Ogilvie 

 Coherency y (c) -- ^-—^ -. 1 - ^-^ 



Then 



^^-> =-'/^(-^- i)f[S, 2, 2(n-l)] 



where n is the integer nearest to 



I n = -k 



also F[S, 2, 2(n- 1)] is defined as 



Prob. {F2(„.i) < F[S, 2, 2(n-l)]} = S. 



At w = 0, and 2V2At,F[S, 2, 2(n- 1)] should be replaced by F[S, l, (n- l)]. Ac- 

 cordingly, the confidence band is drawn as 



Prob. {|H(a)) - H(aj)| < R(a)) lH(a)) | 



and 



|Arg [H(aj)] - (j{co)\ < sin'^ R(w)} > S. 



R(co) should be put equal to 1.00 to indicate the relative error greater than 100%, 

 when the value inside the square root of the definition of R(aj) is greater than 1 

 or less than 0. The value S = 0.95 is used usually in our group. When R(w) had 

 the value, 1.00, the estimate of o-(o)) often showed sudden change of magnitude 

 ±7T, which shows ;mreliability of the results. 



The following approximation formula for F-values can be conveniently used 

 for computer application: 



F(2, n, 0.95) = 3.00 + ^^'^^ 



F(l, n, 0.95) = 3.84 + 



n - 1 . 40 



10.00 

 n- 1.40 



Figures 7 through 14 are the examples of the results obtained by this pro- 

 cedure. The cross correlograms of wave-roll and wave-heave in Figs. 7 and 8 

 are the ones where the origin was shifted by 9At and 7At respectively. Corre- 

 lations were computed to very large lag number ±200, however, m, the largest 

 lag number was taken as 90 in the analysis. All windows w^, Wj and W3 were 

 applied to the calculation of the spectra; however, the results came out so close 

 that it is difficult to show on one sheet. Accordingly, in Figs. 7 through 13, only 



106 



