61^ - 



then averaged. Similarly, the directional estimates obtained from 

 Equations A. 52, A. 53, and A. 54 are block-averaged. 



13. Block-Averaging 



The stability of the generated spectra is enhanced by 

 block-averaging over adjacent frequency bands. If the water surface 

 displacements are assumed to be Gaussian, the Fourier coefficient 

 spectral estimates are distributed according to the chi-square 

 distribution with two degrees of freedom. The block-averaged, or 

 smoothed, Fourier coefficient spectral estimates are represented by 

 the chi-square distribution with the number of degrees of freedom 

 equal to two times the number of adjacent frequencies averaged 

 (Borgman, 1972) . When the analysis program operates upon records from 

 computer simulation or a controlled laboratory environment, each 

 spectral estimate is considered separately; that is, there is no 

 block-averaging. This is equivalent to two degrees of freedom and is 

 done to retain the highest resolution possible for the narrow spectra 

 and shorter time records generated in simulation and the laboratory. 

 When the program operates upon a record from the ocean environment, 

 each signal is block-averaged over four to eight adjacent spectral 

 frequencies to yield eight to sixteen degrees of freedom 

 respectively. It is assumed that the frequency resolution thereby 

 lost in the block-averaged analysis of the ocean's broader spectra is 

 balanced by the increased stability of the record. 



