信号与系统基础PDF电子书下载

Chapter 1 Introduction 1

1.1 Overview of signals and systems 1

1.1.1 What is a signal? 1

1.1.2 What is a system? 2

1.2 Description and classification of signals 5

1.2.1 Continuous-time signals and discrete-time signals 6

1.2.2 Energy signals and power signals 9

1.2.3 Periodic signals and non-periodic signals 11

1.2.4 Deterministic signals and random signals 14

1.2.5 Elementary signals 15

1.3 Description of Systems 22

1.3.1 Elementary systems 22

1.3.2 System modelling 26

1.4 Properties of systems 29

1.4.1 Memoryless and with memory 29

1.4.2 Causality 30

1.4.3 Invertibility 30

1.4.4 Stability 31

1.4.5 Time-invariance 33

1.4.6 Linearity 34

1.5 Summary 37

1.6 Problems 37

Chapter 2 Time-domain Analysis of LTI Systems 43

2.1 Introduction 43

2.2 The unit impulse response and convolutions 43

2.2.1 The convolution sum 45

2.2.2 The convolution integral 49

2.3 Properties of convolutions and equivalent systems 51

2.4 Causality and stability of LTI systems 56

2.5 Systems constrained with LCCDEs 59

2.5.1 Continuous-time systems constrained with LCCDEs 59

2.5.2 Discrete-time systems characterized by LCCDEs 62

2.6 Summary 64

2.7 Problems 65

Chapter 3 Fourier Analysis of Signals 69

3.1 Introduction 69

3.2 Fourier series for continuous-time periodic signals 70

3.3 Fourier series for discrete-time periodic signals 80

3.4 Why should a signal be transformed? 84

3.5 Fourier transform for continuous-time signals 87

3.5.1 Properties of Fourier transform 92

3.5.2 Inverse Fourier transform 100

3.6 The discrete-time Fourier transform 101

3.6.1 Properties of DTFT 106

3.6.2 Inverse DTFT 109

3.7 Fourier series and Fourier transforms 110

3.8 Summary 114

3.9 Problems 115

Chapter 4 Frequency-domain Approach to LTI Systems 121

4.1 Introduction 121

4.2 Frequency response of LTI systems 121

4.3 Bode plots for continuous-time LTI systems 127

4.4 Frequency response of LTIs described with LCCDEs 130

4.5 Frequency domain approach to system outputs 135

4.6 Some typical LTI systems 138

4.6.1 All-pass systems 138

4.6.2 Linear phase response systems 139

4.6.3 Ideal filters 140

4.6.4 Ideal transmission channels 143

4.7 Summary 145

4.8 Problems 146

Chapter 5 Discrete Processing of Analog Signals 149

5.1 Introduction 149

5.2 Sampling of a continuous-time signal 150

5.3 Spectral relationship and sampling theorem 150

5.4 Reconstruction of continuous-time signals 154

5.5 Hybrid systems for discrete processing 159

5.6 Discrete Fourier transform 160

5.7 Compressed sensing 164

5.8 Summary 165

5.9 Problems 166

Chapter 6 Transform-domain Approaches 169

6.1 Motivation 169

6.2 The Laplace transform 169

6.2.1 Derivation of the transform 169

6.2.2 Region of convergence 171

6.2.3 Inverse Laplace transform 176

6.2.4 Properties of Laplace transform 178

6.3 The z-transform 179

6.3.1 Region of convergence 180

6.3.2 Properties of the z-transform 184

6.3.3 Inverse z-transform 186

6.4 Transform-domain approach to LTI systems 187

6.4.1 Transfer function of LTI systems 188

6.4.2 Inverse systems of LTIs and deconvolutions 190

6.4.3 Revisit of LTI system's stability and causality 192

6.4.4 Transfer function of LTI systems by LCCDEs 195

6.5 Transform domain approach to LCCDEs 197

6.6 Decomposition of LTI system responses 200

6.7 Unilateral transforms 202

6.7.1 Unilateral Laplace transform 203

6.7.2 Unilateral z-transform 205

6.8 Summary 207

6.9 Problems 207

Chapter 7 Structures and State-space Realizations 212

7.1 Block-diagram representation 212

7.2 Structures of LTIs with a rational transfer function 214

7.3 State-space variable representation 219

7.3.1 State model and state-space realizations 219

7.3.2 Construction of an equivalent state-space realization 221

7.3.3 Similarity transformations 222

7.4 Discretizing a continuous-time state model 224

7.5 Summary 227

7.6 Problems 228

Chapter 8 Comprehensive Problems 231

8.1 Motivation 231

8.2 Problems 231

Appendices 237

Bibliography 246