Contents PREFACE xvii 1 INTRODUCTION 1.1 Historical Review I 1.2 Elements of an Electrical Communication System 4 1.2.1 Digital Communication System,7 1.2.2 Early Work in Digital Communications,10 1.3 Communication Channels and Their Characteristics 12 1.4 Mathematical Models for Communication Channels 18 1.5 Summary and Further Reading 20 2 SIGNALS AND LINEAR SYSTEMS 21 2.1 Basic Concepts 21 2.1.1 Basic Operations on Signals,21 2.1.2 Classification ofSignals,23 2.1.3 Some.Important Signals and Their Properties,31 2.1.4 Classification of Systems,38 2.1.5 Analysis of LTI Systems in the Time Domain,41 2.2 Fourier Series 43 2.2.1 Fourier Series and Its Properties,44 2.2.2 Response ofLTI Systemns to Periodic Signals,54 2.2.3 Parseval's Relation,56 2.3 Fourier Transform 58 2.3.1 From Fourier Series to Fourier Transforins,58 2.3.2 Basic Properties of the Fourier Transform,64 2.3.3 Fourier Transforin for Periodic Signals,78 2.3.4 Transmission over LTI Systems,81 2.4 Filter Design 85 2.5 Power and Energy 89 2.5.1 Energy-Type Signals,89 2.5.2 Power-Type Signals,92 2.6 Hilbert Transform and Its Properties 95 2.7 Lowpass and Bandpass Signals 98 viiContents 1 2 PREFACE INTRODUCTION 1.1 Historical Review 1.2 Elements of an Electrical Communication System 4 1.2.J Digital Co111111unicatio11 Syste111, 7 1.2.2 Early YVork in Digital Con1111u11icatio11s, 10 1.3 Communication Channels and Their Characteristics 12 1.4 Mathematical Models for Communication Channels 18 1.5 Summary and Further Reading 20 SIGNALS AND LINEAR SYSTEMS 2.1 Basic Concepts 21 2.1.l Basic Operations on Signals, 21 2.1.2 Classification a/Signals, 23 2.1.3 Son1eJ111portant Signals and Their Properties, 31 2.1.4 Classification of Syste111s, 38 2.1.5 Analysis of LT! Systen1s in the Tbne Do111ai11, 41 2.2 Fourier Series 43 2.2.1 Fourier Series and Its Properties, 44 2.2.2 Response of LT! Syste111s to Periodic Signals, 54 2.2.3 Parseval's Relation, 56 2.3 Fourier Transform 58 2.3.l Fro111 Fourier Series to Fourier Transfonns, 58 2.3.2 Basic Properties of the Fourier Trcu1sfonn, 64 2.3.3 Fourier Transfonn for Periodic Signals, 78 2.3.4 Tra11s111issio11 over LT! Syste111s, 81 2.4 Filter Design 85 2.5 Power and Energy 89 2.5.l Energ_v-Type Signals, 89 2.5.2 Power-Type Signals, 92 2.6 Hilbert Transform and Its Properties 95 2.7 Lowpass and Bandpass Signals 98 xvii 1 21 vii