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744
Answers to Selected Problems
5–52 (a) 20 kHz (b) S(f) = 1 2 [M 1(f - f c ) + M 1 (f - f c )] + j 2 [M 2(f + f c ) - M 2 (f - f c )]
5–53 (a) S(f) = 1 2 [X(f - f c) + X *(-f - f c )],
where X(f) = A c
q sin (np>2)
g a b d(f - 1 2
nR), R = 24 kb>s
2 n=-q np>2
(b) 48 kHz
5–57 See MATLAB file P5_57.m
5–62 (a) 96 kHz (b) 101 kHz
5–67 (a) 0.6 (b) no
5–68 (a) See Student Solutions Manual (b) See MATLAB file P5_68.m
5–77 (a) -45°, + 45°, + 135°, -135°, -45°, -45°, -45° (b) 1.13 Mb/s
5–82 See MATLAB file P5_82.m
5–84 (a) See Student Solutions Manual (b) See MATLAB file P5_84.m
5–90 See Student Solutions Manual
Chapter 6
6–2 (a) xq = (212 A>p) cos (v 0 t + p>4) (b) x(t) is not stationary
6–5 2> 1p = 1.128
6–9 (a) 15 W (b) 11 W (c) 19 W
6–11 (a) No (b) Yes (c) Yes (d) No
6–13 B rms = 0.170 Hz See MATLAB file P6_13.m
6–18 (a) 1B (b) R x (t ) = B[(sin pBt)>(pBt)] 2
6–22 (a) (2/ N 0 ) R xy ( t) (b) (2/ N 0 ) xy (f)
6–25 (a) N 0 K 2 >(8p 2 f 2 ) (b) q
6–29 1/ (2pf 0 )
6–34 (a) H(f) = 10>ca1 + j f b d
(b) 0.690 f 0 , where f 0 = 1/ (2pRC)
f 0
6–37 (a) t 2 - t 1 = t = ; n/ 2, n = 0, 1, 2, . . . (b) See Student Solutions Manual
6–39 (a) Not WSS
6–40 x (f) = A 0 2
4 [d(f - f 0) + d(f + f 0 )]
6–41 Yes
6–43 See MATLAB file P6_43.m
2
6–45 (a) v (f) = e 100[ x(f - f c ) + x (f + f c )], | f | 7 f c
(b) 1000 kW
0, f elsewhere f
6–49 x(t) = m 1 (t) + m 2 (t), y(t) = mN 1 (t) - mN 2 (t)
f
m1 (f) = Aßa
2(f 3 - f c ) b, f
m 2
(f) = A a b
f c - f 1
6–52 v (t) = 1 4 [ x(f - f c ) + x (-f - f c )],
where x (f) = T b a 1 - cos pfT 2
b
b
pfT b