Ogilvie 



o-(oj) 



|H(a))| 



Figure 2 



j I^K 





2 1 — vk 

 „ 2T '^ 



where 



w(kj 



dr 



w(t) 



-=k. 



w(k ) = -w(r) 



dr 



This shows, through the averaging effects of the weights, w^ , that the estimated 

 frequency response is much affected by the variation of phase angle do-(aj)/da) 

 around that particular frequency. This fact was entirely disregarded in the 

 paper by Goodman [4], which treated the confidence limit of the frequency re- 

 sponse. For example, if the k^ has values that are shown in Fig. 3, even if 

 a = 0, and /3 = 



^["(i-)] - 5W„H {If (.-.)) -.H(f.).M, 



and w(k^) is much less than 1. As the result, the estimated frequency response 

 becomes much less than the true value. This has been the reason for the low 

 coherencies obtained in some experiments as already pointed out by Mr. Dalzell 

 and me [5]. As an extreme case, when k > T , 



100 



