Communication Systems: An Introduction to Signals and Noise in Electrical Communication, 5th Edition – Solution Manual – Carlson & Crilly

Solutions Manual Communication Systems
An Introduction to Signals and Noise in Electrical
Communication 5th Edition

,Chapter 2

2.1-1
Ae j T0/2
j2p ( m n )f 0t
Ae jf n m
cn
f
∫e dt Ae sinc(m n)
jf

T0 T0 /2 0 otherwise

2.1-2




2 0
c0 v(t) T 2p nt T0 /2 2p nt 2A pn
c Acos dt ( A)cos dt sin
n
0 T T
/4
T T pn 2
0
0 0 0


n 0 1 2 3 4 5 6 7
cn 0 2A/p 0 2 A / 3p 0 2 A / 5p 0 2 A / 7p
arg cn 0 180 0 180


2.1-3




c0  v(t) A /2
2
c T0 /2 2 At 2p nt A A
A co
T0 s
n
T dt sinp n (cosp n 1)

0 0
0
T pn (p n)2
n 0 1 2 3 4 5 6
cn 0.5A 0.2A 0 0.02A 0 0.01A 0
arg cn 0 0 0 0


2.1-4




2 T0 /2 2p t
c Acos 0 (cont.)
0
T 0 T
0 0


2-1

, 2 T /2 2pt 2p nt 2 A sin p p n 2t / sin p n 2t / T T
0
T p
cn A cos cos dt 0 0

T0 0 T0 T0 T0 4(p p n) / T0 4(p p n ) / T0 0

A
sinc(1 n) sinc(1 A/2 n 1
n)
2 0 otherwise

2.1-5




c0  v(t)
2 0
T0 /2 2p nt A
c j Asin dt j (1 cosp n)
n
T 0 T pn
0 0


n 1 2 3 4 5
cn 2A/p 0 2 A / 3p 2 A / 5p
arg cn 90 90 90

2.1-6




c0  v(t) 0
2 T
c j T 2p t 2p nt 2 A sin p p n 2t / T0 sin p n 2t / T
p A sin sin dt j 0

n
T T 4(p p n )/ T 4(p p n )/ T
0 T0 0 0 0
0 0 0
A m jA / 2 n 1
j sinc(1 n ) sinc(1 n )
2  0 otherwise

2.1-71
c T0 /2  jnw0 t
T0
 jnw 0t

n
T0 v ( t) e dt 0 T /2
v(t )e dt

0



 v(t )e jnw t dt 
T0 T0 /2


jnw 0l jnw 0T0 /2
where T /2
0
v(l  T0 /2) e e dl
0 0
T0 /2

 v(t )e
jnp jnw0 t
e dt
0

since e jnp 1 for even n, cn 0 for even n
2-2

, 2.1-8

2 2 2 2 2 2
P c 2 c Af t 2 Af t sinc f t 2 Aft sinc2 ft 2 Aft sinc3 ⋯
ft
0 n 0 0 0 0 0 0 0
n 1
1
where 4f
0
t
1 2 1 A2 21 2 3 2
f 1 2sinc 4  2sinc 2  2sinc
P 0.23 A
t 16 4
2 P  A 
2
2 1 2 1 2 3 2 5 2 3 2 7 
f  2sinc  2sinc  2sinc  2sinc 0.24A2
1 2sinc 2  2sinc  
16A
t 4 2 4 4
1 2
2 1 2 1 2
4 
f P 1 2sinc 4  2sinc 0.21A
2t 16 2

2.1-9
0 n even
2
cn  2 n odd

pn
1 2 2
a) P T
14 t 2 T0 /2 4t 1
T T /2 dt 1 dt 3
0
0
0 0 T0 T 0
4 2 4 2 4 2
P / P 99.6%
P 2 2 2 0.332 so
p 2  9p 2   25p 2 
b) v (t) 8 8
cosw0t 2
cos3w 0t cos5w 0t
8 9p 25p 2
p2




2.1-10
0 n even
cn  j2
n odd
pn 0 2
a) P 1
2 2
T /2 1 dt 1 P 2 2 2 22 0.933 so P / P 93.3%
T
/2 T

0
0 3p
p 5
p


(cont.)
2-3