- m-3 - 



spectrum of the water surface displacement is then as Equation A. 46: 



2 



S^,(-)=|- (4.A6) 



and the energy spectra of the water surface slopes are as Equations 

 4.47 and 4.48: 



S (a) = ^k^ cos^e (^.^7) 



n n 8 



X X 



2 

 S (a) = ^k^ sin^e (4.48) 



Y Y 



Since wavenumber increases with wave frequency, energy leaked into 

 the higher frequency differential pressure bands is enhanced in the 

 generation of the water surface slope spectrum relative to the 

 displacement spectrum. It is for this reason that the frequency 

 bands of greatest energy are selected for directional analysis from 

 the water surface displacement spectrum. (Spectral leakage is the 

 "spilling" of energy from the frequencies that are actually present 

 in the record to other frequencies. It occurs naturally in the 

 analysis of a finite length of record due to the inability of the FFT 

 to exactly resolve the spectral content of a time record on the 

 frequency axis.) 



