We have from Equation (3.2) that 



S(K.e.f.) =S(K,e-ir.-f.) 



If we think in terms of fg > 



s'(K.e.f.) = sS(K.e,t) (7.U) 



We are assuming that the wave number relation of Equation (3.1) holds. 

 Thus Figure 3 is applicable, and we can write the one-sided spectral 

 density as 



S7K,e,O=SQ'(0,t)cf(K-K,) 



This allows us to write, — co^T»^-*"*o , 

 •Tf «o 



P *(^ ,X K) ^W^^ («.<^.)«f{K -K.)Exp[uir Kb cos(e - ni^K^K Ae 



-It 



u>HtRfc i(K-Kj = [ 



P'^CXXi^s fa(0,ik^P&2.1tK,Dcosfe-<l)i]K.(i9 



-tr 



(7.15) 



We have reduced the problem to finding [a(e,fQ • K 1. 

 From Equation (7.15) we see that 



where P(fo) is the power spectral density of frequency f . For better 

 comparison of cases where ^ifj) = ^(Sq)) |f-t | '^ [fgl. it is convenient 

 to express a(e,fQ) in a normalized form 



A(e,fo) = a(e,fo)K^ 



35 



