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

T his s egment w hen r epeated forever in e ither d

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: art b efore t = 0 is a c ausal signal. I n o ther words, j (t) is a causal signal if j (t) = 0 t <0 (1.7) Signals in Figs. 1.3a, b, c, a s well as in Figs. 1.9a a nd 1 .9b are causal signals. A signal t hat s tarts before t = 0 is a n oncausal signal. All t he signals i n Figs. 1.1 a nd 1.2 are noncausal. O bserve t hat a n e verlasting signal is always noncausal b ut a n oncausal signal is n ot necessarily everlasting. T he e verlasting signal in Fig. 1.2b is noncausalj however, t he n oncausal signal in Fig. 1.2a is n ot e verlasting. A signal t hat is zero for all t :2: 0 is called a n a nticausal signal. 60 1 I ntroduction t o Signals a nd S ystems 61 1.3 Some Useful Signal O perations (a) (a) ~ F ig. 1 . 7 G eneration o f a p eriodic s ignal by p eriodic extension o f i ts s egment o f o ne-period d uration. cf== Comment: A t rue e verlasting s ignal c annot b e g enerated in practice for obvious reasons. W hy s hould w e b other t o p ostulate such a signal? In later c hapters we s hall see t hat c ertain s ignals (including a n e verlasting sinusoid) which c annot b e g enerated in practice do s erve a very useful p urpose i n t he s tudy o f signals a nd s ystems. 1.2-4 Energy and Power Signals A s ignal w ith finite energy is a n e nergy s ignal, a nd a s ignal w ith finite a nd n onzero power is a p ower s ignal. Signals in Fig. 1.2a a nd 1.2b a re e xamples of energy a nd p ower signals, respectively. O bserve t hat power is t he t ime average of energy. Since t he averaging is over a n infinitely large interval, a signal w ith finite energy h as z ero power, a nd a s ignal w ith finite power has infinite energy. Therefore, a signal c annot b oth b e a n e nergy a nd a power signal. I f i t is one, i t c annot b e t he o ther. O n t he o ther h and, t here a re signals t hat a re neither energy nor power signals. T he r amp s ignal is such a n e xample. Comments All p ractical signals have finite energies a nd a re therefore energy signals. A power signal m ust necessarily have infinite duration; otherwise i ts power, which is its energy a veraged over a n infinitely large interval, will n ot a pproach a (nonzero) limit. Clearly, i t is impossible t o g enerate a t rue power signal in practice because such a signal h as infinite d uration a nd infinite energy. Also, b ecause o f p eriodic repetition, periodic signals for which t he a rea u nder If(t)1 2 over o ne p eriod is finite are power signals; however, n ot all power signals are periodic. C::. E xercise E 1.4 Show t hat a.n everlasting exponential e - at is neither an energy nor a power signal for any real value of a. However, if a is imaginary, it is a power signal with power P f = 1 regardless of '7 the value of a. 1.2-5 Deterministic and Random Signals A s ignal w hose physical description is known completely, e ither i n a m athematical form or a graphical form, is a d eterministic s ignal. A s ignal whose values ( c) F ig. 1 .8 T ime s hifting a s ignal. c annot b e p redicted pre...
View Full Document

Ask a homework question - tutors are online