738 COMMUNICATION SYSTEMSM(f)−10,000 10,000
fFigure P15.2.1615.2.19An FM station’s modulator has a sensitivitykFM=
5 π× 104 rad/s·V. A receiver uses a discriminator
that has a gain constant of 10−^5 /πV·s/rad. Ne-
glecting noise, determine the signal at the receiver
output.
15.2.20A voice message withWf= 2 π( 3 × 103 )rad/s and
Wrms= 2 π( 1 × 103 )rad/s is transmitted over an
FM broadcast system with standard emphasis. See
Example 15.2.2, and compare the improvements
due to emphasis.
15.2.21Show that the image frequency for an FM station
does not fall in the range of 88.1–107.9 MHz,
regardless of the choice of high- or low-side local
oscillator.*15.2.22Consider the signals given by Equations (15.2.12)
through (15.2.14). Let them be normalized such
that the red, green, and blue signals have a maxi-
mum amplitude of unity. IfmI(t) andmQ(t) are the
real and imaginary components of a color vector,
defined by a magnitude [m^2 I(t)+m^2 Q(t)]^1 /^2 and
phase tan−^1 [−mQ(t)/ml(t)], sketch points cor-
responding to fully saturatedR, G, andBcolors.
15.2.23If a television station operates on UHF channel
20 (band 506–512 MHz), determine the station’s
visual-carrier frequency.
15.2.24For DSB and conventional AM, obtain expres-
sions for the in-phase and quadrature components
xd(t) andxq(t), and envelope and phasev(t) and
φ(t).
15.2.25The normalized signalxn(t) has a bandwidth of
10 kHz and its power content is 0.5 W, while the
carrierAccos 2πfcthas a power content of 200 W.
Find the bandwidth and the power content of the
modulated signal, if the modulation scheme is:
(a) Conventional AM with a modulation index
of 0.6 and a transmitted signal ofAc[1+
mAx(t)] cos 2πfct.
(b) DSB SC with a transmitted signal ofAcx(t)
cos 2πfct.
(c) SSB with a transmitted signal ofAcx(t)
cos 2πfct∓Acx(t) ̄ sin 2πfct, wherex(t) ̄ is
a signal with a 90° phase shift in all frequency
components ofx(t), and the upper−sign
corresponds to the USSB signal, whereas the
lower+sign corresponds to the LSSB signal.
(d) FM withkf=50 kHz.
15.2.26Let the modulating signalm(t) be a sinusoid of the
formm(t)=cos 2πfmt, fm<< fc, and let the
carrier signal be cos( 2 πfct+φc).
(a) Determine the conventional AM signal, its
upper and lower sidebands, and its spectrum
if the modulation index isα.
(b) Determine the DSB SC AM signal, its up-
per and lower sidebands, and its spectrum for
m(t)=αcos 2πfmt, fm<< fc.
(c) Determine the two possible SSB AM signals
and their spectra.
*15.2.27Let the message signalm(t)=αcos( 2 πfmt)
be used to either frequency-modulate or phase-
modulate the carrierAccos( 2 πfct). Find the mod-
ulated signal in each case.
15.2.28If an FM signal is given bysFM(t) = 100
cos [2πfct+ 100∫t
−∞m(τ ) dτ] andm(t) is given
in Figure P15.2.28, sketch the instantaneous fre-
quency as a function of time and determine the
peak frequency deviation.
15.2.29Ifm(t) of Figure P15.2.29 is fed into an FM modu-
lator with peak frequency deviationkf=25 Hz/V,
plot the frequency deviation in hertz and the phase
deviation in radians.