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

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

A. Bruce Carlson
w w


RensselaerwPolytechnicwInstitute

Paul B. Crilly
w w


UniversitywofwTennessee

Janet C. Rutledge
w w


UniversitywofwMarylandwatwBaltimore

,SolutionswManualwtowaccompany
COMMUNICATIONwSYSTEMS:wANwINTRODUCTIONwTOwSIGNALSwANDwNOISEwINwELECTRICALwCOMMUNICATION,wFOURT
HwEDITION
A.wBRUCEwCARLSON,wPAULwB.wCRILLY,wANDwJANETwC.wRUTLEDGE

PublishedwbywMcGraw-HillwHigherwEducation,wanwimprintwofwThewMcGraw-
HillwCompanies,wInc.,w1221wAvenuewofwthewAmericas,wNewwYork,wNYw10020.wCopyrightw©wThewMcGraw-
HillwCompanies,wInc.,w2002,w1986,w1975,w1968.w Allwrightswreserved.

Thewcontents,worwpartswthereof,wmaywbewreproducedwinwprintwformwsolelywforwclassroomwusewwithwCOMMUNICATIONwSY
STEMS:wANwINTRODUCTIONwTOwSIGNALSwANDwNOISEwINwELEwCTRICALwCOMMUNICATION,wprovidedw suchw reproductions
w bearw copyrightwnotice,wbutwmaywnotwbewreproducedwinwanywotherwformworwforwanywotherwpurposewwithoutwthewpriorww
rittenwconsentwofwThewMcGraw-
HillwCompanies,wInc.,wincluding,wbutwnotwlimitedwto,winwanywnetworkworwotherwelectronicwstorageworwtransmission,worwbro
adcastwforwdistancewlearning.

www.mhhe.com

,Chapterw2

2.1-1
Ae j T0/2w Aewj nw m
∫eAe
w
f f
cnw w
j2pw (wm nw)fw 0tw
dtw
jf
w sinc(mw wn)w
T0 0 otherwise
wT0w /
2w



2.1-2




c0w v(t)w 0
2w w 0w Acosw2pwnt 2pwntw 2 A w pwn
T /w4w T0w /2 w
c dtw A)cosw
w dtw sinw
n
T
0 ww T T
T pwn 2
ww/ 4w
0
0 0 0



n 0 1 2 3 4 5 6 7
cn 0 2wAw/w 0 2wAw/w3 0 2wAw/w5 0 2wAw/w7p
p p p
argwc 0 0
n




2.1-3




c0w w v(t)w A w/2 w
2
cw w T w/2w 2wAtw 0 2pwnt A A
Aw co
T0 s
n
T 0

0 dtw sinpwnw w (cospwnw
0
T pwnw (pwn)2w

n 0 1 2 3 4 5 6
cn 0.5A 0.2A 0 0.02A 0 0.01A 0
argwc 0 0 0 0
n




2.1-4


2-1

, 2 2pwtw
cww w
T0w /2 w
Acosw (cont.)

Tww T
0
0
0 0




2-2

, 2wAw sinw pw pwn 2 sinw pwn w2tw
2 tp
2 t pwn
2
www Tw T0w/ 2w
/2 w tw/wT p /wT
cnw dtw
0
0w 0w
A cos cos
T0w w T0 T0 T0w 4(pw pwn)w/w 4(p p n ) /wT0
w w
0
0 T0
A w
w w
sinc(1w wn)w wsinc(1w Aw/w nw
n)
w
2
2 0
w
otherwise

2.1-5




c0w w v(t)
2 w 0
T0w /2 w 2pwnt Aw
cw j
w w Asinw dtw j
w w cospwn)
w
n
Tww 0 T pwn
0 0



n 1 2 3 4 5
cn 2wAw/wp 0 2wAw/w3 2wAw/w5
p p
argwc
n


2.1-6




c0w w v(t)w 0 T0ww/ 2w
2
cw wj
w
T w / 2w 2p tw 2pwntw 2wAw sinw pw pwn 2tw/w pwn w2tw/wTww
T0ww Asin
sinww p sinw dtw j
0
ww 0
w
T T T T 4(pw pwn )/ pwn )/ wT
ww
n w 4(
p
0 T0ww 0 0
0 0 0
mwjAw nw
0ww
A
w w
/w2wjw sinc(1 nw)w wsinc(1 wn ) 1

