Notes on Signal and Systems
Notes on Signal and Systems
Si Chen
Jiangsu University
Copyright © 2025 by Cayley Nielson Press, Inc.
ISBN: 978-1-957274-24-9
Cayley Nielson Press Scholarly Monograph Series Book Code No.: 215-8-1
US$168.50
Preface
These notes aim to render newcomers a gentle guide to Signals and Systems. Many thanks to the authors in the reference list, upon whose knowledge and books I can lay and add my understanding properly
Si Chen
Jiangsu University
301 Xuefu Road, Zhenjiang 212013, Jiangsu, China
August, 2025
Contents
1 What is the signal? 4
2 Linear time-invariant (LTI) systems 5
2.1 Convolution 5
2.1.1 Unit impulse function 8
2.2 Properties of convolution 8
2.3 System taxonomy 10
2.4 Input-output relationship described by an ODE 13
3 Periodic signal decomposition: Fourier Series representation 16
3.1 Fourier Series representation 16
3.2 Convergence of Fourier Series 17
3.3 Properties of Fourier Series 18
4 Aperiodic signal decomposition: Fourier Transform 22
4.1 Derivation of Fourier Transform 22
4.2 Convergence of Fourier Transform 23
4.3 Properties of Fourier Transform 23
4.4 Useful propositions and findings 28
5 Fourier Series/Fourier Transform + LTI systems 33
6 Resolve h(t) of an LTI system described by ODE 35
7 Laplace Transform: the generalization of Fourier Transform 36
7.1 Derivation of Laplace Transform 36
7.2 Signal taxnomy 37
7.3 Properties of LT 40
7.4 Revisit causality and stability from LT 44
8 Discrete-time cases 46
8.1 Discrete-time Fourier Series (DTFS) 46
8.1.1 Derivation of DTFS 47
8.1.2 Properties of DTFS 48
8.2 Discrete-time Fourier Transform (DTFT) 49
8.2.1 Derivation of DTFT 49
8.2.2 Properties of DTFT 50
8.3 Application of DTFS/DTFT to LTI systtems 56
8.4 Z-Transform 56
8.4.1 Signal taxnomy 57
8.4.2 Properties of ZT 60
8.4.3 Revisit causality and stability from ZT 63
8.5 Interrelation between the transforms 64
9 Sampling: bridging the continuous- and discrete-time worlds 66
9.1 Sampling theorem 66
9.2 Zero-Order Hold 69
10 Filter design 72
10.1 Prerequisites 72
10.2 Ideal Filters and Windowing Techniques 73
10.3 FIR Filters 76
10.4 IIR Filters 78
10.4.1 Butterworth Filters 78
10.4.2 Converting Analog IIR Filters to Digital Ones 80
A A little bit more about Fourier Series 87
Readership
This book should be useful for students, scientists, engineers and professionals working in the areas of optoelectronic packaging, photonic devices, semiconductor technology, materials science, polymer science, electrical and electronics engineering. This book could be used for one semester course on adhesives for photonics packaging designed for both undergraduate and graduate engineering students.
