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

Solutions Manual
to accompany
CommunicationSystems
An Introduction to Signals and Noise inElectrical
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
COMMUNICATION SYSTEMS: AN INTRODUCTION TO SIGNALS AND
NOISE IN ELECTRICAL COMMUNICATION, FOURTH EDITION
A. BRUCE CARLSON, PAUL B. CRILLY, AND JANET C. RUTLEDGE

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Companies, Inc., 1221 Avenue of the Americas, New York, NY 10020.
Copyright © The McGraw-Hill Companies, Inc., 2002, 1986, 1975, 1968. All
rights reserved.

The contents, or parts thereof, may be reproduced in print form solely for classroom
use with COMMUNICATION SYSTEMS: AN INTRODUCTION TO SIGNALS
AND NOISE IN ELE CTRICAL COMMUNICATION, provided such reproductions
bear copyright notice, but may not be reproduced in any other form or for any other
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including, but not limited to, in any network or other electronic storage or
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www.mhhe.com

,Chapter 2

2.1-1
T0/2
Ae jf Ae jf n m
cn  ∫
e j2p ( mn )f 0t
dt Ae jf sinc(m  n) 
T0 T0 /2
0 otherwise

2.1-2




c0 v(t)
2 0T 2p nt T0 /2 2p nt 2A pn
c  Acos dt  ( A)cos dt  sin
T  T  T pn 2
n T /4
0
0
0 0 0


n 0 1 2 3 4 5 6 7
cn 0 2A/p 0 2A / 3p 0 2A / 5p 0 2A / 7p
arg cn 0 180 0 180


2.1-3




c0  v(t) A /2
2
c  T /2  2 At  2p nt
0 A A
n
0
A
T0 
cos
T0
dt 
pn
sinp n 
(p n)2
(cosp n 1)
T0 

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


2.1-4




2 T0 /2 2p t
c  Acos 0 (cont.)
0
T 0 T
0 0




2-1

, 2 A sin p p n  2t / T0 sin p p n 2t / T 0
T
2 T /2 2pt 2p nt
cn   Acos cos dt   
0

T0 0 T0 T0 T0  4(p p n) / T0 4(p p n) / T0 0
A
 sinc(1  n)  sinc(1  n) A/ 2 n 1

2 0 otherwise

2.1-5




c0  v(t)
2 0T0 /2 2p nt A
c  j Asin dt  j (1 cosp n)
T 
n
0 T pn
0 0


n 1 2 3 4 5
cn 2A/p 0 2A / 3p 2A / 5p
arg cn 90 90 90

2.1-6




c0  v(t) 0
2 T
c  j T /2 2p t 2p nt 2 A sin p p n  2t /T0 sin p p n  2t / T
sin
0
Asin dt  j   
T T T 4(p p n)/ T 4(p p n)/ T 0
n
T 0

0
A
0 0
m jA / 02  0 0 0
 j sinc(1n )  sinc(1 n)  n 1

2  0 otherwise

2.1-71
c   jnw0 t
T0
 jnw0t

n

T0  0 v(t) e dt  
T
v(t)e dt 
T0 T0 /2
where 
T /2
0
v(t)e  jnw0t dt   v(l  T0 /2) e jnw l e jnw
0
0 0T0 /2
dl
T0 /2
e jnp
v(t)e jnw0 t dt
 0

since e jnp 1 for even n, cn 0 for even n




2-2