to accompany
CommunicationSystems
An Introduction to Signals and
Noise in Electrical Communication
Fourth Edition
A. Bruce Carlson
T T
Rensselaer Polytechnic Institute
T T
Paul B. Crilly T T
University of Tennessee
T T
Janet C. Rutledge
T T
University of Maryland at Baltimore
T T T T
,SolutionsTManualTtoTaccompany
COMMUNICATIONTSYSTEMS:TANTINTRODUCTIONTTOTSIGNALSTANDTNOISETINTELECTRICALTCOMMUNICATION,TFOURTHTEDI
TION
A.TBRUCETCARLSON,TPAULTB.TCRILLY,TANDTJANETTC.TRUTLEDGE
PublishedTbyTMcGraw-HillTHigherTEducation,TanTimprintTofTTheTMcGraw-
HillTCompanies,TInc.,T1221TAvenueTofTtheTAmericas,TNewTYork,TNYT10020.TCopyrightT©TTheTMcGraw-
HillTCompanies,TInc.,T2002,T1986,T1975,T1968.T AllTrightsTreserved.
TheTcontents,TorTpartsTthereof,TmayTbeTreproducedTinTprintTformTsolelyTforTclassroomTuseTwithTCOMMUNICATIONTSYSTEMS:T
ANTINTRODUCTIONTTOTSIGNALSTANDTNOISETINTELETCTRICALTCOMMUNICATION,TprovidedT suchT reproductionsT bearTcopyrig
htTnotice,TbutTmayTnotTbeTreproducedTinTanyTotherTformTorTforTanyTotherTpurposeTwithoutTtheTpriorTwrittenTconsentTofTTheTM
cGraw-
HillTCompanies,TInc.,Tincluding,TbutTnotTlimitedTto,TinTanyTnetworkTorTotherTelectronicTstorageTorTtransmission,TorTbroadcastTfo
rTdistanceTlearning.
www.mhhe.com
,ChapterT2
2.1-1
Ae j T0T/2T AeTjf nT m
cnT
f
∫ee j2pT (Tm nT)fT 0tT
Tjf
T
dtT A sinc(mT Tn)T
T0 0 otherwise
TT0T /2
T
2.1-2
2 T 0
c0T v(t) T0T/T4T 2pTnt T0T /2 T 2pTntT 2 A T pTn
cT T
T
Acos T dt T A)cos T dtT sinT
n
TTT
0 T T
T pTn 2
TT/ 4T
0
0 0 0
n 0 1 2 3 4 5 6 7
cn 0 2TAT/T 0 2TAT/T3p 0 2TAT/T5p 0 2TAT/T7p
p
argTc 0 0
n
2.1-3
c0T T v(t)T A T/2 T
2
cT T T0T/2T 2TAtT 2pTnt A A
AT co
T0 s
n
T 0
0 dtT sinpTnT T (cospTnT
0 T pTnT (pTn)2T
n 0 1 2 3 4 5 6
cn 0.5A 0.2A 0 0.02A 0 0.01A 0
argTc 0 0 0 0
n
2.1-4
2-1
, 2 2pTtT
cTT T
T0T /2 T
Acos (cont.)
0 T
TTT T
0
0
0 0
2-2