Signals and systems

Abstract

This book gives an introductory treatment of signals and systems and is intended to be used as a text for students of electrical and electronic engineering. It is based on the experience of teaching circuits, signals and systems at the Faculty of Electrical and Electronic Engineering as well as the International Faculty of Engineering of the Technical University of Lodi. It is assumed that the reader has some knowledge of complex numbers and functions, basic electrical engineering and circuit theory. These prerequisite skills are mastered by the students during the junior years. The book should also be useful to engineers, enabling them to update and enhance their knowledge of signals and systems through self-study. Since the book is addressed to the electrical and electronic engineering students the material contains, beside the standard subjects of signals and systems, also analog-filter and digital-filter design. For the same reason numerous examples used to illustrate the theoretical material ref er to electric and electronic circuits and systems. The book includes a large number of examples. They are provided to illustrate the concepts and to make the theory more understandable. Furthermore, the examples enable the students to master some techniques and analysis tools and learn to use them effectively. Throughout the book linear, time-invariant systems are studied and continuous-time as well as discrete-time signals and systems are considered simultaneously as much as possible. The book provides the fundamentals of signals and systems and gives a background for later signal processing studies. A brief outline of this material is as follows. Chapter I presents an introduction to continuous-time and discrete-time signals and systems. It provides preliminary concept, basic definitions, and mathematical techniques including the continuous and discrete convolution. Chapter 2 is devoted to the Laplace transform and its application to circuit analysis. It examines in detail basic properties, rules, and techniques of the Laplace transform and derives the operator method for the analysis of linear circuits and systems. The results of Chapter 2 are extended in Chapter 3 where the concept of transfer function of continuous systems is introduced and block diagrams and signal-flow graphs enabling to determine transfer functions are discussed. Starting from Chapter 4 we consider frequency-domain descriptions of signals. Fourier series representation for continuous-time signals is included in Chapter 4. Chapter 5 exploits Fourier series to the analysis of systems driven by periodic excitations. The discrete Fourier series is introduced in Chapter 6. Discrete Fourier transform is developed in Chapter 7 and its effective implementation, known as the fast Fourier transform, is discussed in Chapter 8. Chapter 9 presents in detail the Fourier transform of continuous-time signals whereas Chapter 10 deals with the Fourier transform of discrete-time signals. Some applications of the Fourier transform, including sampling of continuoustime signals, and amplitude modulation, are given in Chapter 11. The concepts of signal energy and power are developed in Chapter 12. Chapter 13 is devoted to the Z-transform of discrete-time signals; it discusses basic properties and introduces the transfer function of a discrete system. The final two chapters are focused on design of analog and digital filters. Both mathematical background and some techniques of design of the analog Butterworth and the Chebyshev filters are developed in Chapter 14. The design techniques of digital filters are presented in Chapter 15. Window approach for designing FIR filters is discussed and bilinear transformation as well as the impulse-invariance technique for designing IIR filters are developed.[...]