Solutions Manual for Communication Systems: An Introduction to Signals and Noise in Electrical Communication, 4th Edition

Solutions Manual
to accompany


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


A. Bruce Carlson
z z

RensselaerzPolytechniczInstitute

Paul B. Crilly
z z

UniversityzofzTennessee

Janet C. Rutledge
z z

UniversityzofzMarylandzatzBaltimore

,SolutionszManualztozaccompany
COMMUNICATIONzSYSTEMS:zANzINTRODUCTIONzTOzSIGNALSzANDzNOISEzINzELECTRICALzCOMMUNICATION,zFOUR
THzEDITION
A.zBRUCEzCARLSON,zPAULzB.zCRILLY,zANDzJANETzC.zRUTLEDGE

PublishedzbyzMcGraw-HillzHigherzEducation,zanzimprintzofzThezMcGraw-
HillzCompanies,zInc.,z1221zAvenuezofzthezAmericas,zNewzYork,zNYz10020.zCopyrightz©zThezMcGraw-
HillzCompanies,zInc.,z2002,z1986,z1975,z1968.z Allzrightszreserved.

Thezcontents,zorzpartszthereof,zmayzbezreproducedzinzprintzformzsolelyzforzclassroomzusezwithzCOMMUNICATIONzSYSTEMS:zANzI
NTRODUCTIONzTOzSIGNALSzANDzNOISEzINzELEzCTRICALzCOMMUNICATION,zprovidedz suchz reproductionszbearz copyrightzno
tice,zbutzmayznotzbezreproducedzinzanyzotherzformzorzforzanyzotherzpurposezwithoutzthezpriorzwrittenzconsentzofzThezMcGraw-
HillzCompanies,zInc.,zincluding,zbutznotzlimitedzto,zinzanyznetworkzorzotherzelectroniczstoragezorztransmission,zorzbroadcastzforzdistance
zlearning.


www.mhhe.com

,Chapterz2

2.1-1
 
Ae jf Aezjf nzm
cnz 
ef z dtz Aez sinc(mzzn)z
T0z/2z
j2p z (zmn z)fz tz j 0


T0
zT0z /2
0 otherwise
z



2.1-2




2 z 0
c0z v(t) T0z/z4z 2pznt T0z /2 z 2pzntz 2A z pzn
cz z  Acosz dtz (zA)cosz dtz  sinz

T0zz 

n 0 T




Tzz/ 4z
0
T pzn 2
0 0


n 0 1 2 3 4 5 6 7
cn 0 2zAz/zp 0 2zAz/z3p 0 2zAz/z5p 0 2zAz/z7p
argzcn 0 180 0 180


2.1-3




c0z z v(t)z A z/2 z
2
cz z 2zAtz 2pznt A A
 
T z/2z 0


n  A
T0 0  T0 
z cos dtz  sinpznzz





(cospznz1)
T0 pznz (pzn)2z
n 0 1 2 3 4 5 6
cn 0.5A 0.2A 0 0.02A 0 0.01A 0
argzcn 0 0 0 0


2.1-4




2 T0z /2 z 2pztz
czz z Acosz 0 (cont.)
T
0
zz 0 T
0 0



2-1

, 2z zzz Tz /2 2zAzsinzpz pzn  2tz/zT
2pt 2pznt sinzp pznz2tz/zT T0z/ 2z

cnz   Acos dtz  0z 
0
cos 0z
 
T0z z z T0 T0 T0z 4(pz pzn)z/zT0 4(p zpzn) /zT0 0
0
zAz

 sinc(1zzn)zzsinc(1zzn) Az/z2 nz1
z
2 0 otherwise

2.1-5




c0z z v(t)
2 z 0T0z /2 z 2pznt Az
cz zjz Asinz dtz zjz (1zcospzn)
Tzz 
n
0 T pzn
0 0


n 1 2 3 4 5
cn 2zAz/zp 0 2zAz/z3p 2zAz/z5p
argzcn 90 90 90

2.1-6




c0z z v(t)z 0
2zAzsinzpz pzn  2tz/zT0zz sinzp pzn z2tz/zTzz
z2 T0zz/ 2z
cz zj T z / 2z 2p tz 2pzntz
dtz zjz zz z 
0
Asinz sinz
n 
T0zz 0
T T T 4(pz pzn)/ zT 4(p pzn)/ zT 0 
0 0
0 0 0
0zz 
zAz mzjAz/z2 nz1
zjz sinc(1nz)zzsinc(1zn) 

2  0 otherwise

2.1-71
cz z zT0z /2z  jnw0zt
T0
 jnwz0t

n

T0zz 0 v(t)ze dtzz z
Tzz
v(t)e dtz
T0z/2 z
v(t)e zjnw0ztzdtz 
 v(l  T0 /2)ze e
0zzzzzz zjnwz lz z jnwz T z/2z
where 0
dl
0 0




T 0
Tzz/z
0
T0z /2z
ez jnpzzzzz v(tz)ezjnw0ztzdt
2

0

since ezjnpz 1z forzevenzn, cnzz0z forzevenzn

2-2