gives the convenient result (Note: For -f^ < we would use (-2.^,-111^) 

 in place of (1^,^^)) 



which agrees with the values of Equation (5.2) at the points (Jl^.m .f^) 

 and (-JlQ,-mQ,-f ). Note that there is not general agreement elsewhere. 

 In fact. Equation (4.16) may (and does) give negative values for the 

 approximation of S(J!,,m,f). This is a problem of probe array design and 

 is directly related to the directional resolving power of a probe array, 

 This problem is discussed later in another section. 



Consider the case of a single frequency, fg > 0, real sea with 

 equal wave energy from all directions; i.e., isotropic waves. In this 

 case, assuming the wave equation (Equation (3.1)) holds, we have 



as the two-sided directional power spectrum for such an isotropic wave. 



Since Z = KcosO and m = KsinO, Equation (3.8) can be expressed in 

 polar coordinate form as 





Letting "^ii - ( \'^ ^ Xi ) 



20 



