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Answers to Selected Problems
2
q
3–63 (a) 6 kHz (b) ƒW s (f)ƒ = f s ƒSa(pft)ƒ a ß((f - kf s )>(2B)) + e jpT s f
((f - kf s )>B)2
-q
3–66 See Student Solutions Manual
3–70 (a) 40 Hz (b) 1280 Hz
Chapter 4
4–3 S(f) = -j25 d (f - f c - 1000) + j25 d(f - f c + 1000) - j25 d (f + f c - 1000)
+ j25 d (f + f c + 1000)
4–9 (a) See Student Solutions Manual
(b) v 2 (t) = (A/p){Si[pB T (t + (T/2))] - Si[pB T (t - (T/2))]} cos(v c t)
z
Where the sine integral is defined by Si(z) = sin(t)>t dt [Zbramowitz and Stegun, 1965]
L
See MATLAB file P4_09.m
4–11 (a) 398 Hz For (b), (c), and (d) see MATLAB file P4_07.m
4–14 (a) g(t) = 500 + 200 sin v a t, AM, m(t) = 0.4 sin v a t
(b) x(t) = 500 + 200 sin v a t, y(t) = 0
(c) R(t) = 500 + 200 sin v a t, u(t) = 0
(d) 2.7 kW
4–15 (a) S( f) = 250 [d( f - f c ) + d(f + f c )]
+ j50 [d(f - f c + f a ) - d( f - f c - f a ) + d( f + f c + f a ) - d(f + f c - f a )]
(b) Same as (a) above
4–19 See MATLAB file P4_19.m
4–22 See MATLAB file P4_22.m
4–25 48.3%
4–28 K3m 2 (t) + [mN (t)] 2 , yes
4–33 0
4–35 (a) (j2pf)>[j2pf + K d K v F 1 (f)] (b) (j2pf)(f 1 + jf)>[j2pf(f 1 + jf) + K d K v f 1 ]
4–37 See Student Solutions Manual
4–42 (a) 107.6 MHz (b) RF: At least 96.81–96.99 MHz; IF: 10.61–10.79 MHz
(c) 118.3 MHz
4–47 (a) See Student Solutions Manual (b) 1990 Hz
o
Chapter 5
5–1 (a) 6.99 dBk (b) 707 V (c) 7025 W (d) 7025 W (e) 18,050 W
5–4 See Student Solutions Manual
5–6
S(f) = 1 2 c gq
n = -q c nd (f - f c - nf m ) + g q
n=-q c n • d (f + f c + nf m ) d
where c n = A c
2p c2u 1a sin nu 1
b + 2A cos nu 1 sin u 1 - n sin nu 1 cos u 1
m
nu 1 1 - n 2 d,
A m = 1.2, and u 1 = 146.4°