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11, Effective Period 



The non-block-averaged frequency band corresponding to the 

 centroid of each power spectrum is then calculated from: 



I S (a ) 

 _ ^ n XX n 



a = (4.55) 



Is (o ) 

 ^ XX n 



where Sxx (6) is the auto-spectrum of a transducer signal. This is 

 an estimate of the "effective wave period" during the record as 

 determined by each transducer. 



12. The Directional Fourier Coefficients 



The directional (or angular) Fourier coefficients are 

 calculated for each frequency band using Equations A. 18 through 4.24. 

 The coefficients are taken as the mean of all those calculated with 

 different combinations (or cross-spectra) of operating channels. 

 These angular coefficients, as well as the water surface displacement 

 power spectrum, are block-averaged over a specified number of 

 adjacent frequency bands. Since an ocean wave time series is 

 composed of random functions, the Fourier coefficients of each 

 channel must not be block-averaged before generation of the angular 

 coefficients. The average of a random function exhibits zero 

 correlation with the average of another, so that the angular 

 coefficients must be calculated from the raw cross-spectra terms and 



