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Answers to Selected Problems 743
5–10 (a) s(t) = (cos v 1 t + 2 cos 2v 1 t) cos v c t, where v 1 = 1000p
(b) S(f) = 1 4 Cd(f - f c + f 1 ) + d(f + f c - f 1 ) + d(f - f c - f 1 )
(c) 1.25 W (d) 4.5 W
5–15 See Student Solutions Manual
+ d(f + f c + f 1 )] + 1 2 [d(f - f c + 2f 1 ) + d(f + f c - 2f 1 )
+ d(f - f c - 2f 1 ) + d(f + f c + 2f 1 )D
ƒ
5–17 (a) See Student Solutions Manual
(b) s(t) =ß(t) cosv c t - 1 p ln ¢ ƒt + 1 2
≤ sinv
ƒt - 1 c t
2
(c) max[s(t)] =q
5–19 (a) See Student Solutions Manual (b) See MATLAB file P5_19.m
5–27 See MATLAB file P5_27.m
5–30 (a) f BPF = 12.96 MHz, B BPF = 48.75 kHz (b) 7.96 or 17.96 MHz (c) 9.38 kHz
5–32 (a) m(t) = 0.2 cos (2000pt), M p = 0.2 V, f m = 1 kHz
(b) m(t) = -0.13 sin (2000pt), M p = 0.13 V, f m = 1 kHz
(c) P AV = 2500 W, P PEP = 2500 W
5–37 See MATLAB file P5_37.m
5–38 S(f) = 1 2 [G(f - f c) + G*(-f - f c )], where
q
G(f) = a n=-q J n(0.7854) d (f - nf m ), f c = 146.52 MHz,
and f m = 1 kHz. B = 3.57 kHz
5–42 S(f) = 1 C 2 a q n=-q c q
nd Af - f c - nf m B + a n=-q c n * d Af + f c + nf m BD, where
c n = 5Ae jb -1 sin (np>2)
B a b, f m = 1 kHz, b = 0.7854, and f c = 60 MHz
np>2
5–46 (a) 5.5 Hz
(b)
S(f) = A c
2 e d(f - f c) + d(f + f c ) + D f
2p
g q
n = -q
n = 0
a c n
nf m
b
* [d(f - f c - nf m ) - d(f + f c - nf m )] f,
5–49
where c n = 5e -jnp>2 sin (np>2)
a b (n Z 0, c 0 = 0)
np>2
D f = 6.98 rad>V-s, f m = 100 Hz, and f c = 30 MHz
(f) L 0.893[2d(f - f c + 5f 0 ) + d(f - f c + 3f 0 )
+ d(f - f c - f 0 ) + 2d(f - f c + 3f 0 ) + d(f - f c - 5f 0 )
+ 2d(f + f c - 5f 0 ) + d(f + f c - 3f 0 ) + d(f + f c + f 0 )
+ 2d(f + f c + 3f 0 ) + d(f + f c + 5f 0 )]
where
f 0 ! D f
2p
= 15.9 kHz and f c = 2 GHz