which defines the integral. 
Stationary processes and stationary time series 
The first three examples given in Plate XIX and the 
Gaussian case of the Lebesgue Power Integral are all specific 
examples of stationary processes. A stationary process is simply 
a function of time, say (t), such that the essential proper- 
ties of the function are not altered by the substitution of 
_t +h for t in the functional representation. Substitution of 
t + h for t in the first three examples simply changes the phase 
of the various sinusoidal waves in the function. The power 
spectrum is still the same, and the function is still composed 
of the same sine waves. Similarly, in the Gaussian case, sub- 
stitution of t + h for t simply changes the values of W(p), 
and the function is still an element in the class of all possible 
functions which can be found by the procedure of integration de- 
fined above for a particular E(p). 
A stationary time series can be made from any of these 
functions by giving their values only at separate points; say, 
at ti to» taeeceeths preferably separated by the same length 
of time. The height of the water against a wave pole in suc- 
cessive frames of a motion picture film strip would be a practical 
example. 
Special note 
The Gaussian case of the Lebesgue Power Integral does not 
have to have any special form for E(w). E(p) can be any 
function as long as it is continuous. In previous chapters, 
the normal probability curve has been used as a special example 
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