bution would be recognizably non-Gaussian. After a sufficient 
number of lags, the autocorrelation function would settle down to 
the form of a pure coSine wave with an amplitude equal to one half 
of the original power. The autocorrelation function could not 
possibly -become small like the one shown in figure 38. 
The lower cumulative power distribution function shows five 
small but still discrete jumps in E(w). Again there would be a 
term of the form of equation (7.7), but now in addition there would 
be five pure sine waves present at 20/T,, 2n/T., 2n/T 35 2r/T, and 
2n/T x. (Let the phases be fixed by defining ~ (yu) at these points.) 
It would be quite difficult to detect these five pure sine waves by 
autocorrelating the record. However after enough lags, they would 
be all that remains of the record. If the record were truly station- 
ary, in fact, the discrete components would still show up upon cor- 
relation of a record, say, 30 minutes long, with another record, 
say 30 minutes long, taken several hours later. 
Final conclusions of the autocorrelation function 
Thus by analogy to the above comments, the autocorrelation 
function of the record studied in figure 38 proves that there is 
not one pure sine wave present with an amplitude squared equal to 
25% to 50 % (or greater) of the total average square of the record. 
It is not proved that there is no pure sine wave present with, say, 
an amplitude squared equal to 1% or .1% of the total average square 
of the record. 
In the derivation of the theory of previous chapters, it has 
been assumed that wave records are essentially pure noise. The most 
powerful argument in favor of this assumption lies in computed power 
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