But it is relatively easy to determine the effect of F(t) on a 
simple trigonometric term of angular frequency, w Ont1* The result 
of operating on any partial sum with F(t) can consequently be found 
very easily. In the limit, then, the complete effect on the inte- 
gral can be determined by considering yw to be a variable. 
One of the many possible F(t) is given by equation (7.40) 
where Do is the duration of the waves. The wave record builds 
up to full amplitude instantaneously at t = O and dies out instant- 
aneously at t = Die When this particular F(t) is applied to one 
of the terms in the partial sum indicated in equation (7.39), it 
can be seen that the problem is essentially the same problem that 
was solved in Chapter 5 except for a shift in the time axis. If 
F(t) is applied to 7 (t), the result is no longer a stationary pro- 
cess, but a sample taken during a time interval in which F(t) is 
essentially one would yield a power spectrum upon analysis indis- 
tinguishable from the one obtainable from the unmodified function, 
1(t). 
In Chapter 5 it was found that the forward edge and the rear 
edge of the wave train advanced with the group velocity, and that 
the edges were modulated by Fresnel Integrals. For the moment, 
although it is physically impossible, assume that the amplitude 
of the train is either zero or one at any x and that the Fresnel 
modulation effects are not present. 
The square cornered or sharp cutoff filter 
The time, te» required for the forward edge of the wave train 
to reach the point x for a fixed # is given by equation (7.41). 
The rear edge, t,, passes De seconds later. Consequently, for a 
- ALSyiL as ] 
