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5. Directional Spectra Smoothing 



The analysis results of six data sets from the DPG over a 

 four day period are presented in Appendix A. The analysis was 

 carried out using the absolute pressure gauge and differential gauges 

 dP2 and dP3. 



The smoothed directional spectra of the six peak energy bands 

 are illustrated for each data set. In the development of these 

 results, the directional spectra is expressed as the partial Fourier 

 series in terms of the wave direction B as in Equation A. 14: 



N N 



S(o,e) = W a (o) + y W a COS ne + y W b sin nO 

 o o ^, n n ^^ n n 



n=l n=l 



where N=2. This is smoothed by the weighting function 



|cos^|(e' - 6) (6.6) 



such that w^j = 1 , w^ = 2/3, and Wg = 1/6. Such smoothing eliminates 

 negative energy side-lobes in the directional spectra by imposing an 

 always-positive function of the same angular frequency upon the 

 directional distribution (Longuet-Higgins , Cartwright and Smith, 

 1963) . The function 



B cos^ be (6.7) 