2  0 otherwise

2.1-7
1
cw w /2w T0w
w
 jnw0wt
T0
 jnww0t

n
T0ww 0 0


2-3

,v ( t)we dtw w
Tww / 2w
v(t )e dtw
T0w/2 w
jnw0w

 v(l  T0 /2)we e w jnww T w/2wdl
0wwwwww wjnww lw
wher v(t )e w
0 0 0

0
t dt
T
e Tww/
w
w
0
T0w /2w
ew jnpwwwww v(tw)e wjnw wtwdt

w2 0

0
jnp
sinc ew w w forweven cnww w forwevenwn
e wn,




2-4

,2.1-8

2 2w 2 2w 2w
Pw w w w2 wcw Af 2w Afwtw sincw fwtw
w w 2 Aftw sinc2wftw
w w w 2w Aftw 2
w ⋯
c w t sinc3 wft
0 n 0 0 0 0 0 0 0
n
1w
w f
wher t 0

e
1 A2w 1 2ww 3w 2
2w1
2ww

fww
nc Pw 1w w2si 4  2sinc 2  2sinc
w 0.23 A
t 16w 4w
PwA w
2
fww 2 2 1 2 w 1 2 3
w 2w 5 2w 3 2w 7w
A2

 2sinc  2sinc  2sinc  2sinc
t1 A2
1
w1w2sinc 4 2 1w 422w 4 2  2sinc 
162ww 4
fww  2sin 0.21A
2t Pw 1 w2si 2
4 c
w
nc 16w


2.1-9
0 nw even
cn  2ww
2
nwodd

pwnw
1
a)w Pw w T0w/w2
2
2 4t w 2 1
w 4wt T
0w /2w
1
dtw
ww
Tww TTww/w2w w 1 w dtw
0
0wwwwwww
0 0www T0 w
0ww 3
4 ww2 w 4 2
www ww 4 2

Pw /wPw
Pww 2wwwso
0.332 w2 w2w
pw2ww  9pw2ww
w w 25pw2ww w


b)wwv (t)w cosw0tw 8 cos3ww0tw 8 cos5ww t
0
8 9pw 25pw
w

pw2 2 2




2.1-10
w nw even
0
cn  wj2 Tw/2 w

pwn nw od
1 d
2-5

, 22ww
2ww22ww 2w
0
a) Pw 1 1 dtw P2 2 w
w w
w
o w s P /wPw 93.3%
T
wwww
/ 2w T www www

0
0
www 3pw
p 5
p


(cont.)




2-6

, 4w 4ww 4ww
b)wwv (tw)w cosw ww tw w90 w ww cosw 3ww tw w90
w w ww cosw 5wwwtw w90
0 0 0
p 3p 5p
4w 4w 4w
w sinw ww tw w w sinw 3w sinw 5ww t
w w t
0
p 0
5p 0

3p




2.1-
2
11 T0ww
dtw 1 nw
t c 1/w
2
Pw
w
1
T0 0
w
T0ww 3
nwww
1 /w2pwn nw 0
wwww
ww
4 w 2 2w
4w
11 1 www1


Pw 2 w 2w w w ⋯w
pwnw w ww  pww
w
  14www 34www
n wwodd 5
 4ww
3

1 1 1 4pw2w 1 1w ww pw2
Thus,ww w w w⋯w ww w
12ww 22w 32w 23ww 4ww 6

2.1- 2w

12 T0w /2w
4tw 1 0 nweven
2
Pw Tww0
w
1 dtw 2
nw odd
T
w
3 cnww
0 (2/wpwn)
0w


1
2 w
ww
www2
ww w1 1 2 1 1 1 1
ww

Pw w 2 2ww w2ww
w
2 2ww 32ww
w ⋯w
3
2w 2pwnw
w w



w n w 4 4pwww 1


1 1 1 pw4w 1 pw4
Thus,www 4ww w 4ww w 4ww w⋯w
1 3 5 2w 24www3w 96

2.2-1
tw / 2w p tw
Vw(wfw)w 2 A cosw cos2pw ftdt
0
tp t p tw
2-7

, sinw tww 2pw f sinw t w 2pw fw w Atw
w
w w
22Aw 2w sinc(wf fwt ) sinc(w
2 pw pwfw 2 p 2pw fw w
ww w
2 wt
w

w
w
t t 

(cont.)




2-8