the disturbance covering the whole y,t plane. F(y,t) can be 
applied to each term in any finite partial sum. As the indicated 
limit is approached, the result of the operation by F(y,t) 
can be treated as a filter operation on [ay (ye) ]° in order to 
find the power spectrum at other times and places as the concentra- 
ted disturbance at the source disperses and spreads over the x,y 
plane. 
The problem of the result of the application of F(y,t) toa 
particular term in the partial sum was solved in Chapter 8, apart 
from minor modifications necessitated by the arbitrary phase, 
VC Home P2pe1)* These modifications only serve to complicate 
the algebra in the analysis and the same filter function is ob- 
tained. The end result is FF(x,y,t) as given in equation (8.62). 
This filter function is repeated with modifications in equation 
(9.56). The time variable has been referred to top by a change of 
variables, and the filter is also given as a function of w and 0. 
IGP sey NACE D, and W, are fixed, FF(x,y,t,#,®) can be varied as 
ob? “w 
a function of “ and 6, and the filter properties can then be deter- 
mined. 
The 6-band cutoff points 
The Fresnel filter, FF(x,y,t,#,9), has the disadvantages of 
the corresponding filter given in eauation (7.50) in that it oscil- 
lates rapidly near the quarter power points as a function of # and 
©. It can be approximated as before by the square cutoff filter. 
In the first term given by equation (9.56) the quarter power points 
occur where equations (8.67) and (8.68) are satisfied. With the 
use of equations (8.53), (8.51) and (8.31), equation (8.68) can be 
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