简介
Fundamentals of Signals and Systems deals with the concepts of signals and systems, which are the corner-stone of a wide variety of areas ranging from home-oriented consumer electronics and multimedia entertainment products to sophisticated communications, aeronautics and astronautics, and control. A course on signals and systems is fundamental and compulsory for an engineering under-graduate curriculum in any well-established tertiary (education) institutions. This book provides readers with the basic principles and methods underlying the analysis of signals and systems in the context of both continuous- and discrete-time, including Fourier analysis based representations for signals and both time- and transform-domain approaches as well as state-space approach to (linear time-invariant) systems. Great emphasis is placed on being concise, easy for self-study, and rigorous. Compared with most of the existing textbooks on the same topics, more effort is made in this book to provide a clear picture of the relationship between linear constant differential/difference equations and linear time-invariant systems. Another significant feature of this book is a separated chapter (Chapter 8) that contains a set of comprehensive exercises, each of which usually involves mathematical deviations and more sophisticated application of the concepts and approaches provided in the entire text book rather than an individual chapter. This book is primarily designed for undergraduate students majoring electrical & electronics and information engineering, the concepts and techniques introduced in the book, however, are of fundamental importance in all other engineering disciplines. Readers of this book are assumed to have a basic background in engineering mathematics, including calculus, complex functions, and linear differential equations. Some knowledge on circuit theory, though not a prerequisite, would be helpful for the study.
目录
1.4.3 Invertibility
1.4.4 Stability
1.4.5 Time-invariance
1.4.6 Linearity
1.5 Summary
1.6 Problems
Chapter 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
Chapter 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
Chapter 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
Chapter 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
Chapter 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
Chapter 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
Chapter 8 Comprehensive Problems
8.1 Motivation
8.2 Problems
Appendices
Bibliography
1.4.4 Stability
1.4.5 Time-invariance
1.4.6 Linearity
1.5 Summary
1.6 Problems
Chapter 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
Chapter 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
Chapter 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
Chapter 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
Chapter 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
Chapter 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
Chapter 8 Comprehensive Problems
8.1 Motivation
8.2 Problems
Appendices
Bibliography
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