Biomedical Engineering Reference
In-Depth Information
4.1.7.3.3 Time-frequency methods
The frequency bands at which the ERD/ERS
effects are observed and ERD/ERS unique temporal and topographic patterns related
to the functional brain activation vary considerably between subjects. In the classical
approach one has to try out a number of possible frequency bands in the search for the
ones that display the most pronounced effects—so called reactive frequency bands.
As was pointed out by [Pfurtscheller, 1999] it is important to examine event-related
changes in signal energy from the broader perspective of the entire time-frequency
plane.
In order to accomplish this, one needs to estimate the energy density of the signal
in the time-frequency space. In the literature many methods were proposed for this
purpose, e.g.:
•
Spectrogram [Makeig, 1993],
•
Bandpass filtering in overlapping bands [Graimann et al., 2002],
•
Scalogram [Tallon-Baudry et al., 1996],
•
Smoothed pseudo Wigner-Ville transform [Lachaux et al., 2000]),
•
Estimate of energy density derived from the matching pursuit (MP) parame-
terization [Durka et al., 2001b],
The mathematical basis, properties, and MATLAB routines to compute the above
mentioned estimators of the energy are described in Sect. 2.4.2. Different estimates
of the time-frequency distribution of signal energy offer different trade-offs between
temporal and spectral resolution. For example, the scalogram has high temporal res-
olution and low frequency resolution at high frequencies, low temporal resolution
and high frequency resolution at low frequencies. The presence of cross-terms in
some of the time-frequency estimators must be taken into account when interpreting
the ERD/ERS in the time-frequency space. In contrast, the matching pursuit (MP)
parameterization theoretically provides optimal time-frequency resolution through-
out the time-frequency plane. Different estimators of energy density were compared
in [Zygierewicz et al., 2005]. The results yielded by different estimators gave com-
patible results, however those obtained by MP procedure provided more detailed
information of the time-frequency structure of the ERD/ERS.
The time frequency estimator of energy density
E
can be used to evaluate
the ERD/ERS in the time-frequency plane in accordance with the general definition
(4.17):
(
t
,
f
)
)=
E
(
t
,
f
)
tr
−
B
(
f
)
ERD
/
ERS
(
t
,
f
(4.23)
B
(
f
)
where
E
(
t
,
f
)
tr
is the energy density at
(
t
,
f
)
averaged across trials, and
B
(
f
)
is the
mean energy of baseline at frequency
f
averaged across trials.
The important question to be answered is: which of the ERD/ERS effects are sig-
nificantly above the fluctuation level? The statistical problem related to that question
is the assessment of significance in the statistical maps (see Sect. 1.5.3.2). In [Durka
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