sm10_8

Prévia do material em texto

Problem 10.8 Show that the integral of the high frequency term in Eq. (10.53) is 
approximately zero. 
 
Solution 
Consider the integral over the period from 0 to T of the high frequency term in 
Eq. (10.53): 
 
( ) ( )
( ) ( )( )
2 2
00
2
2
cos 4 2 ( ) sin 4 2 ( )
2 8
sin 4 2 ( ) sin 2 0
8
4
T TC c
c c
c
c
c
c
c
c
A Af t t dt f t t
f
A f T T
f
A
f
π φ π φπ
π φ φπ
π
+ = +
⎡ ⎤= + −⎣ ⎦
<
∫
 
 
where the first line follows since φ(t) is constant over a symbol interval. By the bandpass 
assumption fc >> 1, so this last line is small. 
 
Excerpts from this work may be reproduced by instructors for distribution on a not-for-profit basis for testing or instructional purposes only 
to students enrolled in courses for which the textbook has been adopted. Any other reproduction or translation of this work beyond that 
permitted by Sections 107 or 108 of the 1976 United States Copyright Act without the permission of the copyright owner is unlawful.