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

Solutions Manual
to accompany


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


A. Bruce Carlson
Rensselaer Polytechnic Institute

Paul B. Crilly
University of Tennessee

Janet C. Rutledge
University of Maryland at Baltimore

,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
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 INTROD
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UCTION TO SIGNALS AND NOISE IN ELECTRICAL COMMUNICATION,provided such reproductions bear copyrightnotice, but may n
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ot 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 learnin
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g.

www.mhhe.com

,Chapter 2 st




2.1-1
 
jf Ae jf nm
cn Ae
e sinc(mn) 
T0/2
j2p (mn )f 0t
dt Ae jf
st
st
ts st
st ts st st st
ts ts st
s t st s t st


T0 /2
T0 0 otherwise
ts st
st




2.1-2




2 0
c0 v(t) T0 /4 2pnt T0 /2 2p nt 2A pn
c  dt  dt 
s t s t
st s t st
st st st ts st


Acos (A)cos sin
st s t





s t ts ts st ts st st ts




T0 

n
0 T




T /4 stst

0
st T pn ts 2
sts t
0 0


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




argcn ts
0 180 0 180


2.1-3




c0  v(t) A / 2
2
s t s t s t ts ts




c 
s T /2 
t 2At 2pnt
st A A 0st st ts st st






A   cos
dt  sinpn (cospn1)

st

n
T0 0  T0  st st st st st st



T0 pn (pn)2 st st st
s t




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


2.1-4




2 T0 /2 2p t
c  0
s t
st st s t


Acos (cont.)
T
sts t st st




0
stst
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


ts s t st st ts st st st ts st st
ts st ts




cn  dt 
ststs t s t st ts
0
Acos cos 0
 0

st s t s t
s t




T0 s t s t s t
0 T0 T0 T0 4(p p n)/T0 s t
s t st ts ts 4(p pn ) /T0
ts ts ts
0
A 
 sinc(1n)sinc(1n) A/2 n1
ts ts


ts ts ts ts ts ts ts ts st





2 0 otherwise
s t




2.1-5




c0  v(t)20T0 /2 2pnt A
c  j dt  j
st st st
s t
st s t


Asin (1cosp n)
s t





s t st s t st st st s t ts st




n
T 0 T pn sts t ts


0 0


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




argcn ts
90 90 90

2.1-6




c0  v(t) 0
2A sinp p n  2t /T0 sinp p n 2t/T 
s t s t s t


2 T
c j
st
s t stst


T 2p t 2pnt 0s t / 2s t
dt j   
st ts st ts st ts s t st st ts ts st ts st ts stst
s t ts


Asin sin sts t




 4(p p n)/ T 4(p p n)/ T 0 
st st st st st st


T T T
sts t


s t st ts st ts

n
T 0 0
0 
stst




m jA/2
0 0 0 0 sts t 0
A
j sinc(1n)sinc(1n )  n1
st ts ts
ts ts


st st ts ts ts ts st





2  0 otherwise

2.1-71
c  T0 /2
s t
 jnw0t
ts
T0
st st
ts  jnw0t ts





ts




n
T0 0 v(t)e dt  v(t)e
stst
ts st st dt ts

T /02 sts t st





T
v(t)e jnw0tdt  
T0

 v(l  T0 /2)e e
 jnw l  jnw T /2
st ts
stststststs t


where T /2
ts dl
ts
st

st ts
st 0
ts s t st 0 0st
st st



stst st
0 0
T0 /2
e jnp  jnw0t
 v(t)e
ts
st


st
ststststs t

ts
st
ts
dt
ts




0

since ejnp 1 for evenn, cn 0 for even n ts s t s t st st
sts t
s t st st




2-2