Multiresolution wavelet analysis of noisy datasets with different measures for decomposition coefficients

The possibility of distinguishing between different types of complex oscillations using datasets contaminated with measurement noise is studied based on multiresolution wavelet analysis (MWA). Unlike the conventional approach, which characterizes the differences in terms of standard deviations of detail wavelet coefficients at independent resolution levels, we consider ways to improve the separation between complex motions by applying several measures for the decomposition coefficients. We show that MWA's capabilities in diagnosing dynamics can be expanded by applying detrended fluctuation analysis (DFA) to sets of detail wavelet coefficients or by computing the excess of the probability density function of these sets. (C) 2021 Elsevier B.V. All rights reserved.