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relation of these events. We may describe the next step as an attempt to crop up
the most significantly different regions from control to target activity out of the bulk
initial signal (may be either significant power increase or decrease while performing
the requested task compared to the control condition). In fact, this study proposes
a way to derive the so-called
significant PS activity
on significantly activated EEG
time segments, by testing for significance in the wavelet-time domain the “active”
task over the control task (Significant PS - Fig. 3.2 - Step 3). The control task
spectra de-fine the
mean time-averaged wavelet power spectrum
over all subjects
performing the control task, as
P
p
=
1
W
n
(
s
)
2
(
)=(
/
)
,
W
s
1
P
(3.8)
where
p
is the subject index and
W
n
(
is computed as in (3.1) for each subject.
P
is the total number of participants. It should be noticed that all EEG signals are
normalized to zero mean and identity variance. Further rescaling and comparisons
may be performed using each subject's actual signal variance in order to include
subject-specific information. Significant power increase on the “active” task is cal-
culated using the 95% confidence level at each scale by multiplying the control task
spectrum in Equation (3.8) by the 95th percentile value for a chi-squared distributed
variable
s
)
2
. This is justified because the wavelet
power spectrum is derived from the Morlet wavelet in a complex product with the
signal, so that both the squares of the real and the imaginary parts of the result are
being
2
χ
with two degrees of freedom
χ
2
distributed with one degree of freedom each [17, 6]. In a similar manner,
significant power decrease is measured using the lower power limit of 5% confi-
dence level at each scale, by multiplying the control task spectrum in Equation (3.8)
by the 5th percentile value for the chi-squared distributed variable
χ
2
2
. Figure 3.3
depicts one subject's initial normalized EEG signal (Fig. 3.3a) together with its WT
(Fig. 3.3b). The significant regions over the time-scale-transformed domain that
differentiate the two tasks are indicated by the closed contours; red for significantly
increased and blue for decreased activity. Figure 3.3c illustrates another view of the
scalogram focusing on a selected averaged band, i.e., (Theta 4-8 Hz). The signifi-
cance levels in this case are indicated by horizontal dashed lines.
Having derived this significant information, we are now able to form the so-called
significant power spectral
(significant PS) features, which are obtained from the
signal energy over those time- and band-localized regions where apparent significant
differentiation is indicated (contours in Fig. 3.3b). For the computation of these
features, Equation (3.6) is adapted as
χ
m
i
+
1
m
=
m
i
W
m
(
s
)
W
s
t
2
2
=(
1
/
m
)
,
i
=
1
, ··· ,
I
,
(3.9)
where
m
is the total number of time points delimited between the boundaries
m
i
and
m
i
+
1
of all significant regions
I
denoted by each contour in Fig. 3.3b and
i
is the
index of each significant region. Finally, the last step (Fig. 3.2 - Step 4) is actually a
repetition of the statistical testing in the second step on the new feature set. ANOVA
