OFFICIAL SOLUTIONS MANUAL FOR COMMUNICATION SYSTEMS BY CARLSON, CRILLY & RUTLEDGE (4TH EDITION)

SolutionsmManualmtomaccompany
COMMUNICATIONmSYSTEMS:mANmINTRODUCTIONmTOmSIGNALSmANDmNOISEmINmELECTRICALmCOMMUNICA
TION,mFOURTHmEDITION
A.mBRUCEmCARLSON,mPAULmB.mCRILLY,mANDmJANETmC.mRUTLEDGE

PublishedmbymMcGraw-HillmHighermEducation,manmimprintmofmThemMcGraw-
HillmCompanies,mInc.,m1221mAvenuemofmthemAmericas,mNewmYork,mNYm 10020.m Copyrightm©mThemMcGraw-
HillmCompanies,mInc.,m2002,m1986,m1975,m1968.m Allmrightsmreserved.

Themcontents,mormpartsmthereof,mmaymbemreproducedminmprintmformmsolelymformclassroommusemwithm COMMUNICATIONmSYS
TEMS:mANmINTRODUCTIONmTOmSIGNALSmANDmNOISEmINmELEmCTRICALmCOMMUNICATION,mprovidedmsuchmreproduc
tionsmbearmcopyrightmnotice,mbutmmaymnotmbemreproducedminmanymothermformmormformanymothermpurposemwithoutmthempriormw
rittenmconsentmofmThemMcGraw-
Hillm Companies,mInc.,mincluding,mbutmnotmlimitedmto,minmanymnetworkmormothermelectronicmstoragemormtransmission,mormbroad
castmformdistancem learning.

www.mhhe.com

,Chapterm2

2.1-1  
Aejϕ
 Aemj nmm
cnm

Tm/
emj2πjϕm(mmnm)fm tmdtm
0
m2m
0 ϕ
Aem sinc(mmn)m
T0
T0m /
0 otherwise
2m


2.1-2




2m Tm0m0
c0m v(t) /m4m m2πnt T0m/2 m 2πntm 2Am πn
cm  Acosm dtmm (A)cosm dtm sinm
Tm T T πn 2
n


0
T
mm

/m4m
0
0 0 0


n 0 1 2 3 4 5 6 7
cn 0 2mAm/mπ 0 2mAm/m3π 0 2mAm/m5π 0 2mAm/m7π
argmcn 0 180 0 180


2.1-3




2
cm  T m/2m 2mAtm 2πnt A A

0

n
Tm 0  A m  cos m dtm sinπn m 2m (cosπmnm1)

T T πn
0  0m  0 (πmn)

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


2.1-4




2-1

, 2 T0m/2 m
cm  Acosm
2πmtm (cont.)
0
Tm
0
0 T
0 0




2-2

, 2/2 mm m Tm 2mAmsinmπmπmn2t
2πt 2πnt sinmπmπmn2tm/ T m/2m 0




cnm  0 Acos cos m/mT mT

dtm  0m

0m

T T T T  4(π
mπmn)m/mT0
 4(πmπn)/mT0 0
0 0m m
Am A / 2mn 1
 sinc(1mn)msinc(1mn)m
0 0 0m m m


m
2  0 otherwise

2.1-5




2 T0m/2m 2πnt Am
cm jm Asinm dtmjm (1cosπmn)
Tm
n
0 T πn
0 0


n 1 2 3 4 5
cn 2mAm/mπ 0 2mAm/m3π 2mAm/m5π
argmcn 90 90 90

2.1-6




2mAmsinmπmπmn2t
mm/mT0sinmπmπmn
T0m /2m
2 2πtm m2πntm
T0m/2m 2tm/mTm 
cnm j dtmjm m
Tm
m m m
Asin sinm 4(πmπmn)/mT
4(πmπmn)/
m m 0
0 T T T
mT
0 0 0
0 0 0
0m 
mAm mmjAm/m2 nm1
jm sinc(1nm)msinc(1n)m

2 m 0 otherwise

2.1-71
cm  2mT0m / jnω0mt
T0
jnω0t

n 0 v(t)me dtmTm0 /m2m v(t)e dtm
T0m

T0
v(t)ejnω0mtmdtm  T m/2 v(λmTm/2)mejnω0λmejnω0/mT20m
m dλ

0
where
T
m m /0m2 
0
0
T0m /m2m
emjnπm v(tm)ejnω0mtmdt

0
sincem emjnπm1m formevenmn,m cm 0m formevenmn
n




2-3