Signal Processing and Linear Systems-B.P.Lathi copy

30103 loglo 3 047712 b7 10 solution o f quadratic and

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Unformatted text preview: -!!-.J!i:+!!2 2 4 27 T he solution o f t he depressed cubic is x =A+B, x = _ AtB + A ;ByC3, I n this chapter we shall discuss certain basic aspects of signals. We shall also introduce important basic concepts a nd q ualitative explanations of the how's and why's of systems theory, thus building a solid foundation for u nderstanding the quantitative analysis in the remainder of the book. a nd y=x-~ References 1 . 'Asimov, I saac, A simov on Numbers, Bell Publishing Co., N.Y., 1982. 2. Calinger, R., Ed., Classics o f M athematics, Moore Publishing Co. ,Oak Park, IL., 1982. 3. Hogben, Lancelot, M athematics i n the Making, Doubleday & Co. Inc., New York,1960. 4. Cajori, Florian, A History o f M athematics, 4 th ed., Chelsea, New York, 1985. 5. E ncyclopaedia Britannica, 15th ed., Micropaedia, vol. 11, p. 1043, 1982. 6. Singh, J agjit, Great Ideas o f Modern Mathematics, Dover, New York, 1959. 7. D unham, William, J ourney through Genius, Wiley, New York, 1990. Signals A s ignal, as t he t erm implies, is a s et of information or data. Examples include a telephone or a television signal, monthly sales of a corporation, or the daily closing prices of a stock market (e.g., t he Dow Jones averages). In all these examples, the signals are functions of the independent variable t ime. T his is n ot always the case, however. When an electrical charge is d istributed over a body, for instance, the signal is t he charge density, a function of space r ather t han time. In this book we deal almost exclusively with signals t hat are functions of time. T he discussion, however, applies equally well t o o ther independent variables. S ystems Signals may be processed further by s ystems, which may modify them 0 1 e xtract a dditional information from them. For example, an antiaircraft gun operato! may want t o know the future location of a hostile moving target t hat is being trackec by his radar. Knowing t he r adar signal he knows t he p ast location a nd velocity 0 t he t arget. By properly processing t he r adar signal (the input) he can approximatel) estimate the future location of t he t arget. Thus, a system is an e ntity t hat processe: a set ofsignals ( inputs) t o yield another set of signals ( outputs). A s ystem may bl made u p o f physical components, as in electrical, mechanical, or hydraulic system: (hardware realization), or i t may be an algorithm t hat computes an o utput frorr an i nput signal (software realization). 51 52 1.1 1 I ntroduction t o Signals a nd Systems 53 1.1 Signals Size o f a Signal T he size of any entity is a number t hat indicates the largeness or strength of t hat entity. Generally speaking, the signal amplitude varies with time. How c an a signal t hat e xists over a certain time interval with varying amplitude be measured by one number t hat will indicate t he signal size or signal strength? Such a measure must consider n ot only the signal amplitude, b ut also its duration. For instance, if we are to devise a single number V asa measure of the size of a human being, we m ust consider n ot only his or her width (girth), b ut also the height. I f we make a simplifying assumption t hat t he sha...
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This note was uploaded on 04/14/2013 for the course ENG 350 taught by Professor Bayliss during the Spring '13 term at Northwestern.

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