Communication Systems – Solutions Manual – Carlso – Complete Worked Problems and Step-by-Step Explanations (A+ Grade Resource)

,
,Chapter 1

1.1-1
jf Ae jf n =ḿ
cn = Ae
T0/2
+e
j2p ( ḿ−n )f 0t
dt =Ae sinc(ḿ − 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

T 
n
0 T T /4
0
T pn 2
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 = 2v(t) =A /2
c = T /2  0 2 At  2p nt A A
n   T0 
T0 0 
A − cos
dt = sinp n − (cosp n −1)
 T0 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 2pt 2 A sin (p −p n ) 2t / T sin (p +p n) 2t / T T / 2
2p nt
T /2

0

cn =  Acos dt = 
0
cos 0
+ 0

T0 0 T0 T0 T0  4(p −p n) / T0 4(p + p n) / T0 0
A
= sinc(1 − n) + sinc(1 + n) A / 2 n =1
=
2 0 otherwise

2.1-5




c0 = v(t)
2 =0T0 /2 2p nt A
c =− j Asin dt =− j (1− cosp n)
T 
n
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
2 A sin (p −p n ) 2t / T0 sin (p +p n ) 2t / T 
T
c =− j T /2 2p t
0 2p nt
Asin sin dt =− j  − 0 
n
T 
0
T T T 4(p −p n)/ T 4(p +p n)/ T
0 0 0 0  0 0 0
A ḿ jA / 2
=− j sinc(1−n ) − sinc(1+ n) = n =1

2  0 otherwise

2.1-71
c =  T0 /2 − jnw0 t
T0
− jnw 0t

n

T0 0 v(t) e dt + 
T
v(t)e dt 
T0 /2

T0
where T /2
v(t)e − jnw0 t dt =  v(l + T0 /2) e− jnw l e− jnw 0 0T0 /2
dl
0 0
T0 /2
=−e v(t )e− jnw0 t dt

jnp
0

since e jnp =1 for even n, cn =0 for even n




2-2