Ingenieria De Control

Signals and Systems: A Fresh Look

Chi-Tsong Chen Stony Brook University

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Copyright c 2009 by Chi-Tsong Chen Everyone is permitted to copy and distribute this book but changing it is not permitted. Email: ctchen@ece.sunysb.edu or profctchen@gmail.com

Also by the same author: • Linear System Theory and Design, Oxford Univ. Press, [1st ed., (431 pp), 1970; 2nd ed., (662 pp), 1980; 3rded., (332 pp), 1999]. • Analog and Digital Control System Design: Transfer-Function, State-Space, and Algebraic Methods, Oxford Univ. Press, 1993. • Digital Signal Processing: Spectral Computation and Filter Design, Oxford Univ. Press, 2001. • Signals and Systems, 3rd ed., Oxford Univ. Press, 2004.

The following are widely recognized: • There is a gap between what is taught at universities andwhat is used in industry. • It is more important to teach how to learn than what to learn. These were the guiding principles in developing this book. It gives an overview of the subject area of signals and systems, discussing the role of signals in designing systems and various mathematical descriptions for the small class of systems studied. It then focuses on topics which are most relevant anduseful in practice. It also gives reasons for not stressing many conventional topics. Its presentation strives to cultivate readers’ ability to think critically and to develop ideas logically. After teaching and writing for over forty years, I am on the verge of retirement and have decided to give this book away as a gift to the students in my class and any other interested readers. It, togetherwith its solutions manual, can be downloaded from www.ece.sunysb.edu/˜ctchen/. If you find the book useful, please spread the word. I also appreciate receiving any feedback you have.

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Preface
Presently, there are over thirty texts on continuous-time (CT) and discrete-time (DT) signals and systems.1 They typically cover CT and DT Fourier series; CT and DT Fourier transforms; discrete Fouriertransform (DFT); two- and one-sided Laplace and z-transforms; convolutions and differential (difference) equations; Fourier and Laplace analysis of signals and systems; and some applications in communication, control, and filter design. About onethird of these texts also discuss state-space equations and their analytical solutions. Many texts emphasize convolutions and Fourier analysis. Feedbackfrom graduates that what they learned in university is not used in industry prompted me to ponder what to teach in signals and systems. Typical courses on signals and systems are intended for sophomores and juniors, and aim to provide the necessary background in signals and systems for follow-up courses in control, communication, microelectronic circuits, filter design, and digital signal procession.A survey of texts reveals that the important topics needed in these follow-up courses are as follows: • Signals: Frequency spectra, which are used for discussing bandwidth, selecting sampling and carrier frequencies, and specifying systems, especially, filters to be designed. • Systems: Rational transfer functions, which are used in circuit analysis and in design of filters and control systems. Infilter design, we find transfer functions whose frequency responses meet specifications based on the frequency spectra of signals to be processed. • Implementation: State-space (ss) equations, which are most convenient for computer computation, real-time processing, and op-amp circuit or specialized hardware implementation. These topics will be the focus of this text. For signals, we develop frequencyspectra2 and their bandwidths and computer computation. We use the simplest real-world signals (sounds generated by a tuning fork and a piano) as examples. For systems, we develop four mathematical descriptions: convolutions, differential (difference) equations, ss equations, and transfer functions. The first three are in the time domain and the last one is in the transform domain. We give reasons...