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

291 48 angle modulation pt a cos ot where ot

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: r i '-- A I d 293 We have seen t hat P M a nd F M a re not different kind o f m odulation, b ut t wo. special cases o f generalized angle modulation. Such a view is very fruitful because i t shows t he convertibility of one t ype of angle modulation (such as P M) t o a nother (such as FM). This convertibility is q uite clear in Fig. 4.42. For instance, we show l ater t hat t he b andwidth of F M is a pproximately 2kfm p, where m p is t he peak amplitude of m (t). We c an derive t he equivalent result for P M by referring t o Fig. 4.42b, which shows t hat P M is a ctually t he F M when t he m odulating signal is m (t). Clearly, t he b andwidth of P M is approximately 2kpmp', where m p ' is t he p eak a mplitude o f m (t). T his argument shows t hat if we analyze one type of angle modulation (such as FM), we could readily extend those results t o a ny other kind. Historically, the angle modulation concept began with FM. Hence, i t is c ustomary t o analyze F M a nd t hen modify those results for o ther forms, such as P M. B ut t his does n ot imply t hat F M is s uperior t o o ther kinds of angle modulation. O n t he contrary, P M is superior t o F M for most analog signals such as audio a nd video. Actually, t he o ptimum performance is realized neither by P M nor FM, b ut by some o ther form, depending on t he n ature o f t he b aseband (message) signal. "'FM(t) , , m (t) 4.8 Angle Modulation "'PM(t) -I / 2 X 10-4 V - ---I / \t(a) "V 20,000 - 20,000 -----'U D I [_ (c) D Phase Modulator F ig. 4.42 Phase and frequency modulation are inseparable. All In The Family E quations (4.84b) and (4.85c) indicate t hat P M a nd FM are n ot only very similar b ut a re inseparable. Replacing m (t) in Eq. (4.84b) with m (a) da changes P M i nto FM. T hus, a signal t hat is a n F M wave corresponding to m (t) is also t he P M wave corresponding t o m (a) da (Fig. 4.42a). Similarly, a P M wave corresponding t o m (t) is t he F M wave corresponding t o m (t) (Fig. 4.42b). We c onclude t hat j ust by looking a t an angle-modulated carrier, we c annot tell whether it is F M or P M. I n fact, it is meaningless to enquire if a certain angle m odulated wave is FM o r P M. A n analogous situation would be t o ask a person (who is m arried, w ith children), whether he is a f ather or a son. T he person would be puzzled because he is b oth, a father (of his child) and a son (of his father). t ( b) t (d) F ig. 4.43 FM and PM waveforms. • E xample 4.21 Sketch FM and PM waves for the modulating signal m (t) depicted in Fig. 4.43a. The constants k f and kp are 27r (10 5 ) and 107r, respectively, and the carrier frequency F e is 100 MHz. 294 4 4 .8 C ontinuous-Time S ignal A nalysis: T he F ourier T ransform + ~~ m (t) (Fi) min = 10 8 (F;)max = 108 = 10 8 5 + 105 [m(t)]max = Because m (t) switches back a nd f orth from 1 to - 1 a nd vice versa, t he F M wave frequency switches back a nd f orth from 99.9 MHz t o 100.1 MHz and vice versa, as shown in Fig. 4.44b. This scheme of a carrier frequency modulation by a digital signal is known as f requencyshift k...
View Full Document

Ask a homework question - tutors are online