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BELL SYSTEM TECHNICAL JOURNAL 



there is equality among subscripts so that the terms become hi^h-^ or 

 hj^ the integration gives {h?y or A^, respectively. However, if such 

 equality does not exist, or if one of the subscripts is zero or w + 1, the 

 integration gives zero. By integrating term by term in the manner 

 above indicated, adding the results, and finally thereafter putting 

 r = m and s = m, the following result is obtained: 



EJ -^ (1 - Bcos ct>yn¥ + n^ - 1 - 2(n^ + n - 2)B cos <f> 



+ 2{n - \)B^ cos 20 + {n^ + 4n - 6)B^ cos ^ 



+ \ H (6w — 6m)B^"' cos- m<i> \ 



- 8 I Y. {n - m - D^^'^+i cos { {m + 1)0} cos m0 1 



+ 2 I I^ (w - w - l)52'»+2cos [{m + 2)0) cosm0 1 W. (31) 



If the distribution of the lis is assumed to be a normal distribution, 

 then: 



¥ = 3(^2)2. (32) 



Making this substitution and subtracting {EcrY gives: 



■tLcr yJ-icr) 



3n - 1 - Sin - ^)B cos + 2(w - 1)^2 ^qs 20 



+ WJ52 C0S2 + ] Z! (6» — 6m)52m (,Qg2 ^0 I 



-8|E(w-m- i)52-+i (^ 



cos { (2m + 1)0} COS 



+ 2 Z (^i-?w- l)-5' 



2 ' 2 



, /cos { (2m + 2)0} COS 20 



)} 



h^\ (33) 



When n is large, it is permissible to use the assumption that m has <» 

 for its upper limit in the above summations. It is likewise permissible 

 to neglect terms in the result which do not contain the factor n. 

 Accordingly, 



(EcrY = 



3+^2 cos2 + 2 



+ 4 



(I - B cos 0)2 

 1 - j52 



(I + B cos 0) 



1 + ^2 ^ 25 COS 



nh"^. (34) 



