would be equal to the square of the amplitude of the discrete com- 
ponent. 
Thus, to within the resolving power of the analysis which has 
been carried out, there is no proof of the presence of any discrete 
components, nor is there any proof that they are not present. A 
little thought shows that one can never prove either the presence 
or absence of very small power discrete components by taking one fin- 
ite section of a time series since there is always the possibility 
that the function being studied is represented by a sum over a finite 
net such as in Chapter 7 with many more terms than could possibly 
be resolved by the choice of m and N in the numerical analysis. 
The analysis of the pressure record given above has yielded the 
power spectrum of the pressure record. The time has now come to put 
back the high frequency waves (low period) filtered out by the effects 
of depth. The power spectrum of the free surface will be the result. 
The filtering process is not completely reversible because the waves 
with periods below four seconds have been irretrievably lost. Since 
the water is essentially infinitely deep for these low periods, a 
modified application of the results of Chapter 11 could estimate the 
amount of power left out completely. 
It will be assumed that the pressure recorder responds to the 
actual pressure fluctuations at its indicated depth. This statement 
is equivalent to stating that purely sinusoidal pressure fluctuations 
at the depth of the instrument and of equal amplitude but different 
periods are recorded with the same amplitude. 
The procedures are then straightforward and the results of 
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