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Sec. 6–1 Some Basic Definitions 417
x (t, E 1 )
0
t
x (t, E 2 )
0
t
x (t, E 3 )
0
t
x (t, E 4 )
0
t
Figure 6–2
Sample functions of a binary random process.
This definition implies that if a stationary process of order N is translated in time, then
the Nth-order statistics do not change. Furthermore, the N-dimensional PDF depends on N-1
time differences t 2 - t 1 , t 3 - t 1 ,.. . , t N - t 1 since t 0 could be chosen to be -t 1 .
Example 6–2 FIRST-ORDER STATIONARITY
Examine a random process x(t) to determine whether it is first-order stationary. From Eq. (6–3),
the requirement for first-order stationarity is that the first-order PDF not be a function of time. Let
the random process be
x(t) = A sin (v 0 t + u 0 )
(6–4)