Windowed Scalogram Entropy: Wavelet-Based Tool to Analyze the Temporal Change of Entropy of a Time Series

Abstract

In this paper, we propose a new entropy calculation method to observe the temporal change of the entropy of dynamical systems. The proposed entropy calculation method is based on the windowed scalogram which has been introduced recently. Therefore, we name this new method "windowed scalogram entropy." With this method, we can show the evolution of the Boltzmann-Gibbs-Shannon entropy over time using the probability distribution obtained by the normalized windowed scalogram. Before applying the method to time series with complex dynamics, we test the reliability of the method on some well-defined signals. Then, we employ seismic signals and pneumocardiogram signals to demonstrate the effectiveness of the method in the analysis of empirical data. We also compare the method with the windowed scale index and the sample entropy. It is observed that the windowed scalogram entropy is successful in analyzing the evolution of the entropy of seismic signals and pneumocardiogram signals over time. We understand that the windowed scalogram entropy can be used to observe the evolution of the entropy of nonlinear dynamical time series obtained in diverse fields.