Analysis of the measured data yield the six cross-spectra as expressed by 



Longuet-Higgins et al. and Ewing and Pitt . Based on Equations (l) and (3), it 

 can "be shown that 



cjf) = / * (2t£) k E(f,e)de 



11 o 



c n n (f ) = / k2 cos2 e E(f,6)d9 



'x ^X O 



c t, n (f) = / k2 sin2e E ( f »e) dl 



V^ o 



.f) = J k(2TTf) 2 cose E(f,e)de 



) (f) = / k(2Trf) 2 sine E(f,e)di 



Illy 



.2tt 



l n _ (f) = / " k 2 sine cose E(f,e)d0 {h) 



n x'y o 



where k is the wave number and C is the co-incident spectrum and Q is the quadrature 

 spectrum of wave surface elevation ( n) and surface slopes (n and ru). By using 

 the following dispersion relation, 



C 



(2lTf) = tanh kd = [ IIS ]V2 (5) 



ek C +C 



S n x n x ryry 



the normalized Fourier coefficients can be estimated, as demonstrated by Ewing and 

 Pitt 21 by 



A, = Q /[C (C + C )] 1/2 (6) 

 l nn x nn n x n x T V T V 



B, = Q /[C (C + C )] 1/ 2 (T) 



1 ^nny' l nn v n x ri x T V T V 



a q = (c - c )/(C + c ) (8) 



2 n x Ti x \y M n x n x lyn^ 



B = 2 C /(C + C ) (9) 



2 n x ny /v n x n x n^' 



