Fundamentals Of Signals And Systems

by Boulet, Benoit

• ISBN13: 9781584503811
• ISBN10: 1584503815
• Edition: CD
• Format: Hardcover
• Copyright: 2005-09-30
• Publisher: Cengage Learning

Summary

This book is a self-contained introduction to the theory of signals and systems, which lies at the basis of many areas of electrical and computer engineering. In the seventy short, glectures, formatted to facilitate self-learning and to provide easy reference, the book covers such topics as linear time-invariant (LTI) systems, the Fourier transform, the Laplace Transform and its application to LTI differential systems, state-space systems, the z-transform, signal analysis using MATLAB, and the application of transform techniques to communication systems. A wide array of technologies, including feedback control, analog and discrete-time fi lters, modulation, and sampling systems are discussed in connection with their basis in signals and systems theory. The accompanying CD-ROM includes applets, source code, sample examinations, and exercises with selected solutions.

Table of Contents

Acknowledgments	xiii
Preface	xv
Elementary Continuous-Time and Discrete-Time Signals and Systems	1	(52)
Systems in Engineering	2	(1)
Functions of Time as Signals	2	(2)
Transformations of the Time Variable	4	(4)
Periodic Signals	8	(1)
Exponential Signals	9	(8)
Periodic Complex Exponential and Sinusoidal Signals	17	(4)
Finite-Energy and Finite-Power Signals	21	(2)
Even and Odd Signals	23	(2)
Discrete-Time Impulse and Step Signals	25	(1)
Generalized Functions	26	(8)
System Models and Basic Properties	34	(8)
Summary	42	(1)
To Probe Further	43	(1)
Exercises	43	(10)
Linear Time-Invariant Systems	53	(38)
Discrete-Time LTI Systems: The Convolution Sum	54	(13)
Continuous-Time LTI Systems: The Convolution Integral	67	(7)
Properties of Linear Time-Invariant Systems	74	(7)
Summary	81	(1)
To Probe Further	81	(1)
Exercises	81	(10)
Differential and Difference LTI Systems	91	(40)
Causal LTI Systems Described by Differential Equations	92	(4)
Causal LTI Systems Described by Difference Equations	96	(5)
Impulse Response of a Differential LTI System	101	(8)
Impulse Response of a Difference LTI System	109	(3)
Characteristic Polynomials and Stability of Differential and Difference Systems	112	(4)
Time Constant and Natural Frequency of a First-Order LTI Differential System	116	(1)
Eigenfunctions of LTI Difference and Differential Systems	117	(1)
Summary	118	(1)
To Probe Further	119	(1)
Exercises	119	(12)
Fourier Series Representation of Periodic Continuous-Time Signals	131	(44)
Linear Combinations of Harmonically Related Complex Exponentials	132	(2)
Determination of the Fourier Series Representation of a Continuous-Time Periodic Signal	134	(3)
Graph of the Fourier Series Coefficients: The Line Spectrum	137	(2)
Properties of Continuous-Time Fourier Series	139	(2)
Fourier Series of a Periodic Rectangular Wave	141	(3)
Optimality and Convergence of the Fourier Series	144	(2)
Existence of a Fourier Series Representation	146	(1)
Gibbs Phenomenon	147	(1)
Fourier Series of a Periodic Train of Impulses	148	(2)
Parseval Theorem	150	(1)
Power Spectrum	151	(2)
Total Harmonic Distortion	153	(2)
Steady-State Response of an LTI System to a Periodic Signal	155	(2)
Summary	157	(1)
To Probe Further	157	(1)
Exercises	158	(17)
The Continuous-Time Fourier Transform	175	(48)
Fourier Transform as the Limit of a Fourier Series	176	(4)
Properties of the Fourier Transform	180	(4)
Examples of Fourier Transforms	184	(4)
The Inverse Fourier Transform	188	(3)
Duality	191	(1)
Convergence of the Fourier Transform	192	(1)
The Convolution Property in the Analysis of LTI Systems	192	(7)
Fourier Transforms of Periodic Signals	199	(3)
Filtering	202	(8)
Summary	210	(1)
To Probe Further	211	(1)
Exercises	211	(12)
The Laplace Transform	223	(36)
Definition of the Two-Sided Laplace Transform	224	(2)
Inverse Laplace Transform	226	(8)
Convergence of the Two-Sided Laplace Transform	234	(1)
Poles and Zeros of Rational Laplace Transforms	235	(1)
Properties of the Two-Sided Laplace Transform	236	(5)
Analysis and Characterization of LTI Systems Using the Laplace Transform	241	(2)
Definition of the Unilateral Laplace Transform	243	(1)
Properties of the Unilateral Laplace Transform	244	(3)
Summary	247	(1)
To Probe Further	248	(1)
Exercises	248	(11)
Application of the Laplace Transform to LTI Differential Systems	259	(26)
The Transfer Function of an LTI Differential System	260	(4)
