0195136047.pdf

PROBLEMS 739

m(t)

− 1

− 5

5

(^012)...

...
t

Figure P15.2.28

m(t)

− 1

− 2

2

1

134526

t

Figure P15.2.29

15.2.30An angle-modulated signal has the formu(t)=

100 cos[2πfct+4 sin 2πfmt], wherefc=10 MHz

andfm=1 kHz. Determine the modulation index

βforβpand the transmitted signal bandwidth,

withBFM= 2 (βf+ 1 )fmorBPM= 2 (βp+ 1 )fm,

(a) If this is an FM signal.

(b) If this is a PM signal.

15.2.31Letm 1 (t) andm 2 (t) be two message signals, and

letu 1 (t) andu 2 (t) be the corresponding modulated

versions.

(a) When the combined message signalm 1 (t)+

m 2 (t) DSB modulates a carrierAccos 2πfct,

show that the result is the sum of the two DSB

AM signalsu 1 (t)+u 2 (t). That is to say, AM

satisfies the superposition principle.

(b) Ifm 1 (t)+m 2 (t) frequency modulates a carrier,

show that the modulated signal is not equal to

u 1 (t)+u 2 (t). That is to say, FM does not sat-

isfy the principle of superposition, and angle

modulation is not a linear modulation method.

15.2.32Figure P15.2.32 shows an FM discriminator. As-

sume the envelope detector to be ideal, with an

infinite input impedance. Choose the values forL

andCif the discriminator is to be employed to

demodulate an FM signal with a carrier frequency

fc=80 MHz and a peak frequency deviation of 6

MHz.

*15.2.33Let a message signalm(t) have a bandwidth of 10
kHz and a peak magnitude of 1 V. Estimate the

bandwidth, by using Carson’s rule, of the signal

u(t) obtained whenm(t) modulates a carrier with

a peak frequency deviation of:

(a)fd=10 Hz/V.

(b) 100 Hz/V.

(c) 1000 Hz/V.

15.2.34The operating frequency range of a superhetero-

dyne FM receiver is 88–108 MHz. The IF and LO

frequencies are so chosen thatfIF<fLO.Ifthe

image frequencyfc′must fall outside of the 88–

108-MHz range, determine the minimum needed

fIFand the corresponding range offLO.

15.2.35The television audio signal of Figure 15.2.29 is

frequency modulated withf=25 kHz and has

Wf∼=10 kHz. By usingWFM∼= 2 (ω+ 2 Wf)

forω >> Wf (for wide-band FM), find the

percentage of the channel bandwidth occupied by

the audio signal.

15.2.36Suppose that a video signal, havingW=5 MHz,

is transmitted via FM withf =20 MHz. For

1 / 100 ≤B/fc≤ 1 /10, determine the bounds on

the carrier frequency. UseWFM∼= 2 (ω+ 2 Wf)

forω >> Wf(for wide-band FM).

15.2.37A TDM signal, like that of Figure 14.2.9(b), is

formed by sampling 5 voice signals atfs=8 kHz.

The signal is then transmitted via FM on a radio

channel with 400-kHz bandwidth. Estimate the

maximum allowable frequency deviationf[use