N.B.C., be so weak that it is drowned out audibly by static and 
tube noise. Also suppose that a long record of the voltage graphed 
as a function of time is available. The noise can be described by 
an integral similar to, say, equation (7.1). The chime would be 
the fundamental and harmonics of a pure sine wave. An autocorre- 
lation of the record would cancel out the noise, and eventually the 
oscillation due to the sine waves would be all that is left. The 
discrete components correspond to jumps in the cumulative power 
density such as in the first examples in Chapter 7, and the noise 
yields a continuous increase between the jumps. 
If the signal is very weak, many autocorrelations must be made 
and the weak oscillation cannot be detected until the autocorrelation 
of the noise has gone nearly to zero. If the signal is strong, not 
so many lags must be taken in order that it become visible as an 
oscillation in the autocorrelation function. 
The cumulative power distribution functions for the case with 
eee 
cyclic components 
Figure 42 shows two cumulative power distribution functions 
which illustrate the problems connected with the analysis of wave 
records. The first contains an easily recognizable cyclic component. 
The second contains many small cyclic components. 
The upper one shows a discrete jump in E(p# ) at 20/74. Let 
Y(p) at ps 2r/T, be 1/4. The jump has about half of the power of 
the total record. Given this form for E(#), then equation (7.1) 
would consist in part of a limiting form like equation (7.7) plus 
jump in the record). With such a pure sine wave present, the distri- 
102 
