Biomedical Engineering Reference
In-Depth Information
φ
xy
(
t
) esti-
mated using (4.10) for the three examples of Figure 4.1. It is clear that the phase dif-
ferences of example B are much more stable than the one of the other two examples.
The values of phase synchronization for the three examples are shown in Table 4.1
and are in agreement with the general tendency found with the other measures; that
is, Sync
B
>
Figure 4.4 shows the time evolution of the (1:1) phase differences
Sync
C
. Given that with using the Hilbert transform, we can
extract an instantaneous phase for each signal, (the same applies to the wavelet
transform) we can see how phase synchronization varies with time, as shown in the
Sync
A
>
60
Example A
Example B
40
Example C
20
0
−
20
−
40
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
Time (sec)
A
B
C
150
150
150
100
100
100
50
50
50
0
0
0
−
pi
−
pi
−
pi
+
pi
+
pi
+
pi
0
0
0
γ
H
1
0.8
0.6
0.4
0.2
0
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
Time (sec)
Figure 4.4
(Top) (1:1) phase difference for the three examples of Figure 4.1. (Middle) Correspond-
ing distribution of the phase differences. (Bottom) Time evolution of the phase synchronization
index.
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