311 



The energy spectra were calculated by means of the following relation: 

 ♦ (f) = / R(t) cos2Trft dt . (11) 



The scheme for evaluating the integral in Eq. (ll) for a finite record is 

 given by Blackman and Tukey, (1958). However, instead of the usual technique 

 of "hanning, " it was preferred to obtain a suitable lag window by multiplying 

 the function R(t) by: 



g(T) = (1 + cos ^ ) , (12) 



m 



where Tj^^ for our data is 3 •5- The fading function g(T) l^a-s the advantage 

 of suppressing the periodic component in the autocorrelation function at 

 large lags without removing any information at short lags . An example of 

 the faded autocorrelation R'(t) (=Rg) corresponding to the curve of R(t) 

 Is shown in Figure I3. 



The spectrum corresponding to the faded autocorrelation R'(t) in 

 Figure 13 is shown in Figure ik. Note that the tendency toward periodicity 

 in the wave train also is indicated in this spectrum. Higher harmonics of 

 the frequency fjjj for which the energy is maximum appear as indicated in this 

 Figure . If the waves were perfectly periodic, the idealized spectnam based 

 on the R(t) curve would develop as spikes of infinite height at n 

 multiples of fjj^. However, because the waves are not truly periodic, and 

 because of the random components which exist in the signal, the spectrum 

 actually takes the bumpy shape indicated in Figure 1^+. 



_ Typical values of fj„ are shown with corresponding values of l/P and 

 c^gA in Table II. Because of the narrowness of the region containing 

 most of the energy in the spectra for wind generated waves in the channel, 

 these three frequencies are approximately equal. Thus, for practical 



