponential γη
254(3)
3.3-4 Discrete-Time Sinusoid cos(Ωη + theta)
257(2)
3.3-5 Discrete-Time Complex Exponential ejΩη
259(1)
3.4 Examples of Discrete-Time Systems
259(11)
3.4-1 Classification of Discrete-Time Systems
268(2)
3.5 Discrete-Time System Equations
270(6)
3.5-1 Recursive (Iterative) Solution of Difference Equation
271(5)
3.6 System Response to Internal Conditions: The Zero-Input Response
276(6)
3.7 The Unit Impulse Response h[η]
282(4)
3.8 System Response to External Input: The Zero-State Response
286(18)
3.8-1 Graphical Procedure for the Convolution Sum
294(6)
3.8-2 Interconnected Systems
300(2)
3.8-3 A Very Special Function for LTID Systems: The Everlasting Exponential zη
302(1)
3.8-4 Total Response
303(1)
3.9 Classical Solution of Linear Difference Equations
304(7)
3.10 System Stability: The External (BIBO) Stability Criterion
311(29)
3.10-1 Internal (Asymptotic) Stability
312(2)
3.10-2 Relationship Between BIBO and Asymptotic Stability
314(3)
3.11 Intuitive Insights into System Behavior
317(1)
3.12 Appendix 3.1: Impulse Response for a Special Case
318(1)
3.13 Summary
318(2)
MATLAB Session 3: Discrete-Time Signals and Systems
320(6)
Problems
326(14)
4 CONTINUOUS-TIME SYSTEM ANALYSIS USING THE LAPLACE TRANSFORM
4.1 The Laplace Transform
340(20)
4.1-1 Finding the Inverse Transform
348(12)
4.2 Some Properties of the Laplace Transform
360(11)
4.2-1 Time Shifting
360(3)
4.2-2 Frequency Shifting
363(1)
4.2-3 The Time-Differentiation Property
364(2)
4.2-4 The Time-Integration Property
366(2)
4.2-5 Time Convolution and Frequency Convolution
368(3)
4.3 Solution of Differential and Integro-Differential Equations
371(13)
4.3-1 Zero-State Response
376(5)
4.3-2 Stability
381(3)
4.3-3 Inverse Systems
384(1)
4.4 Analysis of Electrical Networks: The Transformed Network
384(13)
4.4-1 Analysis of Active Circuits
393(4)
4.5 Block Diagrams
397(2)
4.6 System Realization
399(16)
4.6-1 Direct Form I Realization
400(2)
4.6-2 Direct Form II Realization
402(2)
4.6-3 Cascade and Parallel Realizations
404(3)
4.6-4 Transposed Realization
407(3)
4.6-5 Using Operational Amplifiers for System Realization
410(5)
4.7 Application to Feedback and Controls
415(8)
4.7-1 Analysis of a Simple Control System
417(6)
4.8 Frequency Response of an LTIC System
423(7)
4.8-1 Steady-State Response to Causal Sinusoidal Inputs
429(1)
4.9 Bode Plots
430(64)
4.9-1 Constant kappaα1α2/b1b3
432(1)
4.9-2 Pole (or Zero) at the Origin
433(1)
4.9-3 First-Order Pole (or Zero)
434(3)
4.9-4 Second-Order Pole (or Zero)
437(9)
4.9-5 The Transfer Function from the Frequency Response
446(1)
4.10 Filter Design by Placement of Poles and Zeros of H(s)
446(32)
4.10-1 Dependence of Frequency Response on Poles and Zeros of H(s)
447(3)
4.10-2 Lowpass Filters
450(1)
4.10-3 Bandpass Filters
451(1)
4.10-4 Notch (Bandstop) Filters
451(3)
4.10-5 Practical Filters and Their Specifications
454(2)
4.11 The Bilateral Laplace Transform
456(6)
4.11-1 Properties of Bilateral Laplace Transform
462(1)
4.11-2 Using the Bilateral Transform for Linear System Analysis
463(4)
4.12 Summary
467(1)
References
468(1)
MATLAB Session 4: Continuous-Time Filters
468(10)
Problems
478(16)
5 DISCRETE-TIME SYSTEM ANALYSIS USING THE z-TRANSFORM
5.1 The z-Transform
494(12)
5.1-1 Finding the Inverse Transform
501(5)
5.2 Some Properties of the z-Transform
506(9)
5.3 z-Transform Solution of Linear Difference Equations
515(10)
5.3-1 Zero-State Response of LTID Systems: The Transfer Function
519(4)
5.3-2 Stability
523(1)
5.3-3 Inverse Systems
524(1)
5.4 System Realization
525(6)
5.5 Frequency Response of Discrete-Time Systems
531(13)
5.5-1 The Periodic Nature of the Frequency Response
537(4)
5.5-2 Aliasing and Sampling Rate
541(3)
5.6 Frequency Response from Pole-Zero Location
544(9)
5.7 Digital Processing of Analog Signals
553(7)
5.8 Connection Between the Laplace Transform and the z-Transform
560(2)
5.9 The Bilateral z-Transform
562(116)
5.9-1 Properties of the Bilateral z.-Transform
568(1)
5.9-2 Using the Bilateral z-Transform for Analysis of LTID Systems
569(2)
5.10 Summary
571(1)
References
572(1)
MATLAB Session 5: Discrete-Time IIR Filters
572(9)
Problems
581(13)
6 CONTINUOUS-TIME SIGNAL ANALYSIS: THE FOURIER SERIES
6.1 Periodic Signal Representation by Trigonometric Fourier Series
594(84)