Block Diagram Realizations of LTI Differential Systems	264	(8)
Analysis of LTI Differential Systems with Initial Conditions Using the Unilateral Laplace Transform	272	(2)
Transient and Steady-State Responses of LTI Differential Systems	274	(2)
Summary	276	(1)
To Probe Further	276	(1)
Exercises	277	(8)
Time and Frequency Analysis of BIBO Stable, Continuous-Time LTI Systems	285	(44)
Relation of Poles and Zeros of the Transfer Function to the Frequency Response	286	(4)
Bode Plots	290	(6)
Frequency Response of First-Order Lag, Lead, and Second-Order Lead-Lag Systems	296	(4)
Frequency Response of Second-Order Systems	300	(7)
Step Response of Stable LTI Systems	307	(8)
Ideal Delay Systems	315	(1)
Group Delay	316	(1)
Non-Minimum Phase and All-Pass Systems	316	(3)
Summary	319	(1)
To Probe Further	319	(1)
Exercises	319	(10)
Application of Laplace Transform Techniques to Electric Circuit Analysis	329	(22)
Review of Nodal Analysis and Mesh Analysis of Circuits	330	(4)
Transform Circuit Diagrams: Transient and Steady-State Analysis	334	(6)
Operational Amplifier Circuits	340	(4)
Summary	344	(1)
To Probe Further	344	(1)
Exercises	344	(7)
State Models of Continuous-Time LTI Systems	351	(30)
State Models of Continuous-Time LTI Differential Systems	352	(9)
Zero-State Response and Zero-Input Response of a Continuous-Time State-Space System	361	(6)
Laplace-Transform Solution for Continuous-Time State-Space Systems	367	(3)
State Trajectories and the Phase Plane	370	(2)
Block Diagram Representation of Continuous-Time State-Space Systems	372	(1)
Summary	373	(1)
To Probe Further	373	(1)
Exercises	373	(8)
Application of Transform Techniques to LTI Feedback Control Systems	381	(44)
Introduction to LTI Feedback Control Systems	382	(12)
Closed-Loop Stability and the Root Locus	394	(10)
The Nyquist Stability Criterion	404	(5)
Stability Robustness: Gain and Phase Margins	409	(4)
Summary	413	(1)
To Probe Further	413	(1)
Exercises	413	(12)
Discrete-Time Fourier Series and Fourier Transform	425	(34)
Response of Discrete-Time LTI Systems to Complex Exponentials	426	(1)
Fourier Series Representation of Discrete-Time Periodic Signals	426	(4)
Properties of the Discrete-Time Fourier Series	430	(5)
Discrete-Time Fourier Transform	435	(4)
Properties of the Discrete-Time Fourier Transform	439	(6)
DTFT of Periodic Signals and Step Signals	445	(4)
Duality	449	(1)
Summary	450	(1)
To Probe Further	450	(1)
Exercises	450	(9)
The z-Transform	459	(38)
Development of the Two-Sided z-Transform	460	(4)
ROC of the z-Transform	464	(1)
Properties of the Two-Sided z-Transform	465	(3)
The Inverse z-Transform	468	(6)
Analysis and Characterization of DLTI Systems Using the z-Transform	474	(9)
The Unilateral z-Transform	483	(3)
Summary	486	(1)
To Probe Further	487	(1)
Exercises	487	(10)
Time and Frequency Analysis of Discrete-Time Signals and Systems	497	(44)
Geometric Evaluation of the DTFT From the Pole-Zero Plot	498	(6)
Frequency Analysis of First-Order and Second-Order Systems	504	(6)
Ideal Discrete-Time Filters	510	(9)
Infinite Impulse Response and Finite Impulse Response Filters	519	(12)
Summary	531	(1)
To Probe Further	531	(1)
Exercises	532	(9)
Sampling Systems	541	(36)
Sampling of Continuous-Time Signals	542	(4)
Signal Reconstruction	546	(6)
Discrete-Time Processing of Continuous-Time Signals	552	(5)
Sampling of Discrete-Time Signals	557	(7)
Summary	564	(1)
To Probe Further	564	(1)
Exercises	564	(13)
Introduction to Communication Systems	577	(40)
Complex Exponential and Sinusoidal Amplitude Modulation	578	(3)
Demodulation of Sinusoidal AM	581	(6)
Single-Sideband Amplitude Modulation	587	(4)
Modulation of a Pulse-Train Carrier	591	(1)
Pulse-Amplitude Modulation	592	(3)
Time-Division Multiplexing	595	(2)
Frequency-Division Multiplexing	597	(2)
Angle Modulation	599	(5)
Summary	604	(1)
To Probe Further	605	(1)
Exercises	605	(12)
System Discretization and Discrete-Time LTI State-Space Models	617	(28)
Controllable Canonical Form	618	(3)
Observable Canonical Form	621	(1)
Zero-State and Zero-Input Response of a Discrete-Time State-Space System	622	(3)
z-Transform Solution of Discrete-Time State-Space Systems	625	(3)
Discretization of Continuous-Time Systems	628	(8)
Summary	636	(1)
To Probe Further	637	(1)
Exercises	637	(8)
Appendix A: Using MATLAB	645	(2)
Appendix B: Mathematical Notation and Useful Formulas	647	(2)
Appendix C: About the CD-ROM	649	(2)
Appendix D: Tables of Transforms	651	(14)
Index	665