Biomedical Engineering Reference
In-Depth Information
15
×
10
5
10
5
0
30
20
f
(Hz)
1
10
30
25
20
10
15
0
5
0
f
(Hz)
2
(a)
15
×
10
5
10
5
0
30
20
f
(Hz)
1
10
30
25
20
15
0
10
5
0
f
(Hz)
2
(b)
15
×
10
5
10
5
0
30
20
f
(Hz)
1
10
30
20
25
15
0
10
5
0
f
(Hz)
2
(c)
Figure 3.24
Magnitude of bispectra
S
3
(
f
1
,
f
2
) of the EEG segments with cumulants
C
3
(
τ
1
,
τ
2
) depicted
in Figure 3.23 for (a) preictal, (b) ictal, and (c) postictal periods of a seizure. The two-dimensional fre-
quency (
f
1
,
f
2
) domain of the bispectra has units in hertz. Bispectral peaks occur in the neighborhood
of 10 Hz in the ictal period, and at lower frequencies in the preictal and postictal periods.
is typically the case for a system to exist, the analysis of a single observable can pro-
vide information about all related variables to it. The technique of obtaining a state
space representation of a system from a single time series is called state space recon-
struction, or embedding of the time series, and it is the first step for a nonlinear
dynamic analysis of the system under consideration.
A time series is obtained by sampling a single observable of a system usually
with a fixed sampling period
Dt
:
(
)
(
)
s
=
s xn
⋅
t
+ ψ
(3.54)
n
n
where
t n·Dt
and the signal
x
(
t
) is measured through some measurement function
s
and under the influence of some random fluctuation
ψ
n
(measurement noise). An
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