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BELL SYSTEM TECHNICAL JOURNAL 



(A2-1) 



mined by the second moments of the variables. Here we state these 

 moments. Some of the moments have already been given in Sections 3.7 

 and 3.8 of Reference A. For the sake of completeness we shall also give 

 them here. The new results given below are derived in much the same way 

 as those given in Reference A. 

 Let 



hn = {lirT f wif)(f-fXdf 

 Jo 



^0 = / wif) df = xf/o 

 Jo 



g= f w{f)cos2ir{f- fdrdf 

 Jo 



h= f wif) sin 2T{f-f,)Tdf 

 Jo 



and let g', g^\ h\ h" denote the first and second derivatives of g and h with 

 respect to r. For example, 



g' = -2t [ w{f)(f - U) sin lirif - f,)r df 

 Jo 



Incidentally, in many of our cases w(f) is assumed to be symmetrical about 

 fq. This introduces considerable simplification because bi, bs, 65, • * • , 

 A, h', h" ^ reduce to zero. 



The following table gives values of bnS and g for two cases of frequent 

 occurrence 



w{f) 

 bo 



h 

 g 



\l/oe 



-2CTffT)2 



{irT)-^Wo sin ir(fb - fa)r 



If we write 7^, /«, I'c for /c(/), l'e{t), l'c\t), where the primes denote differ- 

 *• Section 2.9 of Reference A. 



