Systems and Signals, 3rd, rev. & enlarged, ed., 1992, 240 pp., ISBN 0-911575-63-4, $45.00

This is a junior-senior level textbook in Engineering on Systems and Signals. Written by an award-winning educator. Presents in a lucid, elementary way the basic foundations of Signal Processing in Communication and Control. Covers Time-domain and Frequency-domain concepts, Laplace transforms, z-transforms, as well as fundamentals of State Space theory. A unique feature of the book is the well-organized and extensive set of problems. Suitable for self-study as well as classroom use.

Preface to the Third Edition ..... xi

Preface to the Second Edition ..... xiii

Preface to the First Edition ..... xv
 

1.1. Systems: Model and Mathematical Model ..... 1

1.2. Properties of an Input-Output Transformation ..... 4

Linear ..... 4
Nonlinear ..... 5
Time-Invariant ..... 5
Time-Varying ..... 6
Causal ..... 7
Continuous-Time, Discrete-Time ..... 9
Problems to Chapter 1 ..... 10

2.1. The Dirac Delta (or Impulse) Function ..... 11

2.2. The Unit Step Function ..... 14

2.3. The Impulse Response Function of a Linear System ..... 17

2.4. Input-Output Relation of a Linear System ..... 22

2.5. Impulse Response Function of a Cascaded System ..... 27

Problems to Chapter 2 ..... 32

3.1. The Laplace Transform ..... 37

Definition ..... 37
Some Important Transforms ..... 39
Basic Properties ..... 40
Inverse Transforms ..... 46

3.3. Analysis of Linear Time-Invariant and Causal Systems by the Laplace Transform Method ..... 51

The Laplace Transform of a Convolution Integral and the System Function of a Linear Time-Invariant and Causal System ..... 51
System Function of Systems Described by Differential Equations ..... 55
System Function of a Cascaded System ..... 56
Problems to Chapter 3 ..... 58

4.1. Orthogonal Decomposition of a Signal ..... 65

4.2. Periodic Signals and Fourier Series ..... 68

The Complex Exponentials  ..... 68
The Complex Exponentials  ..... 69
Amplitude and Phase Spectra ..... 71
Parseval’s Relation ..... 75
Mean (or Least) Square Approximation ..... 76
The Mean Square Error ..... 79

Notes: [1] Dirichlet Conditions; [2] Gibb’s Phenomenon ..... 82
Problems to Chapter 4 ..... 83

5.1. Fourier Transforms ..... 89

Properties of Fourier Transforms ..... 93
Transform of (t) and Inverse Transform of () ..... 95
Parseval’s Theorem ..... 97
Fourier Transform and Laplace Transform ..... 99

5.3. Band-Limited Signals: Sampling Theorem ..... 103

Table of Fourier Transforms ..... 106
Problems to Chapter 5 ..... 108

6.1. Introduction and Definitions ..... 113

Discrete-Time Signals ..... 114
The Unit Step Sequence U(n) ..... 114
The Unit Delta Sequence (n) ..... 115
Discrete-Time Systems ..... 116

6.3. Analysis of Linear Time-Invariant Discrete-Time Systems by the z-Transforms ..... 119

Definition of z-Transforms ..... 120
Properties of z-Transforms ..... 121
The Inverse z-Transform ..... 124
Problems to Chapter 6 ..... 130

7.1. Systems: Inputs, Outputs and States ..... 133

7.2. Linear Spaces and Linear Transformation ..... 135

Span, Dimension and Subspace ..... 137
Linear Transformations on Finite-Dimensional Linear Spaces ..... 137
Matrix Representation of a Linear Transformation ..... 138
Inner Product, Norm and Orthogonality ..... 140
The Adjoint Transformation ..... 141
Eigenvalues and Eigenvectors ..... 143
Functions of Matrices and , t0 ..... 144
The Cayley-Hamilton Theorem ..... 144
The Matrix Function , t0 ..... 146
Computation of  by Laplace Transform ..... 147
Computation of , t0, by the Cayley-Hamilton Theorem ..... 148
The Vector Differential Equation ..... 150

7.4. Observability ..... 158

Problems to Chapter 7 ..... 162

Bibliography ..... 217

Index ..... 219