6.1-1 The Fourier Spectrum
600(9)
6.1-2 The Effect of Symmetry
609(2)
6.1-3 Determining the Fundamental Frequency and Period
611(3)
6.2 Existence and Convergence of the Fourier Series
614(1)
6.2-1 Convergence of a Series
615(2)
6.2-2 The Role of Amplitude and Phase Spectra in Waveshaping
617(6)
6.3 Exponential Fourier Series
623(4)
6.3-1 Exponential Fourier Spectra
627(7)
6.3-2 Parseval's Theorem
634(3)
6.4 LTIC System Response to Periodic Inputs
637(4)
6.5 Generalized Fourier Series: Signals as Vectors
641(1)
6.5-1 Component of a Vector
641(1)
6.5-2 Signal Comparison and Component of a Signal
642(3)
6.5-3 Extension to Complex Signals
645(1)
6.5-4 Signal Representation by an Orthogonal Signal Set
646(12)
6.6 Numerical Computation of Dn
658(2)
6.7 Summary
660(1)
References
661(1)
MATLAB Session 6: Ferrier Series Applications
662(7)
Problems
669(9)
7 CONTINUOUS-TIME SIGNAL ANALYSIS: THE FOURIER 'IRANSFORM
7.1 Aperiodic Signal Representation by Fourier Integral
678(9)
7.1-1 Physical Appreciation of the Fourier Transform
685(2)
7.2 Transforms of Some Useful Functions
687(11)
7.2-1 Connection Between the Fourier and Laplace Transforms
697(1)
7.3 Some Properties of the Fourier Transform
698(19)
7.4 Signal Transmission Through LTIC Systems
717(9)
7.4-1 Signal Distortion During Transmission
719(3)
7.4-2 Bandpass Systems and Group Delay
722(4)
7.5 Ideal and Practical Filters
726(3)
7.6 Signal Energy
729(3)
7.7 Application to Communications: Amplitude Modulation
732(14)
7.7-1 Double-Sideband, Suppressed-Carrier (DSB-SC) Modulation
732(5)
7.7-2 Amplitude Modulation (AM)
737(5)
7.7-3 Single-Sideband Modulation (SSB)
742(3)
7.7-4 Frequency-Division Multiplexing
745(1)
7.8 Data Truncation: Window Functions
746(7)
7.8-1 Using Windows in Filter Design
751(2)
7.9 Summary
753(1)
References
754(1)
MATLAB Session 7: Fourier Transform Topics
754(6)
Problems
760(10)
8 SAMPLING: THE BRIDGE FROM CONTINUOUS TO DISCRETE
8.1 The Sampling Theorem
770(8)
8.1-1 Practical Sampling
775(3)
8.2 Signal Reconstruction
778(14)
8.2-1 Practical Difficulties in Signal Reconstruction
781(9)
8.2-2 Some Applications of the Sampling Theorem
790(2)
8.3 Analog-to-Digital (A/D) Conversion
792(3)
8.4 Dual of Time Sampling: Spectral Sampling
795(3)
8.5 Numerical Computation of the Fourier Transform: The Discrete Fourier Transform (DFT)
798(19)
8.5-1 Some Properties of the DFT
811(2)
8.5-2 Some Applications of the DFT
813(4)
8.6 The Fast Fourier Transform (FFT)
817(4)
8.7 Summary
821(1)
References
822(1)
MATLAB Session 8: The Discrete Fourier Transform
822(7)
Problems
829(8)
9 FOURIER ANALYSIS OF DISCRETE-TIME SIGNALS .
9.1 Discrete-Time Fourier Series (DTFS)
837(10)
9.1-1 Periodic Signal Representation by Discrete-Time Fourier Series
838(2)
9.1-2 Fourier Spectra of a Periodic Signal x[η]
840(7)
9.2 Aperiodic Signal Representation by Fourier Integral
847(12)
9.2-1 Nature of Fourier Spectra
850(8)
9.2-2 Connection Between the DTFT and the z-Transform
858(1)
9.3 Properties of the DTFT
859(11)
9.4 LTI Discrete-Time System Analysis by DTFT
870(5)
9.4-1 Distortionless Transmission
872(2)
9.4-2 Ideal and Practical Filters
874(1)
9.5 DTFT Connection with the CTFT
875(3)
9.5-1 Use of DFT and FFT for Numerical Computation of DTFT
876(2)
9.6 Generalization of the DTFT to the z-transform
878(2)
9.7 Summary
880(1)
Reference
881(1)
MATLAB Session 9: Working with the DTFS and the DTFT
881(9)
Problems
890
10 STATE-SPACE ANALYSIS
10.1 Introduction
899(2)
10.2 A Systematic Procedure for Determining State Equations
901(62)
10.2-1 Electrical Circuits
902(2)
10.2-2 State Equations from a Transfer Function
904(8)
10.3 Solution of State Equations
912(1)
10.3-1 Laplace Transform Solution of State Equations
912(7)
10.3-2 Time-Domain Solution of State Equations
919(7)
10.4 Linear Transformation of State Vector
926(4)
10.4-1 Diagonalization of Matrix Α
930(4)
10.5 Controllability and Observability
934(5)
10.5-1 Inadequacy of the Transfer Function Description of a System
939(1)
10.6 State-Space Analysis of Discrete-Time Systems
940(2)
10.6-1 Solution in State-Space
942(5)
10.6-2 The z-Transform Solution
947(1)
10.7 Summary
948(1)
References
949(1)
MATLAB Session 10: Toolboxes and State-Space Analysis
949(8)
Problems
957(6)
INDEX 963

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