ISBN 9789353273156
Author Charlie Mcelroy
Year 2022
Publisher J.Walter Publisher
Subject Engineering & Technology
Sub Subjects Electrical & Electronics Engineering
Binding Hardcover
Cover Image Available
The term "signal" refers to a collection of facts or information. A system modifies or extracts additional information from input signals in order to generate output signals (response). A linear system is a mathematical model of a system in systems theory that is based on the usage of a linear operator. Linear systems often display much simpler characteristics and behaviours than nonlinear systems. Linear systems are widely used in automated control theory, signal processing, and telecommunications as a mathematical abstraction or idealisation. A system may be composed of physical components (hardware realisation) or it can be comprised of an algorithm that generates an output signal from an input signal (software realization). A handy way to determine the magnitude of a signal is to look at its energy, assuming it is limited. If the energy of the signal is limitless, the suitable unit is its power, if it exists. Continuous systems, such as those used in analogue electronics, accept and output continuous signals. This book is a valuable compilation of topics, ranging from the basic to the most complex theories and principles in the field of signals and linear systems. It explores all the important aspects of this field in the present day scenario. It is a compilation of chapters that discuss the most vital concepts of this field. It deals with convolution, discrete time systems, continuous time systems and fourier analysis. It also focuses on design of digital filters, analog filters and filters preserving phase. Such selected concepts that redefine this field have been presented in this book. It discards the physical significance of many derivations and deprives pupils of intuitive comprehension and the pleasurable experience of logically unravelling the subject matter. This book presents the complex subject of signals in the most comprehensible and easy to understand language. For all those who are interested signals and linear systems, this book can prove to be an essential guide.
Charlie McElroy received his Ph.D. in Electrical Engineering from University of Science and Technology, Sheffield. His interest areas of working are electric safety, system's operation and control power systems, renewable energy and intelligent systems. He serves as an Associate Professor at Technical Institute, Dublin. Mcelroy has written numerous articles and research papers on power engineering, telecommunications, control systems, radio-frequency engineering and signal processing. He holds prominent memberships of international electronics associations and has been an active participant at international conferences and forums.
| Preface IX 1. Introduction 1 1. Introduction to Signals 1 2. Types of Signals 2 3. Signals Size and Norms 15 4. Signals and Systems 17 5. Systems Analysis 21 6. Basic System Properties 23 7. Functions of Signal Processing 30 8. Analog Signal Processing 32 9. Digital Signal Processing 35 Summary 39 References 39 Multiple Choice Questions 40 Answers 42 2. Linear Systems 43 1. Introduction to Linear systems 43 2. Systems, Inputs, and Responses 45 3. Homogeneity and Additivity 45 4. Sinusoidal stimuli 50 5. Requirements of Linearity 52 6. Static Linearity and Sinusoidal fidelity 55 7. Special Properties of Linearity 57 8. Superposition: the foundation of DSP 58 9. Common Decompositions 61 10. Alternatives to Linearity 64 11. Linear time-invariant system 66 Summary 69 References 69 Multiple Choice Questions 70 Answers 71 3. Convolution 72 1. Introduction to Convolution 72 2. Properties of Convolution 85 3. Convolution Operations 97 4. Correlation and Convolution 102 Summary 109 References 109 Multiple Choice Questions 110 Answers 111 4. Discrete Time Systems 112 1. Introduction 112 2. Block Diagram representation of Discrete-time systems 114 3. Representation of Discrete Time Systems 115 4. Classification of DTS 116 5. Linear Discrete Time Systems 119 6. Shift Invariant Discrete Time Systems 122 7. Static Systems 122 8. Linear and nonlinear systems 124 9. Causal Systems 124 10. Linearity and Time Invariance 125 11. Discrete Time Impulse Response 126 12. Discrete Time Signals 127 13. Classification Of Discrete Time Systems 130 14. Block Diagram Representation 133 Summary 138 References 138 Multiple Choice Questions 139 Answers 140 5. Continuous Time Systems 141 1. Introduction to Continuous Time Systems 141 2. Linearity and Time Invariance 142 3. Properties of Continuous- Time Systems 142 4. Continuous-Time Signals and Systems 147 Summary 153 References 154 Multiple Choice Questions 154 Answers 155 6. The Z-Transforms 156 1. Introduction 156 2. Inverse Z-transform 158 3. Concept of Z-Transform and Inverse Z-Transform 159 4. Properties of Z-Transforms 161 5. Region of Convergence (ROC) of Z-Transform 168 6. Z-Transform Existence 171 7. Commonly used z-transforms 172 8. Linear constant-coefficient difference equation 173 9. Advanced Z-Transforms 174 Summary 175 References 176 Multiple Choice Questions 176 Answers 177 7. Fourier Analysis 178 1. Introduction 178 2. Variants of Fourier analysis 180 3. Fourier Analysis and Synthesis 183 4. Fourier Series Representation 184 5. Introduction to Fourier Transforms 186 6. Fast Fourier Transforms 203 Summary 219 References 220 Multiple Choice Questions 220 Answers 222 8. Laplace Transforms 223 1. Introduction to Laplace Transforms 223 2. Region of convergence 226 3. Laplace Transform Table 227 4. Inverse Laplace Transforms 230 5. Properties of Laplace Transforms 231 6. Relation between Laplace and Fourier transforms 234 7. Relationship to other transforms 237 8. Region of Convergence (ROC) 240 Summary 242 References 242 Multiple Choice Questions 243 Answers 244 9. An Introduction to the Design of Digital Filters 245 1. Introduction 245 2. Linear continuous-time filters 246 3. Introduction to Digital filters 252 4. Finite Impulse Response Filters 269 5. Infinite Impulse Response Filters 272 6. Transfer function Filters 277 7. Filter Designs 281 Summary 287 References 287 Multiple Choice Questions 288 Answers 290 10. Analog Filters and Filters Preserving Phase 291 1. Introduction 291 2. Resonance of Analog Signals 294 3. One-Zero Filters 301 4. One-Pole Filters 302 5. Two-Pole filters 304 6. Two-Pole Partial Fraction Expansion 308 7. Introduction to Linear Phase Filter 309 8. Zero Phase Filter 310 9. Odd Impulse Response 312 10. Symmetric Linear phase filters 312 11. Asymmetric Linear phase filters 313 12. Forward Backward filtering 313 13. Minimum Phase Filters 315 14. Maximum Phase Filters 317 Summary 318 References 318 Multiple Choice Questions 319 Answers 321 Index 323 |