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Table of Contents 1 Introduction to Signals and Systems 1 1.1 A Little Philosophy 2 1.2 Basic Concepts 3 1.3 Mathematical Modeling 5 1.4 Signals and Systems 7 1.5 Continuous-Time and Discrete-Time Signals and Systems 14 1.6 Organization of the Material 14 1.7 How to Use MATLAB with This Book 16 2 Real Functions 19 2.1 Continuous-Time Functions 19 2.2 Common Functions 22 2.3 Discrete-Time Functions 28 2.4 Homework for Chapter 2 32 3 Review of Complex Variables 35 3.1 Complex Numbers 36 3.2 Complex Functions 42 3.3 Homework for Chapter 3 49 4 Review of Matrix Theory 53 4.1 Basic Definitions and Elementary Operations 54 4.2 Vectors 60 4.3 Homework for Chapter 4 65 5 Introduction to Signals 67 5.1 Definition of a Signal 68 5.2 Time Scaling, Time Shifting, and Limits of Signals 76 5.3 Signals Defined on Intervals 84 5.4 Digital Waveforms 90 5.5 Signals as Sums of Sinusoids 95 5.6 Chapter Summary 98 5.7 Homework for Chapter 5 99

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ii Contents 6 Introduction to Systems 105 6.1 Definition of a System 107 6.2 System Representations 111 6.3 Electrical Networks 116 6.4 Mass-Spring-Damper System 120 6.5 Proof-Mass Actuators 124 6.6 Chapter Summary 128 6.7 Homework for Chapter 6 130 7 Fourier Series and Fourier Transforms 133 7.1 Introduction to Fourier Series 135 7.2 Three Representations of a Fourier Series 142 7.3 Computational Formulas for the Fourier Series Coefficients 149 7.4 Definition of the Fourier Transform 159 7.5 Properties of the Fourier Transform and the Generalized Fourier Transform 165 7.6 Chapter Summary 174 7.7 Homework for Chapter 7 178 8 Spectral Content of a Signal 187 8.1 Amplitude and Phase Spectra 189 8.2 Energy and Power Signals 200 8.3
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