Correction of filter for the finite time of observation 
At the point, x, and at the time, top» an observation for 
some finite time must be made in order to obtain a wave record 
from which an observed power spectrum can be obtained in order 
to compare it with the forecasted power spectrum for verification 
purposes. If the observed record is too short, the measured power 
Spectrum will be inaccurate. If the observed record is fairly 
long, the square filter will tune through part of thew axis during 
the time required for the observation. The measured power spect- 
rum will be more accurate, but the forecasted spectrum must be 
corrected for the effect of the finite time of observation. 
If the wave record is observed at the point x, from the time 
ee By) /2UBO) as) Mae Ne) S top + tm /2, the smoothed filter 
. can be computed by averaging the square filter given by equation 
(7.60) over the time, ty. The smoothed filter is then given by 
equation (7.61) and it has the shape of a trapezoid. 
In figure 16, for the other forecasted spectra indicated in 
the other curves of the figure, the effect of the trapezoidal 
figure given by equation (7.61) is shown by the heavy curves. The 
Square filter is shown by the dashed curves. The appropriate 
Fresnel Filters have been eliminated because the fringe effects 
appear to be unrealistic. A ty of one hour has been chosen. 
Note the varying width of the spectrum as top increases. 
Other smoother filters 
The three filters which have just been described are not too 
realistic for the practical purpose of developing an easily applied 
wave forecasting theory. Probably an F(t) which rose smoothly 
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