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

SolutionsManual r




to accompany
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Communication
Systems
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AnIntroductiontoSignalsandNoisein
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ElectricalCommunication
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Fourth Edition r




A. Bruce Carlson
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Rensselaer Polytechnic Institute
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Paul B. Crilly r r




University of Tennessee r r




Janet C.Rutledge r r




University of Maryland at Baltimore
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,Solutions Manual to accompany
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COMMUNICATION SYSTEMS: AN INTRODUCTION TO SIGNALS AND NOISE IN ELECTRICAL COMMUNICATION,FOURTH
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EDITION
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A. BRUCE CARLSON, PAUL B. CRILLY, AND JANET C. RUTLEDGE
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Published by McGraw-Hill Higher Education, an imprint of The McGraw-Hill Companies, Inc., 1221 Avenue of the Americas,
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New York, NY 10020. Copyright © The McGraw-Hill Companies, Inc., 2002, 1986, 1975, 1968. All rights reserved.
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The contents, or parts thereof, may be reproduced in print form solely for classroom use with COMMUNICATION SYSTEMS: AN
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INTRODUCTION TO SIGNALS AND NOISE IN ELECTRICAL COMMUNICATION,provided such reproductions bear copyrightnotice,
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but may not be reproduced in any other form or for any other purpose without the prior written consent of The McGraw-Hill Companies, Inc.,
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including, but not limited to, in any network or other electronic storage or transmission, or broadcast for distance learning.
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www.mhhe.com

,Chapter 2 r




2.1-1
jf Ae jf n=m
cn = Ae sinc(m−n) =
+e
T0/2
j2p (m−n )f 0t
dt =Ae
r
r
r
r r r r r jf r r r
r


r r r r


−T0 /2
T0 r
r
r

0 otherwise

2.1-2




2 =0
c0 v(t) T0 /4 2pnt T0 /2 2p nt 2A pn
c = dt + dt =
r r r r r
r r r r r


Acos (−A)cos sin
r r





r r r r r r r r




T
n
0 T T /4rr

0
r T pn
r 2
0
r r
0 0


n 0 1 2 3 4 5 6 7
cn 0 2A/p r r r 0 2A/3p
r r r 0 2A/5p
r r r 0 2A/7p r r r




argcn r
0 180 0 180


2.1-3




c0 = 2v(t) =A / 2
r r r r r




c = r T /2  2At r 2pnt A 0rA r r r r




n   T0 
T0 0 
A − cos
dt = sinpn− (cospn−1)
r




 T0 pn (pn)2
r



r r
r r r



r
r
r r




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


2.1-4




2 T0 /2 2p t
c = =0
r
r r r


Acos (cont.)
T
r r r r




0
rr
0 T
0 0




2-1

, 2 2pt 2pnt 2Asin(p −p n ) 2t /T sin(p +p n)2t /T T
T /2


r r r r r r r r r r r
r r r




cn = dt=
rr r r r r
0
r
Acos cos  r 0 r

+ 0 r



T0 r r r
0 T0 T0 T0 4(p −p n)/T0 r r r r 4(p +pn ) /T0
r r r
0
A 
= sinc(1−n)+sinc(1+n)
r




A/2 n=1
r r


r r r r r r r r r




=
2 0 otherwise
r




2.1-5




c0 = v(t)2=0T0 /2 2pnt A
c =− j dt =− j
r r r
r
r r


Asin (1−cosp n)
r





r r r r r r r r r




n
T 0 T pn r r r


0 0


n 1 2 3 4 5
cn 2A/p r r r 0 2A/3p r r r 2A/5p r r r




argcn r
−90 −90 −90

2.1-6




c0 = v(t) =0
2Asin(p −p n ) 2t /T0 sin(p +p n )2t/T 
2
r r r

T
c =−j
r
r rr


T /2 2p t 2pnt
dt =−j −
0r
 0 
r r r r r r r r r r r rr
r r r r r r r


Asin sin r r




 4(p −p n)/ T 4(p +p n)/ T
r r r r r r


T T T
r r


r r r r r

n
T 0
m jA/2 0  0
rr


0 0 0 0 r r 0
A
=−j sinc(1−n)−sinc(1+n ) = n=1
r r r
r r


r r r r r r r





2  0 otherwise

2.1-71
c = T0 /2
r
− jnw0t r
T0
r r
r − jnw0t r





r




n
T0 0 v(t)e dt + v(t)e
rr
r r r dt r

T /02 r r r





T0 T0 /2


− jnw l − jnw T /2
v(t)e −jnw0tdt = v(l + T0 /2)e
r r
r r r rr r


where T /2
r
r
r

r e dl r
r 0
r r r 0 0r
r r




0
rr r
0
T0 /2
=−e jnp − jnw0t
 v(t)e
r
r


r
rrrr r

r
r
r
dt
r




0

since ejnp =1 for evenn, r r r r r cn =0 for even n r r
r r r




2-2