Information Technology Reference
In-Depth Information
As noted before, there exists a concrete relationship between each scale and an
equivalent set of Fourier frequencies, often known as
pse
udo
f requencies
[10]. For
the Morlet wavelet used this relationship is
f
ω
0
+
√
2
+
ω
0
=
, which in our case
4π
s
(
. In this study the power spectra is
classified in six sequential frequency bands that are coarsely mapped to the scales
tabulated in Table 3.1.
ω
0
=
6); this gives a value of
f
=
1
/
(
1
.
03
s
)
Table 3.1: Frequency bands - scale set mapping
Band
Frequency
Scale
Theta (
θ
)
4-8
21, 22, 23, 24
Alpha1 (
α
1
)
8-10
20
Alpha2 (
α
2
)
10-13
18, 19
Beta (
β
)
13-30
14, 15, 16, 17
Gamma1 (
γ
1
)
30-45
11, 12, 13
Gamma2 (
γ
2
)
45-90
7, 8, 9, 10
The first stage of our fe
atu
re extraction method is based on capturing the
time-
averaged power spectrum W
n
2
f
or
each electrode and scale, which is computed by
2
averaging the power spectrum
W
n
over time:
N
−
1
n
=
0
W
n
(
s
)
W
n
2
2
(
s
)=(
1
/
N
)
.
(3.6)
Further averaging in scale is performed, in order to map a single f
eat
ure per fre-
quency band of interest. Thus, the
scale-averaged power spectrum W
n
2
is defined
(
)
as the weighted sum of the wavelet power spectrum
over scales
s
j
1
to
s
j
2
within each frequency band, with scale correspondences defined in Table 3.1.
Based on these definitions, the average power over time and frequency band is
obtained as
W
n
s
j
=
j
1
W
n
(
s
j
)
j
2
s
j
,
2
W
s
,
n
=(
δ
j
/
δ
t
/
C
δ
)
/
(3.7)
where
C
δ
is a constant scale-independent factor used for the exact reconstruction
of a
function from its wavelet transform (for the Morlet wavelet it equals to
0.776) [17]. Once the average PS for each of the studied EEG bands is calculated
for each EEG channel and task, we have a high number feature vectors (bands x
channels) per task (class), representing each participant (subject), which is actu-
ally the time-scale-averaged PS (Global PS - Fig. 3.2 - Step 1) over the band of
interest.
δ
(
·
)
