zero. The value of F.F.G. is then one fourth. Similarly, the 
value at # = g(t, - D)2x is one fourth. For # outside of 
this range, which is the same range as that of the square cornered 
filter, the Fresnel Filter falls to zero. Inside this range, it 
rises to one rapidly, overshoots and oscillates about one very 
rapidly, and finally settles down to one near the center of the 
band, if x is small. For very, very large x, the filter does not 
achieve the value one at the center of the band. 
To employ the filter in the forecasting diagram, it is only 
necessary to evaluate equation (7.50) for top equal to zero, and 
for various x as a function of uw . Then if the filter is located 
at the same place as the square cornered filter was located in 
the figure, which can be accomplished by setting the lower quarter 
power point at wm = g(t, - D,,)/2Xy the product of the Fresnel 
filter times the power spectrum at the source then gives the power 
spectrum at the point and time of the forecast. 
The Fresnel filter has been applied to the power spectrum 
at the source according to the above rules. The line of dots 
above and below the results for the square cornered filter show 
the envelope of the very rapid oscillations at the edges of the band 
as produced by the Fresnel Filter. Since a wave record is of 
finite duration and since the filter tunes through the power spect- 
rum at the source, these rapid fringe oscillations could be con- 
sidered to cancel themselves out in a twenty minute record and 
the simplest filter to use would probably be a slightly smoothed 
Square cornered filter. 
- 156 - 
