Slight approximation the square cutoff filter is given by equa- 
tion (9.63). The result is then an equation analogous to equa- 
tion (7.45), in which R has been substituted for x. Equations 
similar to equations (7.46), (7.47) and (7.48) would also result 
and remarks similar to those in Chapter 7 could be made about them. 
The @-band width 
From equation (9.58) and (9.60), it is possible to form the 
difference given by 0 TeeE and determine the 6-band width. The 
result is equation (9.64) where A © is the angular width of the 
Square cutoff filter. 
The 6-band width is not of equal width above and below the 
value ©)- This is shown in equations (9.65) and (9.66) which show 
that Ae.) the variation in radians from 8p to 8 (the upper cut- 
off angle), is smaller than Ae, the variation in radians from 
the lower cutoff angle to ®p- 
The square filter for the Gaussian case of a short crested sea 
surface generated by a storm of finite duration D., finite width, 
We» over a fetch of length, F. 
With the realization that the wave systems under study are 
only 3 first approximation to actual wave systems from a storm 
at sea (mainly because of the nature of the functional form of 
F which has been assumed; and not because of the inadequacy of 
the Gaussian Lebesgue Power Integral), it is possible to account 
for the effect of a fetch of finite length. If a wave record is 
observed at a point x = 0, y = 0, (or any value between + W,/2), 
there is of course an ambiguity as to where the waves come from 
= 233n— 
