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Fundamentals of Electrical Engineering Don H. Johnson J.D. Wise, Jr. Rice University c 1999 Contents 1 Introduction 1.1 Themes 1.2 What is Information? 1.2.1 Analog Information 1.2.2 Digital Information 1.3 Communication Systems 1.4 The Fundamental Signal 1.5 Communicating Information with Signals Problems 2 Signals and Systems 2.1 Signal Theory 2.2 System Theory 2.2.1 Connecting Systems Together 2.2.2 Simple Systems 2.3 Signal Decomposition Problems 11 11 15 15 16 19 20 3 Analog Signal Processing 3.1 Voltage and Current 3.2 Linear Circuit Elements 3.3 Sources 3.4 Ideal and Real-World Circuit Elements 3.5 Electric Circuits and Interconnection Laws 3.6 Equivalent Circuits 3.7 Circuits with Capacitors and Inductors 3.7.1 Impedance 3.7.2 Transfer Function 23 23 24 25 25 26 35 39 39 43 i 1 1 3 3 4 4 7 8 9 ii Contents 3.7.3 Equivalent Circuits Revisited 3.7.4 Summary 3.8 Formal Circuit Methods 3.9 Circuit Models for Communication Channels 3.9.1 Wireline Channels 3.9.2 Wireless Channels 3.10 Electronics 3.10.1 Dependent Sources 3.10.2 Operational Amplifiers 3.11 Nonlinear Circuit Elements Problems 45 47 49 53 55 60 62 62 65 70 72 4 The Frequency Domain 4.1 Fourier Series 4.1.1 A Signal’s Spectrum 4.1.2 Equality of Representations 4.2 Complex Fourier Series 4.3 Encoding Information in the Frequency Domain 4.4 Filtering Periodic Signals 4.5 The Fourier Transform 4.6 Linear, Time-Invariant Systems 4.7 Modeling the Speech Signal 4.8 The Sampling Theorem 4.9 Analog-to-Digital Conversion Problems 83 83 86 90 94 98 100 102 109 112 119 122 123 5 Digital Signal Processing 5.1 Discrete-Time Signals and Systems 5.1.1 Real- and complex-valued signals 5.1.2 Symbolic Signals 5.2 Digital Processing Systems 5.3 Discrete-Time Fourier Transform (DTFT)