TM No, 377 



where L = i l j) 2 5 ooe is J and m is the number of lags used* 



The energy estimate of the spectrum function (equation (lll-l8)) is 

 approximated "by: 





|(,vcos^)cos^ A ( L ) +A (o) 



... 



L=> 



', (Hl-Jil) 



where 



and 



<^<H 



K* 0,1,1,- 



M 



(111-42) 



Here K represents the index number of a particular frequency (analogous to the 

 L for lags) It is used to index both the lag number for the auto~covariance 

 and covariance functions, and also to index the frequency scalej i e 05 the K 

 frequency is defined from equation (lXJ-6) as: 



K 



2MAT 



M 



(in-43) 



The value of V(o) is the variance of n(t); hence, because of equation (lll°2l), 

 60= l/2 in equation (lll-4l)„ The term (l + cos ^) in equation (111-41) is a 

 type of filter or lag window, which slowly varies from 2 at L = to 1 at L « m. 

 ■This filter provides an inherent correction for gross truncation errors in the 

 series records OJU t , ai a , M% ~ ~ - Uy, qmo yj k , fcvj. > ^3 - - - U/^ . 

 The cross~covariance functions are indicated ass 



CCO = 





for the even or positive par; of the covariance, and 



0(L)- 



1 



(fh-i.) 



» w-ijw 



for the odd or negative part o:. the covariance. 



(III-W-) 



(III-45) 



60 



