,SolutionsQManualQtoQaccompany
COMMUNICATIONQSYSTEMS:QANQINTRODUCTIONQTOQSIGNALSQANDQNOISEQINQELECTRICALQCOMMUNICATION,
QFOURTHQEDITION
A.QBRUCEQCARLSON,QPAULQB.QCRILLY,QANDQJANETQC.QRUTLEDGE
PublishedQbyQMcGraw-HillQHigherQEducation,QanQimprintQofQTheQMcGraw-
HillQCompanies,QInc.,Q1221QAvenueQofQtheQAmericas,QNewQYork,QNYQ10020.QCopyrightQ©QTheQMc
Graw-HillQCompanies,QInc.,Q2002,Q1986,Q1975,Q1968.Q AllQrightsQreserved.
TheQcontents,QorQpartsQthereof,QmayQbeQreproducedQinQprintQformQsolelyQforQclassroomQuseQwithQCOMM
UNICATIONQSYSTEMS:QANQINTRODUCTIONQTOQSIGNALSQANDQNOISEQINQELEQCTRICALQ COMMUNICATION,Qpro
videdQ suchQ reproductionsQ bearQ copyrightQnotice,QbutQmayQnotQbeQreproducedQinQanyQotherQformQorQfor
QanyQotherQpurposeQwithoutQtheQpriorQwrittenQconsentQofQTheQMcGraw-
HillQCompanies,QInc.,Qincluding,QbutQnotQlimitedQto,QinQanyQnetworkQorQotherQelectronicQstorageQorQtransm
ission,QorQbroadcastQforQdistanceQlearning.
www.mhhe.com
,ChapterQ2
2.1-1
Ae j
T0/2Q
Q
Ae nQ m
∫eQQ Qjf
f
cnQ j2pQ (Qm nQ)fQ 0t
sinc(mQ Qn)Q
dtQ AeQjf
T0 0 otherwise
QT0
Q /2Q
2.1-2
c0Q v(t)QT=0
0Q/Q4Q 2p T0Q /2 Q 2pQntQ 2AQ pQn
cQ 2 Qnt AcosQ
Q dtQ ( QA)cosQ dtQ sinQ
n
0 TQQ T T pQn 2
TQQ
/ 4Q
0
0 0 0
n 0 1 2 3 4 5 6 7
cn 0 2QAQ 0 2QAQ/Q 0 2QAQ/Q 0 2QAQ/Q
/Qp 3p 5p 7p
argQ 0 180 0 18
cn 0
2.1-3
c0Q =Q v(t)Q =A Q/2 Q
cQQ2 T Q/2 2QAt
Q
0
Q
2pQnt A A
n
T AQ cos
0 dtQ sinpQnQ Q (cospQnQ 1)
(pQn)2Q
0
0 T0 T pQnQ
n 0 1 2 3 4 5 6
cn 0.5A 0.2A 0 0.02A 0 0.01A 0
argQ 0 0 0 0
cn
2-1
, 2.1-4
2 2p
cQQQ
tQ QT0Q/2 Q (cont.)
0 AcosQ
TQQ T
0
0
0 0
2-2
COMMUNICATIONQSYSTEMS:QANQINTRODUCTIONQTOQSIGNALSQANDQNOISEQINQELECTRICALQCOMMUNICATION,
QFOURTHQEDITION
A.QBRUCEQCARLSON,QPAULQB.QCRILLY,QANDQJANETQC.QRUTLEDGE
PublishedQbyQMcGraw-HillQHigherQEducation,QanQimprintQofQTheQMcGraw-
HillQCompanies,QInc.,Q1221QAvenueQofQtheQAmericas,QNewQYork,QNYQ10020.QCopyrightQ©QTheQMc
Graw-HillQCompanies,QInc.,Q2002,Q1986,Q1975,Q1968.Q AllQrightsQreserved.
TheQcontents,QorQpartsQthereof,QmayQbeQreproducedQinQprintQformQsolelyQforQclassroomQuseQwithQCOMM
UNICATIONQSYSTEMS:QANQINTRODUCTIONQTOQSIGNALSQANDQNOISEQINQELEQCTRICALQ COMMUNICATION,Qpro
videdQ suchQ reproductionsQ bearQ copyrightQnotice,QbutQmayQnotQbeQreproducedQinQanyQotherQformQorQfor
QanyQotherQpurposeQwithoutQtheQpriorQwrittenQconsentQofQTheQMcGraw-
HillQCompanies,QInc.,Qincluding,QbutQnotQlimitedQto,QinQanyQnetworkQorQotherQelectronicQstorageQorQtransm
ission,QorQbroadcastQforQdistanceQlearning.
www.mhhe.com
,ChapterQ2
2.1-1
Ae j
T0/2Q
Q
Ae nQ m
∫eQQ Qjf
f
cnQ j2pQ (Qm nQ)fQ 0t
sinc(mQ Qn)Q
dtQ AeQjf
T0 0 otherwise
QT0
Q /2Q
2.1-2
c0Q v(t)QT=0
0Q/Q4Q 2p T0Q /2 Q 2pQntQ 2AQ pQn
cQ 2 Qnt AcosQ
Q dtQ ( QA)cosQ dtQ sinQ
n
0 TQQ T T pQn 2
TQQ
/ 4Q
0
0 0 0
n 0 1 2 3 4 5 6 7
cn 0 2QAQ 0 2QAQ/Q 0 2QAQ/Q 0 2QAQ/Q
/Qp 3p 5p 7p
argQ 0 180 0 18
cn 0
2.1-3
c0Q =Q v(t)Q =A Q/2 Q
cQQ2 T Q/2 2QAt
Q
0
Q
2pQnt A A
n
T AQ cos
0 dtQ sinpQnQ Q (cospQnQ 1)
(pQn)2Q
0
0 T0 T pQnQ
n 0 1 2 3 4 5 6
cn 0.5A 0.2A 0 0.02A 0 0.01A 0
argQ 0 0 0 0
cn
2-1
, 2.1-4
2 2p
cQQQ
tQ QT0Q/2 Q (cont.)
0 AcosQ
TQQ T
0
0
0 0
2-2
