Application of the nonlinear methods in pneumocardiogram signals

Abstract

In this work, the pneumocardiogram signals of nine rats were analysed by scale index, Boltzmann Gibbs entropy and maximum Lyapunov exponents. The scale index method, based on wavelet transform, was proposed for determining the degree of aperiodicity and chaos. It means that the scale index parameter is close to zero when the signal is periodic and has a value between zero and one when the signal is aperiodic. A new entropy calculation method by normalized inner scalogram was suggested very recently. In this work, we also used this method for the first time in an empirical data. We compared the both methods with maximum Lyapunov exponents and observed that using together the scale index and the entropy calculation method by normalized inner scalogram increases the reliability of the pneumocardiogram signal analysis. Thus, the analysis of the pneumocardiogram signals by those methods enables to compare periodical and/or nonlinear aspects for further understanding of dynamics of cardiorespiratory system.

Windowed scalogram entropy: wavelet-based tool to analyze the temporal change of entropy of a time series

“…The BGS entropy (20) can be generalized for a continuous scale interval. Let's define the probability density function instead of expression ( 18) as (21) The continuous BGS entropy (20) can be written as ( 22)…”

“…Benefiting from this feature, it is possible to obtain the correct probability distribution of the energy densities in the determined scale interval for the time series recorded from diverse dynamical processes. This method has been successfully used in the entropy measures of different dynamical systems such as the logistic map [20] and Pneumocardiography (PNCG) signals [21]. Nevertheless, this method simply provides an average measure of entropy for the entire time series, and it is independent of the time location.…”

Automated system for weak periodic signal detection based on Duffing oscillator

“…It is used for measuring the degree of non‐periodicity of a signal [21, 22]. One can numerically separate the periodic and non‐periodic states of the Duffing oscillator using the wavelet scale index [23–26]. Hence, the classification of the periodic and non‐periodic signals by the wavelet scale index allows the conventional method to be automated in practice.…”