Multiresolution wavelet analysis of transient processes

Abstract

Analysis of complex systems based on experimental data is mainly carried out for nearly stationary time series produced, e.g., by systems with slowly changing parameters, if their variation throughout the analyzed segments is treated as insignificant. Consideration of such data sets allows the use of a wide range of standard and special signal processing tools, assuming that the amount of data is sufficient to quantify signal properties with the required accuracy and reliably diagnose the state of the system.

Studying of complex systems for diagnostic purposes is not always limited to stationary dynamics. For example, important information about physiological systems can be obtained when they operate under conditions different from the baseline behavior. Changing the state of the system with subsequent restoration of dynamics is applied to study adaptive capabilities. Due to this, the responses caused by functional tests, stresses, and other factors are often more informative than the purely stationary dynamics of such systems.

In this study, we analyze how transitions between different types of complex oscillatory behavior can be quantified based on multiresolution wavelet analysis (MWA). This mathematical tool is currently widely applied to solve many scientific and technical problems, and the processing of nonstationary signals is one from them. The purpose of this study is to analyze the applicability of MWA for determining transitions between system states and answer the question about the possibility of reducing the amount of data to determine inter-state transitions.

This work was supported by the Russian Science Foundation (Agreement 19-12-00037).

Speaker

German A. Guyo
Saratov State University
Russia

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