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

Solutions Manual x




to accompany
x




CommunicationSystem x




s
An Introduction to Signals and Noise inEle
x x x x x x x




ctrical Communication
x




Fourth Edition x




A. Bruce Carlson
x x

RensselaerxPolytechnicxInstitute

Paul B. Crilly x x

UniversityxofxTennessee

Janet C. Rutledge x x

UniversityxofxMarylandxatxBaltimore

,SolutionsxManualxtoxaccompany
COMMUNICATIONxSYSTEMS:xANxINTRODUCTIONxTOxSIGNALSxANDxNOISExINxELECTRICALxCOMMUNICATION,xFOU
RTHxEDITION
A.xBRUCExCARLSON,xPAULxB.xCRILLY,xANDxJANETxC.xRUTLEDGE

PublishedxbyxMcGraw-HillxHigherxEducation,xanximprintxofxThexMcGraw-
HillxCompanies,xInc.,x1221xAvenuexofxthexAmericas,xNewxYork,xNYx10020.xCopyrightx©xThexMcGraw-
HillxCompanies,xInc.,x2002,x1986,x1975,x1968.x Allxrightsxreserved.

Thexcontents,xorxpartsxthereof,xmayxbexreproducedxinxprintxformxsolelyxforxclassroomxusexwithxCOMMUNICATIONxSYSTEMS:xANx
INTRODUCTIONxTOxSIGNALSxANDxNOISExINxELExCTRICALxCOMMUNICATION,xprovidedxsuchxreproductionsxbearxcopyrightx
notice,xbutxmayxnotxbexreproducedxinxanyxotherxformxorxforxanyxotherxpurposexwithoutxthexpriorxwrittenxconsentxofxThexMcGraw-
HillxCompanies,xInc.,xincluding,xbutxnotxlimitedxto,xinxanyxnetworkxorxotherxelectronicxstoragexorxtransmission,xorxbroadcastxforxdistan
cexlearning.

www.mhhe.com

,Chapterx2

2.1-1
 
Ae jf Aexjf nxm
cnx 
ejf x dtx Aex sinc(mxxn)x
T0x/2x
j2p x (xmn x)fx tx 0


T0
xT0x /2
0 otherwise
x



2.1-2




2 x 0
c0x v(t) T0x/x4x 2pxnt T0x /2 x 2pxntx 2A x pxn
cx x  Acosx dtx (xA)cosx dtx  sinx

Txx  

n 0 T 




Txx / 4
T pxn 2
x
0
0 0 0


n 0 1 2 3 4 5 6 7
cn 0 2xAx/xp 0 2xAx/x3p 0 2xAx/x5p 0 2xAx/x7p
argxcn 0 180 0 180


2.1-3




c0x x v(t)x A x/2 x
2
cx x T x/2x 2xAtx 2pxnt A A
 
0


n  Ax cos dtx  sinpxnxx 2x (cospxnx1)
T0 0  T0 





T0 pxnx (pxn)
n 0 1 2 3 4 5 6
cn 0.5A 0.2A 0 0.02A 0 0.01A 0
argxcn 0 0 0 0


2.1-4




2 T0x/2 x 2pxtx
cxx x Acosx 0 (cont.)
0
Txx  0 T
0 0

2-1

, 2x xxx Tx /2 2xAxsinxpx pxn  2tx/xT
2pt 2pxnt sinxp pxnx2tx/xT T x/ 2x

0



 x  0x 
0
cnx Acos cos dt  0x
 

T0x x x T0 T0 T0x 4(px pxn)x/xT0 4(p xpxn) /xT0 0
0
xAx

 sinc(1xxn)xxsinc(1xxn) Ax/x2 nx1
x
2 0 otherwise

2.1-5




c0x x v(t)
2 x 0T0x /2 x 2pxnt Ax
cx xjx Asinx dtx xjx (1xcospxn)
Txx 
n
0 T pxn
0 0


n 1 2 3 4 5
cn 2xAx/xp 0 2xAx/x3p 2xAx/x5p
argxcn 90 90 90

2.1-6




c0x x v(t)x 0
2xAxsinxpx pxn  2tx/xT0xx sinx pxn x2tx/xTxx
x2 T0xx/ 2x
cx xj T x / 2x 2p tx 2pxntx
dtx xjx x
0

p Asinx sinx 0
xx 
n 
T0xx 0
T T T 4(px pxn)/ xT 4(p pxn)/ xT 
0 0
0 0 0
0xx 
xAx m jA / 2 nx1
xjx sinc(1nx)xxsinc(1xn) 
x x x



2  0 otherwise

2.1-71
cx x xxT0x /2  jnw0xt
T0
 jnwx0t

n

T0xx 0 v(t)xe dtxxx
Txx
v(t)e dtx
T0x/2 x
v(t)e xjnw0xtxdt 
 v(l  T0 /2)xe e
0xxxxxx xjnwx lx x jnwx T x/2x
where 0
dl
0 0




T 0
x
Txx /x
0
T0x /2x
ex jnpxxxxx v(tx)exjnw0xtxdt
2

0


2-2