The points determined by the circles represent the average 
value of [Apy(#)]° over the band which straddles the point. The 
curve joining the points is simply an aid to the eye since any 
curve can be drawn over each band under study just as long as the 
area under it equals the value which has been determined. Thus 
the true power spectrum can be an extremely irregular function with 
very rapid (even if continuous) fluctuations. Even worse than that 
the power spectrum could have been of the form discussed in Chapter 
10 and the same graph would have been obtained in figure 39. 
To discover if really rapid fluctuations in the power spectrum 
are present, it would be necessary to increase m and the length of 
the record. Thus a 50 minute record and twice as many lags would 
give 60 bands of the w axis instead of 30 with the same reliability. 
A 100 minute record with 120 lags would give four times as many 
values. Would the 120 values (instead of 30) thus determined follow 
the same general curve as shown by the solid line? The question can- 
not be answered until the work is done, (and it is not planned to do 
it), but it is very difficult to think of any physical mechanism which 
would cause the power spectrum to be irregular within any conceivable 
limits of resolution. 
The above process of narrowing the band width and increasing 
the length of the record would also detect any purely sinusoidal com- 
ponent in the record. Thus with greater resolution, a discrete com- 
ponent would produce a sharp narrow spike rising out of the general 
function. The spike could be made as high as desired and as narrow 
as desired, and in the limit it would become infinitely high and in- 
finitesimally wide such that the product of the height and the width 
gL 
