Biomedical Engineering Reference
In-Depth Information
x
1
(
t
)
x
2
(
t
)
x
3
(
t
)
x
4
(
t
)
x
5
(
t
)
x
6
(
t
)
Random data ensemble
25
t
1
t
1
+
20
15
10
5
0
1
61
121
181
241
301
361
Time window
FIGURE 7.1
:
Random data ensemble. Values at an instant of time are taken across channels
require the selection of a specific time (
t
1
). Each function's value at
t
would be summed
and divided by
N
(where
N
is the number of functions) to determine the ensemble
average, where the subscript of
x
denotes a separate channel or function as in (7.7).
[
x
1
(
t
1
)
+
x
2
(
t
1
)
+
x
3
(
t
1
)
+·····+
x
N
(
t
1
)]
x
(
t
1
)
=
(7.7)
N
Accordingly, a random process is stationary if the ensemble's averages are inde-
pendent of time (referred to as
time invariant
) at which the group averages are computed,
and if time averages are independent of functions making up this group. Thus, from the
ensemble point of view, a stationary random process is one in which the statistics derived
from observations on the ensemble members at any two distinct instants of time are the
same (Fig. 7.1).
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