Solutions manual communication systems carlso

Solutions Manual n




to accompany
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Communication
Systems
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AnIntroductiontoSignalsandNoisein
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ElectricalCommunication
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Fourth Edition n




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




University of Tennessee n n




Janet C. Rutledge n n




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 n




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


n n n n


−T0 /2
T0 n
n
n

0 otherwise

2.1-2




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


Acos (−A)cos sin
n n





n n n n n n n n




T
n
0 T T /4 nn

0
n T pn n 2
0
n n
0 0


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




argcn n
0 180 0 180


2.1-3




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




c = n T /2  2At n 2pnt A 0n A n n n n




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




 T0 pn (p n)2
n



n n
n n n



n
n
n n




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


2.1-4




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


Acos (cont.)
T
n n n n




0
nn
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


n n n n n n n n n n n
n n n




cn = dt=
nn n n n n
0
n
Acos cos  n 0 n

+ 0

n




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




A/2 n=1
n n


n n n n n n n n n




=
2 0 otherwise
n




2.1-5




c0 = v(t)2=0T0 /2 2p nt A
c =− j dt =− j
n n n
n
n n


Asin (1−cosp n)
n





n n n n n n n n n




n
T 0 T pn n n n


0 0


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




argcn n
−90 −90 −90

2.1-6




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

T
c =−j
n
n nn


T /2 2p t 2pnt
dt =− j −
0n
 0 
n n n n n n n n n n n nn
n n n n n n n


Asin sin n n




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


T T T
n n


n n n n n

n
0
0 0 0 0
0
nn n

0 0

m jA/2 n=1
n


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


n n n n n n





2  0 otherwise

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





n




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

T /02 n n n





T0 T0 /2
v(t)e −jnw0tdt =  v(l + T0 /2)e− jnw l e− jnw T /2dl
n n
nnnnn n


where T /2
n
n
n

n n
n 0
n n n n 0 0n n




0
nn n
0
T0 /2
=−e jnp − jnw0 t
 v(t)e
n
n


n
nnnn n

n
n
n
dt
n




0

since ejnp =1 for even n, cn =0 for even nn n n n n
n n
n n n




2-2