of an ordinary Fourier spectrum to study the propagation of a 
finite wave group and to study the propagation of various finite 
wave trains. The accidental fact that the spectrum was connected 
with a normal probability (or Gaussian) curve should not be con- 
fused with the very important fact that values of 7 (t) at 
greatly separated values of t, chosen at random, are distributed 
according to the Gaussian probability law. 
Wave record analysis 
Any given wave record as a function of time can be considered 
to be a short piece of an infinitely long record which is one 
of the infinite number of records possible from the integration 
of the Gaussian case of the Lebesgue Power Integral. The problem 
is to find (An ))*, given the short piece of the record. This 
problem is the basic problem of wave analysis if it is general- 
ized to permit representation of short crested waves. The function, 
CG a. and the extension to what corresponds to it for a short 
crested sea surface can only be estimated because of the finite 
length of the record. The longer the record, the more reliable 
the estimate of (a(m))°. The problem of wave analysis will 
be considered for the short crested case in a later chapter. 
Wave forecast models for wave systems with infinitely long 
crests in the Gaussian case 
Consider again equation (7.1), for the Gaussian case. 
Instead of %(t), equation (7.35) employs 7 (0,t) to point out 
the fact that the function is presumably known only at the origin 
of the x coordinate system. Assume that (AC pw ))® is known. 
This wave record as a function of time at the origin never started 
SWS 
