Nächste Seite: DFG Projekt: Das dynamische
Aufwärts: Effiziente WaveletAlgorithmen
Vorherige Seite: BMFTProjekt: Bilddatenkompression mit WaveletMethoden
Inhalt
M. Ende, P. Maaß , G. MayerKress^{4}(Finanziert mit Mitteln der DFG)
The basic goal of signal processing is to extract some desired information from a
given set of measured data.
Amongst the most powerful tools are timefrequency or timescalerepresentations
of the signal. They can be obtained e.g. by WignerVille, Gabor
or wavelet transforms. Both types of representation
aim at transforming and displaying the given data in such a way, that (in
the case of a onedimensional signal) a dominant value at , resp.
at , reflects the presence of a
significant detail at time with local
frequency , resp. with size .
The present investigation intends to highlight the power of wavelet transfroms for
the detection of significant structures or unexpected events in EEG signals.
The data under consideration was taken from an experiment,
it consists of EEG measurements from various people which were exposed to different acoustic sequences.
We will demonstrate the use of wavelet methods by analyzing the EEG measurement of
five people which resulted from the sequence ``periodic, melody''.
Abbildung:
EEG measurements, Fz electrodes, subjects c01104 and c01107

A local extremum of at therefore indicates a significant structure of size at time . In the case of
the Morletwavelet this can moreover be interpretate as the existence of a localized oscillation with frequency
at time
, hence in the following example, where EEG signals were sampled at a rate of
256 Hz, a local maximum at corresponds to a physical frequency of
.
Abbildung:
The indicator function for subjects c01104 and c01107.
Subject c01104 reacts strongly near , subject c01107 shows no
reaction.

Hence we display with a fine discretization for ,
see Figure (3.8, left).
According to



(3.1) 
we search for local extrema which account for a localization in time of the
significant reactions, Figure (3.8, right).
Hence simple thresholding was performed on three electrodes (Fz, Cz, Pz)
of person c01104.
Abbildung:
The wavelettransform of the Fzmeasurement of subject c01104 zoomed to
the intervall (left), the most significant events after thresholding
are marked in the plane (right). We erased a certain region around
each detected event since a local extremum spreads over some area.

Nächste Seite: DFG Projekt: Das dynamische
Aufwärts: Effiziente WaveletAlgorithmen
Vorherige Seite: BMFTProjekt: Bilddatenkompression mit WaveletMethoden
Inhalt
Udo Schwarz
20060918