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

# I f w i w2 the integrand of the third term contains a

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Unformatted text preview: o f t he sinusoids. I t a ppears t hat t he p ower o f + f2(t) is P h + P h' U nfortunately, t his conclusion is n ot t rue i n general. I t is t rue o nly u nder a c ertain c ondition (orthogonality) discussed l ater i n Sec. 3.1-3. 'SS '89 '90 '91 '92 '93 (b) IDI. • Comment: I n p art ( b) we have shown t hat t he power of t he s um o f two sinusoids '87 F ig. 1 .4 1.2 Continuous-time and Discrete-time Signals. Classification o f Signals h (t) 6. E xercise E l.1 Show t hat the energies of the signals in Figs. 1.3a,b,c and d are 4, 1, 4/3, and 4/3, respectively. Observe t hat doubling a signal quadruples the energy, and time-shifting a signal has no effect on the energy. Show also that the power of the signal in Fig. 1.3e is 0.4323. What is the rms value of signal in Fig. 1.3e? \ l 6. E xercise E 1.2 Redo Example 1.2a to find the power of a sinusoid C cos (wot + Ii) by averaging the signal energy over one period To = 27r/wo (rather than averaging over the infinitely large interval). Show also t hat the power of a constant signal f (t) = Co is C6, and its rrns value is Co. \ l 6. E xercise E l..3 Show that if WI = W2, the power of f (t) = C1 cos (Wit + iii) + C2 cos (W2t + 1i2) is IC1 2 + C 22 +2C1C2 COS(1i1-1i2)l!2, which is not equal to (C1 2 + C2 2 )/2. \l T here a re s everal classes of signals. Here we shall consider only t he following classes, which a re s uitable for t he s cope o f t his b ook: 1. 2. 3. 4. 5. C ontinuous-time a nd d iscrete-time signals A nalog a nd d igital s ignals P eriodic a nd a periodic signals E nergy a nd p ower signals D eterministic a nd p robabilistic signals 1 .2-1 Continuous-Time and Discrete-Time Signals A s ignal t hat is specified for every value o f t ime t (Fig. 1.4a) is a c ontinuoustime s ignal, a nd a s ignal t hat is specified only a t d iscrete values o f t (Fig. l .4b) iE a d iscrete-time s ignal. T elephone a nd v ideo c amera o utputs a re continuous-tim~ 58 1 I ntroduction t o Signals a nd S ystems 1.2 59 Classification of Signals f (t) (b) - V r- i i~To~ t- - t- f(t) - '--- - F ig. 1 .6 A periodic signal of period To. f (t) (d) (c) tt- Fig. 1 .5 Examples of Signals: (a) analog, continuous-time (b) digital, continuous-time (c) analog, discrete-time (d) digital, discrete-time. signals, whereas t he q uarterly gross n ational p roduct ( GNP), m onthly sales of a corporation, a nd s tock m arket d aily averages are discrete-time signals. 1.2-2 Analog and Digital Signals T he c oncept o f continuous-time is often confused with t hat o f analog. T he two are n ot t he s ame. T he s ame is t rue o f t he c oncepts of discrete-time a nd d igital. A s~gnal who~e a mplitude c an t ake o n a ny v alue in a continuous range is a n a nalog s ignal. ThiS m eans t hat a n a nalog signal a mplitude c an take on a n infinite n umber o f values. A d igital s ignal, on t he o ther h and, is one whose a mplitude c an t ake o n o nly a finite n umber o f values. Signals associated with a digital c omputer a re digital because t hey t ake o n o nly two values (binary signals). A digital signal wh...
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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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