When two measurements are in phase , such as the heave and slope of a wave orbital 

 following buoy, they can be related by the coincident spectrum, i.e., C-, 2 . Since 

 the n-s and the e-w slopes of both the wave orbital following buoy and the wave 

 slope following buoy are also in phase, they can be related by the coincident 

 spectrum, i.e., C 2 o. As expressed by Ewing and Pitt , the normalized Fourier 

 coefficients can be determined from the following equations 



a Q = C n (2a) 



a-L = C 12 //C 11 (C 22 + C 33 ) (2b) 



b 1 = C 13 //C 11 (C 22 + C 33 )' (2c) 



a 2 = ( C 22 _C 33^^ C 22 + C 33^ ^ 2d ^ 



b 2 = 2C 23 /(C 22 + C 33 ) (2e) 



where C^ is the coincident spectrum of an auto spectrum 



C^- is the coincident spectrum of a cross spectrum 



1 refers to heave 



2 refers to north-south slope 

 and 3 refers to east-west slope 



The first coefficient, ag , is the wave energy spectral density. The mean direction 

 the waves are coming from is defined by 



y = tan" 1 (b 1 /a 1 ) (3) 



The significant wave height and significant period are defined as, 



(y 1/3 = «°o) V2 <■>> 



m l 



