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

Solutions Manual
to accompany


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


A. Bruce Carlson
fp fp




Rensselaer Polytechnic Institute
fp fp




Paul B. Crilly fp fp




University of Tennessee fp fp




Janet C. Rutledge fp fp




University of Maryland at Baltimore
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,Solutions Manual to accompanyfp fp fp



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-
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Hill Companies, Inc., 1221 Avenue of the Americas,New York, NY 10020. Copyright © The McGraw-
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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 INTRO
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DUCTION TO SIGNALS AND NOISE IN ELECTRICAL COMMUNICATION, provided such reproductions bear copyrightnotice, but ma
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y not be reproduced in any other form or for any other purpose without the prior written consent of The McGraw-
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Hill Companies, Inc., including, but not limited to, in any network or other electronic storage or transmission, or broadcast for distance learn
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ing.

www.mhhe.com

,Chapter 2 fp




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




dt =Ae jf
fp
fp fp
fp fp fp fp fp
fp fp fp
f p fp f p fp



T0 −T0 /2
fp
fp
fp

0 otherwise

2.1-2




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



Acos (−A)cos sin
fp fp fp fp fp
fp fp





f p fp fp fp fp fp fp fp




T 
n
0 T T /4 fpfp

0
fp T pn fp 2
0
fpf p
0 0


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




argcn fp
0 180 0 180


2.1-3




c0 = 2v(t) =A / 2
f p f p f p fp fp




c =
f p T /2  2At fp 2pnt A 0fp A fp fp fp fp




n   T0 
T0 0 
A − cos
dt = sinp n − (cosp n −1)
fp




 T0 pn (p n)2
fp



fp fp
fp fp fp



fp
f p
fp fp




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


2.1-4




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



Acos
fp fp f p



(cont.)
T
fpf p fp fp




0
fpfp
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

fp fp





fp fp fp f p fp fp fp fp fp fp fp fp




cn = dt=
f p fp fp
fpfpf p
0
Acos cos  0
+ 0

fp f p f p
f p




T0 f p f p f p
T0 T0 T0 4(p −p n)/T0 f p
f p fp fp fp 4(p +pn ) /T0
fp fp fp
0
A
0

= sinc(1−n)+sinc(1+n) A/2 n =1
fp fp


fp fp fp fp fp fp fp fp fp




=
2 0 otherwise
f p




2.1-5




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



Asin (1−cosp n)
fp f p
f p




T 
f p fp f p fp fp fp f p fp fp




n 0 fpf p T pn fp


0 0


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




argcn fp
−90 −90 −90

2.1-6




c0 = v(t) =0
2
+p n )2t /T 
T
f p f p f p




c =−j 2A sin(p −p n ) 2t /T0 sin(p
fp



2p t 2pnt
f p fpfp


T /2 0f p
Asin sin dt =− j  − 0 
fp fp f p fp fp fp fp fp fp fp fp fpfp
f p fp fp fp fp fp fp
fpf p




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




n
f p fp fp fp fp


0
0 0 0
0
fpfp


0 0
 0
A m jA/2 n=1
fpf p




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


fp fp fp fp fp fp





2  0 otherwise

2.1-71
c = T0 /2
f p
− jnw0t
fp
T0
fp fp
fp − jnw0t fp





f
p




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

T 0/ 2
fpfp
fpf p fp




T0 /2

T0
v(t)e −jnw0tdt =  v(l + T0 /2)e− jnw l e− jnw
fp fp

0T0fp/2fp
where dl
fpfpfpfpfpf p

fp
fp fp 0fp f p fp fp



T /2
fp fp fp



0
fpfp fp
0
T0 /2
=−e jnp v(t)e− jnw0tdt

fp
fp
fpfpfpfpf p fp fp
fp
fp fp



0

since ejnp =1 for even n, cn =0 for even n fp f p f p fp fp
fpf p
f p fp fp




2-2