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Answers to Selected Problems
Chapter 2
2–1 See Student Solutions Manual
2–4 (a) See Student Solutions Manual (b) 3.18 volts 0.064 amps
(c) 5 volts 0.1 amps (d) 0.5 watts
2–10 36 dB
2–11 (a) 4.08 10 -14 W (b) -103.9 dBm (c) 1.75 µV
2–15 W(f) = e-a e -j2pf
a + j2pf
2–18
ƒ ƒ
Note that S(0) = AT 2 0>2.
2–24 See MATLAB file P2_24.m
2–32 See MATLAB file P2_32.m
2–37 See Student Solutions Manual
2–42 (a) (sin 4t)/ (4t) (b) 7
2–48 (a) -0.4545A (b) 0.9129A
2–50 (a) (A 1 + A 2 )> 12 (b) 12A 2 1 + A 2 2 2> 12 (c) A 2 - A 1 > 12
(d) 12A 2 1 + A 2 2 2> 12 (e) 12A 2 1 + A 2 2 2> 12
2–52 (a) See Student Solutions Manual (b) w j (t)> 18, j = 1, 2, 3
2–53 w(t) = 12 w 1 (t)’ - 12 w 2 (t)’ where the prime denotes an orthonormal function
2–54 0.756
2–61 c n = (Ab>T) e -jnv (t0+b>2) Sa(npb>T)
2–64
S(f) = - A v 2 + Ae-jvT 0
a 1 v 2 + jT 0
v b,
c n =
d
where v = 2pf
AT 2
,
2T 0
n = 0
A{e -j2pnT>T 0
[1 + j2pn(T>T 0 )] - 1}
(2pn) 2 ,
>T 0
n Z 0
0, n = even
2–70 (a) c n = 4
(b) 1
L
n 2 p , 2 n = odd 3 W
Also, see MATLAB file P2_70.m
2–72 See MATLAB file P2_72.m
2–80 200 Hz
2–84 See MATLAB file P2_84.m
2–87 See MATLAB file P2_87.m
2–90 (a) 6.28 ms (b) 160
2–92 See MATLAB file P2_92.m
2–100 (a) q (b) 0.38T 0 (c) 1(3T 0 ) (d) 1T 0