2 percent of the main passband. The result of applying the hanning pro- 
cedure yields the refined spectral density estimates. Further details 
are given in the reference cited in Footnote 4. 
In this method of calculating the power spectrum, error may be 
introduced by aliasing, which is serious because its presence cannot be 
detected in the final result. Aliasing (also known as spectrum folding) 
arises from the fact that the data is taken at discrete time intervals 
At . The highest frequency at which spectral density estimates can be 
made is the Nyquist frequency fy = (at)! If appreciable power is 
present at frequencies greater than f, , they will appear at the fre- 
N 
quencies 
For example, Fig. 6 shows how the aliased spectrum of the form faa will 
appear. Hence, in the design of the experiment, one must insure that the 
upper frequency cutoff of the measuring instruments is less than fy 
Alternately, the data may be lowpass filtered by digital computation before 
the spectrum analysis is performed. An example of aliasing is shown in the 
experimental data taken by BI's in Fig. 9, discussed later. 
Some typical results of the autocorrelation computation are given 
in Fig. 7. For zero delay, the value of the autocorrelation is the vari- 
ance of the record. For the three records shown, this varies by a factor 
of four, which is typical of the range of values obtained for all the units. 
The autocorrelation decreases with delay time at differing rates, reaching 
zero most quickly fo: the second day while remaining large for the third 
day. It is tempting to interpret the autocorrelation in terms of the re- 
sults for known functions. For example, if the time series were composed 
of a set of random numbers, then the autocorrelation should be a delta 
function. Again, if the time series were a cosine function,then the auto- 
4 T. Arase, A Guide to the Usage of Power Spectrum Calculations According 
to the Methods of Tukey (Columbia University, Hudson Laboratories, 1960), 
Technical Memorandum-to-File No. 47. 
siilke 
