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where
s
0
=
2
δ
t
is the smallest scale chosen and
δ
j
specifies the width of the wavelet
function. In our case
25, implying that there is a scale resolution of four sub-
octaves per octave [5]. The larger scale is determined by the value of
J
specified in
(3.5), which in our case is
J
δ
j
=
0
.
=
29:
j
−
1
log
2
(
J
=
δ
N
δ
t
/
s
0
)
.
(3.5)
Finally, the
power spectrum
of the WT is defined by the square of coefficients in
(3.1) of the wavelet series as
2
. By adopting the above settings a smooth
wavelet power diagram is constructed as in Fig. 3.3b for the signal in Fig. 3.3a.
W
n
(
s
)
Fig. 3.3: (
a
) A typical normalized EEG signal acquired from a single electrode. (
b
)
The wavelet power spectrum presented as a color-coded picture. Mapped scales to
frequencies are calibrated on the
y
-axis, with the
horizontal dashed lines
indicating
the different frequency bands. The significant regions over the time-scale transform
are indicated by
closed contours
. Power increase and decrease is bounded by
blue
and
red
contours, respectively. The outer elliptical region at the edges of this second
graph indicates the cone of influence in which errors (edge effects) may be apparent
due to the transformation of a finite-length series EEG signal. (
c
) The scalogram
of a selected averaged band (Theta 4-8 Hz) reflecting characteristic EEG activity
while the participant is performing a complex mathematical calculation [14]. The
significance levels are indicated by the
horizontal dashed lines
. PS values greater
above the
upper dashed line
indicate significant increase, whereas PS values below
the
lower dashed line
indicate significant decrease over the expected control power
levels.
