Multiresolution wavelet analysis of noisy signals

Abstract

Multiresolution wavelet analysis (MWA) is one of the mostly used approaches that is applied for fast signal processing. The application of this tool requires the selection of a suitable basis for decomposition of the signal and further characterization of its features at different levels of resolution. A widespread way for this characterization is to compute the standard deviations of detail wavelet-coefficients. This simple approach does not take into account many peculiarities of the sets of decomposition coefficients. In an effort to expand the capabilities of MWA in diagnosing complex dynamics, we intended to perform a more thorough analysis of the decomposition coefficients within the MWA&DFA approach or other measures reflecting the complexity of the probability density function or the features of its ‘‘tails’’. Our analysis was carried out on particular examples of complex dynamics associated with chaotic oscillations. Using noisy sequences of return times into Poincaré sections, we examined how statistics of fluctuations affects the quality of separation between complex motions. This analysis showed that the effectiveness of the conventional MWA method can be improved by taking into account the correlation features of the decomposition coefficients, characterized in terms of the DFA scaling exponents and the excess. Further we illustrate such approach for physiological data sets. We conclude that a more thorough analysis of wavelet-coefficients can improve diagnostics of complex processes, although the effectiveness of different measures may depend on the system under study and the properties of the available datasets.

Speaker

German A. Guyo
Saratov State University
Russia

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