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

Solutions Manual
to accompany

Communication
Systems
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

Published by McGraw-Hill Higher Education, an imprint of The McGraw-Hill 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 ELECTRICAL
COMMUNICATION, provided such reproductions bear copyrightnotice, 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., including, but not limited to, in any network or other electronic storage or transmission, or broadcast
for distance learning.

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