Solutions Manual
to accompany
CommunicationSystems
An Introduction to Signals and
Noise in Electrical Communication
Fourth Edition
A. Bruce Carlson
gt gt
RensselaergtPolytechnicgtInstitute
Paul B. Crilly
gt gt
UniversitygtofgtTennessee
Janet C. Rutledge
gt gt
UniversitygtofgtMarylandgtatgtBaltimore
,SolutionsgtManualgttogtaccompany
COMMUNICATIONgtSYSTEMS:gtANgtINTRODUCTIONgtTOgtSIGNALSgtANDgtNOISEgtINgtELECTRICALgtCOMMUNICATION,gtFOU
RTHgtEDITION
A.gtBRUCEgtCARLSON,gtPAULgtB.gtCRILLY,gtANDgtJANETgtC.gtRUTLEDGE
PublishedgtbygtMcGraw-HillgtHighergtEducation,gtangtimprintgtofgtThegtMcGraw-
HillgtCompanies,gtInc.,gt1221gtAvenuegtofgtthegtAmericas,gtNewgtYork,gtNYgt10020.gtCopyrightgt©gtThegtMcGraw-
HillgtCompanies,gtInc.,gt2002,gt1986,gt1975,gt1968.g t Allgtrightsgtreserved.
Thegtcontents,gtorgtpartsgtthereof,gtmaygtbegtreproducedgtingtprintgtformgtsolelygtforgtclassroomgtusegtwithgtCOMMUNICATIO
NgtSYSTEMS:gtANgtINTRODUCTIONgtTOgtSIGNALSgtANDgtNOISEgtINgtELEgtCTRICALgt COMMUNICATION,gtprovidedgt suchgt repr
oductionsgt beargt copyrightgtnotice,gtbutgtmaygtnotgtbegtreproducedgtingtanygtothergtformgtorgtforgtanygtothergtpurposegtwith
outgtthegtpriorgtwrittengtconsentgtofgtThegtMcGraw-
HillgtCompanies,gtInc.,gtincluding,gtbutgtnotgtlimitedgtto,gtingtanygtnetworkgtorgtothergtelectronicgtstoragegtorgttransmission,gto
rgtbroadcastgtforgtdistancegtlearning.
www.mhhe.com
,Chaptergt2
2.1-1
Ae j T0/2ggtt Ae ngt m
cng t
f
∫eg tgtj2pAe
gt (gtm ngt)fgt tg t
gt
jf dt 0
sinc(mgt n)gt
gt
jf
gt
T0 0 otherwise
gtT0g
t /2gt
2.1-2
c0g t v(t)g t T=0
0gt/gt4g t 2pgtn T0g t /2 gt 2pgtntgt 2 A gt pgtn
cg t 2 t
gt
Acosgt
dtgt ( A)cosgt
gt dtg t singt
n
0 Tgtg t T T pgtn 2
Tgtgt/
4gt
0
0 0 0
n 0 1 2 3 4 5 6 7
cn 0 2gtAgt/gt 0 2gtAgt/gt3 0 2gtAgt/gt5 0 2gtAgt/gt7p
p p p
arggtc 0 180 0 18
n 0
2.1-3
c0g t =g t v(t)g t =A gt/ 2 gt
cg tgt2 T gt/2g 2gtAtgt0 2pgtnt A A
t
n
A cos
T 0 gt 0 dtgt sinpgtngt gt (cospgtngt 1)
0 T0 T pgtngt (pgtn)2g t
n 0 1 2 3 4 5 6
cn 0.5A 0.2A 0 0.02A 0 0.01A 0
arggtc 0 0 0 0
n
2.1-4
2-1
, 2 2pgt
ctggtgt t T /2 g t
gt 0gt
Acosgt (cont.)
0
Tgtgt T
0
0
0 0
2-2
to accompany
CommunicationSystems
An Introduction to Signals and
Noise in Electrical Communication
Fourth Edition
A. Bruce Carlson
gt gt
RensselaergtPolytechnicgtInstitute
Paul B. Crilly
gt gt
UniversitygtofgtTennessee
Janet C. Rutledge
gt gt
UniversitygtofgtMarylandgtatgtBaltimore
,SolutionsgtManualgttogtaccompany
COMMUNICATIONgtSYSTEMS:gtANgtINTRODUCTIONgtTOgtSIGNALSgtANDgtNOISEgtINgtELECTRICALgtCOMMUNICATION,gtFOU
RTHgtEDITION
A.gtBRUCEgtCARLSON,gtPAULgtB.gtCRILLY,gtANDgtJANETgtC.gtRUTLEDGE
PublishedgtbygtMcGraw-HillgtHighergtEducation,gtangtimprintgtofgtThegtMcGraw-
HillgtCompanies,gtInc.,gt1221gtAvenuegtofgtthegtAmericas,gtNewgtYork,gtNYgt10020.gtCopyrightgt©gtThegtMcGraw-
HillgtCompanies,gtInc.,gt2002,gt1986,gt1975,gt1968.g t Allgtrightsgtreserved.
Thegtcontents,gtorgtpartsgtthereof,gtmaygtbegtreproducedgtingtprintgtformgtsolelygtforgtclassroomgtusegtwithgtCOMMUNICATIO
NgtSYSTEMS:gtANgtINTRODUCTIONgtTOgtSIGNALSgtANDgtNOISEgtINgtELEgtCTRICALgt COMMUNICATION,gtprovidedgt suchgt repr
oductionsgt beargt copyrightgtnotice,gtbutgtmaygtnotgtbegtreproducedgtingtanygtothergtformgtorgtforgtanygtothergtpurposegtwith
outgtthegtpriorgtwrittengtconsentgtofgtThegtMcGraw-
HillgtCompanies,gtInc.,gtincluding,gtbutgtnotgtlimitedgtto,gtingtanygtnetworkgtorgtothergtelectronicgtstoragegtorgttransmission,gto
rgtbroadcastgtforgtdistancegtlearning.
www.mhhe.com
,Chaptergt2
2.1-1
Ae j T0/2ggtt Ae ngt m
cng t
f
∫eg tgtj2pAe
gt (gtm ngt)fgt tg t
gt
jf dt 0
sinc(mgt n)gt
gt
jf
gt
T0 0 otherwise
gtT0g
t /2gt
2.1-2
c0g t v(t)g t T=0
0gt/gt4g t 2pgtn T0g t /2 gt 2pgtntgt 2 A gt pgtn
cg t 2 t
gt
Acosgt
dtgt ( A)cosgt
gt dtg t singt
n
0 Tgtg t T T pgtn 2
Tgtgt/
4gt
0
0 0 0
n 0 1 2 3 4 5 6 7
cn 0 2gtAgt/gt 0 2gtAgt/gt3 0 2gtAgt/gt5 0 2gtAgt/gt7p
p p p
arggtc 0 180 0 18
n 0
2.1-3
c0g t =g t v(t)g t =A gt/ 2 gt
cg tgt2 T gt/2g 2gtAtgt0 2pgtnt A A
t
n
A cos
T 0 gt 0 dtgt sinpgtngt gt (cospgtngt 1)
0 T0 T pgtngt (pgtn)2g t
n 0 1 2 3 4 5 6
cn 0.5A 0.2A 0 0.02A 0 0.01A 0
arggtc 0 0 0 0
n
2.1-4
2-1
, 2 2pgt
ctggtgt t T /2 g t
gt 0gt
Acosgt (cont.)
0
Tgtgt T
0
0
0 0
2-2
