Solutions Manual to accompany Communication Systems An Introduction to Signals and Noise in Electrical Communication Fourth Edition

Solutions Manual a




to accompany
a




Communication
Systems
a




An Introduction to Signalsand Noise in
a a a a a a




Electrical Communication
a a




Fourth Edition a




A. Bruce Carlson
a a


Rensselaer Polytechnic Institute
a a




Paul B. Crilly a a


University of Tennessee a a




Janet C. Rutledgea a


University of Maryland at Baltimore
a a a a

,Solutions aManual ato aaccompany
COMMUNICATION aSYSTEMS: aAN aINTRODUCTION aTO aSIGNALS aAND aNOISE aIN aELECTRICAL aCOMMUNICATION,
aFOURTH a EDITION

A. aBRUCE aCARLSON, aPAUL aB. aCRILLY, aAND aJANET aC. aRUTLEDGE

Published aby aMcGraw-Hill aHigher aEducation, aan aimprint aof aThe aMcGraw-Hill aCompanies, aInc., a1221 aAvenue aof
athe aAmericas,aNew aYork, aNY a10020. aCopyright a© a The a McGraw-Hill aCompanies, aInc., a2002, a1986, a1975, a1968.

a All arights areserved.


The acontents, aor aparts athereof, amay abe areproduced ain aprint aform asolely afor aclassroom ause awith aCOMMUNICATION
aSYSTEMS: aAN aINTRODUCTION aTO aSIGNALS aAND aNOISE aIN aELEaCTRICAL a COMMUNICATION, aprovided a such

a reproductions a bear a copyrightanotice, abut amay anot abe a reproduced ain aany aother aform aor afor aany aother apurpose awithout athe
aprior awritten aconsent aof aThe a McGraw-Hill aCompanies, aInc., aincluding, abut anot alimited ato, ain aany anetwork aor aother

aelectronic astorage aor atransmission, aor abroadcast afor adistance a learning.


www.mhhe.com

,Chapter a2

2.1-1
jf Ae n a=m
cn a =Ae
+e=Ae
T0a/2a
j2p a ( am−n a)f a 0t a jf
a jf dt
sinc(ma−an) a=
a
a a

− aT0
T0
a /2 a
0 otherwise

2.1-2




c0 a v(t) aT=0 / a4 a 2p T0 a /2 a 2p ant a 2A a p an
c2 a = ant 0 a
dt a = sin a
dt a+Acos a (−aA)cos a

a

n
a
T
0 a
T
a/ 4 a
T a
0
T p an 2
0 0 0


n 0 1 2 3 4 5 6 7
cn 0 2aAa/ap 0 2aAa/a3p 0 2aAa/a5p 0 2aAa/ a7p
argacn 0 180 0 180


2.1-3




c0 a = a v(t) a =A a/2 a
c2 a = T a/2 2aAt a 2p ant A A
a
0


  T0  −
a
A cos
dt a = sinp an a− a (cosp an a−1)
a
n
T0 0   T0 p an a (p an)2 a




n 0 1 2 3 4 5 6
cn 0.5A 0.2A 0 0.02A 0 0.01A 0
argacn 0 0 0 0


2.1-4




2 T0 a/2 a 2p at
a a a=a
c=0 Acos a (cont.)
T a a
0
0 T
0 0

2-1

, 2a /2a aa 2pt 2p ant 2aA asin a(p a −p an ) 2t a/ sin a(p +p an)a2t a/aT T a/ 2 a

0
aT
aT


 dt a= 
0
cn Acos cos 0 a
+ 0 a
a=

T0 a
T0 T0 T0 4(p a −p an) a/ 4(p +ap an) /aT0 0
a 
0 aT0
a a

= sinc(1a−an)a+ asinc(1a+an) Aa/a2
aAa
n a=1
= a
2  0 otherwise

2.1-5




c0 a = a v(t) a =0
2 T0 /2 a 2p ant A
c a =− aj a dt a =− aj
a a
Asin a (1−acosp an)
T a a
a

n 0 T p an
0 0


n 1 2 3 4 5
cn 2aAa/ap 0 2aAa/a3p 2aAa/a5p
argacn −90 −90 −90

2.1-6




c0 a = a v(t) a =0
2aA asin a(p a −p an ) 2t a/aT0 a +p an )a2t a/aT a a
T0 a a/ 2 a
ac2 a =− aj 2p t a 2p ant a
a(p
T a/ 2 a
dt a =− aj a
0

sinAsin a sin a 0
a
−a a a 
T an)/ aT4(p a −p 4(p +p an)/ aT
n

0 T0a
T T
0 0 0 a
0
a
0 0
a
 m jA / 2
=− aj a sinc(1−na) a−asinc(1+an) =
aAa a a a n
a=1


2  0 otherwise

2.1-7
ca = a1  a
− jnw0 at
a /2Ta0 − jnw a0t
T0


n

T0aa0 v(t)ae dt a+ a
T0 a a / 2 a
v(t)e dta
T0 a/2 a
v(t)e −ajnw0 at  v(l + T0 /2)ae− ajnwa l a e− a jnw a T a/2 adl
0 a a a a a a
where 0 0 0



dt
T 0
T
a
a
a =
0
T /2 a
=−e v(ta)e− ajnw0 at adt

jnp a a a a a 0 a
a/ a2 a
0
2-2