where the various terms are defined in item 1, and the assumptions listed 

 there" hold. Let a2(T'^'^)) be the variance o£ t'^'^^ . Then, 



mg+r 



I 



m=mn+l 



n->°°\ / L \ml m2/ 



"0' 



The probability law of 



.(N) 



m=mQ+l 



converges to a normal probability law with zero mean and unit variance as 

 N tends to infinity. 



Proof: The terms U and V are asymptotically uncorrelated with 

 m m ^ 



each other and with other pairs ( U , V j provided < m < N/2 



and < m' < N/2 (Borgman, 1973). The asymptotic variance of both 



u'-'^-' and V*-^-* is p N At/2 (Borgir.an, 1973). Hence, Uj/N Atp /2 and 

 m m ^m * ' m' ^m 



Vj. ^ /}/N~KvpIT2 have unit variance. It follows that: 



mg+r 



Z 



m=mA+l 



mg+r 



'0" 



as N -^ °° (Freund, 1971) . 



After substitution for U and V in terms of Y , T*-^-* can be 



expressed as: 





a(T^^)) ,ti^a(TfN)) 



I ^0- {\, cos 2.Hfp . X, 



I 



m=mn+l 



2Trm 



m2 



N / 



/p At/2 

 ^m 



99 



