Natalia Filimonova (Kiev/Kassel): The method of study of synchronization (coupling) of signals of different nature based on wavelet analysis using Krawtchouk functions

The method of study of synchronization (coupling) of signals of different nature based on wavelet analysis using Krawtchouk functions

Dr. Natalia Filimonova (Kiev/Kassel)

Abstract:
Currently, research interest has shifted from studying stationary signals to their dynamics. The study of synchronization (coupling) of signals of different nature during their dynamics confronts some challenges. One approach is to use a windowed Fourier transform to analyze non-stationary signals. But the Heisenberg uncertainty principle for Fourier makes it impossible to determine time and frequency simultaneously, so it is impossible to determine for some point in time which spectral components are present in the signal. Another approach to investigate the dynamics of impulse signals is the wavelet transform theory. As mother-wavelet we used the Krawtchouk functions. Unfortunately, the uncertainty principle is also true for wavelet analysis, making it challenging to identify the temporal localization of the impulse components in a wide window (for low frequencies). Thus, neither classical Fourier analysis nor wavelet analysis gives us a method of finding the answer to the questions "what?" and "when?". Therefore, we propose to supplement the wavelet analysis by the method of extracting the invariant to the shift features of the signal, which is based on the model of the visual system.
We applied the proposed method to study functional connectivity of the brain. In the first stage, we worked out an adaptive filter on the basis of the wavelet. After the filtration, we built the maps of functional connectivity in different EEG leads and at different frequencies. As a result of the analysis of individual dynamics of synchronization of different brain parts during cognitive load or during the performance of various functional tests, brain connectivity dynamics can be visualized: how quickly specific neural networks are formed, how adequate they are, how stable they are, etc. with different types of lesions of the human brain, including in neurodegenerative diseases such as Alzheimer's disease, Parkinson's disease, dementia of various etiologies and others. This method can provide medical staff with objective visualized information about the individual's brain connectivity and monitor the effectiveness of treatment and rehabilitation procedures.

Mit freundlichen Grüßen,
Prof. Dr. Elfriede Friedmann (AG AAM)