Signals and Systems: Fundamentals

Description

Signals and systems enjoy wide application in industry and daily life, and understanding basic concepts of the subject area is of importance to undergraduates majoring in engineering. With rigorous mathematical deduction, this introductory text book is helpful for students who study communications engineering, electrical and electronic engineering, and control engineering. Additionally, supplementary materials are provided for self-learners. Illustrates basic concepts in signals and systems in a concise way. Demonstrates mathematical nature of signals and systems. Designed to facilitate self-learning with PPTs and solutions to tutorials. Contents Preface 1 Introduction 1.1 Overview of signals and systems 1.1.1 What is a signal? 1.1.2 What is a system? 1.2 Description and classification of signals 1.2.1 Continuous-time signals and discrete-time signals 1.2.2 Energy signals and power signals 1.2.3 Periodic signals and nonperiodic signals 1.2.4 Deterministic signals and random signals 1.2.5 Elementary signals 1.3 Description of systems 1.3.1 Elementary systems 1.3.2 System modelling 1.4 Properties of systems 1.4.1 Memoryless and with memory 1.4.2 Causality 1.4.3 Invertibility 1.4.4 Stability 1.4.5 Time-invariance 1.4.6 Linearity 1.5 Summary 1.6 Problems 2 Time-domain analysis of LTI systems 2.1 Introduction 2.2 The unit impulse response and convolutions 2.2.1 The convolution sum 2.2.2 The convolution integral 2.3 Properties of convolutions and equivalent systems 2.4 Causality and stability of LTI systems 2.5 Systems constrained with LCCDEs 2.5.1 Continuous-time systems constrained with LCCDEs 2.5.2 Discrete-time systems characterized by LCCDEs 2.6 Summary 2.7 Problems 3 Fourier analysis of signals 3.1 Introduction 3.2 Fourier series for continuous-time periodic signals 3.3 Fourier series for discrete-time periodic signals 3.4 Why should a signal be transformed? 3.5 Fourier transform for continuous-time signals 3.5.1 Properties of Fourier transform 3.5.2 Inverse Fourier transform 3.6 The discrete-time Fourier transform 3.6.1 Properties of DTFT 3.6.2 Inverse DTFT 3.7 Fourier series and Fourier transforms 3.8 Summary 3.9 Problems 4 Frequency-domain approach to LTI systems 4.1 Introduction 4.2 Frequency response of LTI systems 4.3 Bode plots for continuous-time LTI systems 4.4 Frequency response of LTIs described with LCCDEs 4.5 Frequency domain approach to system outputs 4.6 Some typical LTI systems 4.6.1 All-pass systems 4.6.2 Linear phase response systems 4.6.3 Ideal filters 4.6.4 Ideal transmission channels 4.7 Summary 4.8 Problems 5 Discrete processing of analog signals 5.1 Introduction 5.2 Sampling of a continuous-time signal 5.3 Spectral relationship and sampling theorem 5.4 Reconstruction of continuous-time signals 5.5 Hybrid systems for discrete processing 5.6 Discrete Fourier transform 5.7 Compressed sensing 5.8 Summary 5.9 Problems 6 Transform-domain approaches 6.1 Motivation 6.2 The Laplace transform 6.2.1 Derivation of the transform 6.2.2 Region of convergence 6.2.3 Inverse Laplace transform 6.2.4 Properties of Laplace transform 6.3 The z-transform 6.3.1 Region of convergence 6.3.2 Properties of the z-transform 6.3.3 Inverse z-transform 6.4 Transform-domain approach to LTI systems 6.4.1 Transfer function of LTI systems 6.4.2 Inverse systems of LTIs and deconvolutions 6.4.3 Revisit of LTI system’s stability and causality 6.4.4 Transfer function of LTI systems by LCCDEs 6.5 Transform domain approach to LCCDEs 6.6 Decomposition of LTI system responses 6.7 Unilateral transforms 6.7.1 Unilateral Laplace transform 6.7.2 Unilateral z-transform 6.8 Summary 6.9 Problems 7 Structures and state-space realizations 7.1 Block-diagram representation 7.2 Structures of LTIs with a rational transfer function 7.3 State-space variable representation 7.3.1 State model and state-space realizations 7.3.2 Construction of an equivalent state-space realization 7.3.3 Similarity transformations 7.4 Discretizing a continuous-time state model 7.5 Summary 7.6 Problems 8 Comprehensive problems 8.1 Motivation 8.2 Problems Appendices A. Proof of the condition of initial rest (1.49) B. Proof of Theorem 2.5 C. Orthogonality principle D. Residue theorem and inverse transforms E. Partial-fraction expansion Bibliography Index