power to contribute an important part to the total power, then the 
autocorrelation function would not have died down completely and 
there would have been a cosine wave present out at the far end of 
the autocorrelation function. 
If there had been several pure sinusoidal waves present in 
the record, it is possible that by accident they would be in phase 
cancellation at the end of the number of lags shown. Under these 
conditions more lags might show that the autocorrelation function 
would rise to more substantial amplitudes. 
Thus it is proved that this record does not contain one pure sine 
wave of appreciable amplitude. No finite number of lags can prove 
the absence of several discrete sine waves (several can be 3, 5 or 
50). A finite number of lags only makes it more and more unlikely 
that there are some given number of pure sine waves present. With 
more lags, one is more sure that a small number of discrete components 
are not present. 
Although it is possible for there to be several pure sine conm- 
ponents of appreciable amplitude in this record, the autocorrelation 
function seems to contradict the possibility of just a few, say one, 
two, or three. Also the fact that the record is Gaussian, seems to 
suggest that the record is of the form of equation (12.19) although 
again a few pure sine waves of low amplitude plus a superimposed 
Gaussian disturbance would yield an autocorrelation function quite 
Similar to the one obtained, and the sampling procedures of Table 18 
above might not detect any difference. The presence or absence of 
"cyclic" or purely periodic discrete components in wave records in 
general will be discussed in detail later in this chapter. 
86 
