engleski

COMPLEXITY ESTIMATION OF NONSTATIONARY SIGNALS BY MEANS OF THE RÉNYI ENTROPY

The entropy measure is a well-known tool for estimating the information content of a probability density function. It has been adapted to the (t, f) plane in order to quantify the information content and complexity of individual signals, as well as the concentration and resolution quality of TFDs [1]. The generalized Rényi entropy, when applied to a TFD, acts as an indicator of the number of components present in a given signal. Several important restrictions are assumed: one of the signal components must be known a priori, all components must present equal time and frequency supports in the (t, f) plane, and they need to exhibit similar spectral amplitudes. Since in real-life applications these highly limiting conditions are rarely satisfied [2], the signal information content is generally evaluated with respect to a reference signal, obtaining the information on how many reference signals are required to form the analyzed signal [3]. These limitations have served as a motivation for a generalization of the counting property of the Rényi entropy. Recently, a methodology has been proposed for estimating the instantaneous (local) number of components in a nonstationary multicomponent signal based on the local application of the Rényi entropy counting propriety [4]. The presented estimation avoids the need for prior information on the analyzed signal and puts no limitations on the signal structure. Unlike the classic approaches for estimation of the local number of signal components, which involve counting the peaks in the (t, f) plane at each time instant for as long as the peak amplitude exceeds a fixed threshold, the estimation based on the Short-term Rényi entropy detects a component whenever it locally presents the entropy characteristics of a reference signal. The reference signal is an arbitrarily chosen analytic signal, with constant or variable IF. The applicability of the Short-term Rényi entropy is supported by the fact that the estimated number of components is invariant to the parameters that characterize the selected TFD or the entropy order. When the counting property of the Short- term Rényi entropy is extended to nonstationary signals, important insights on the signal structure (i.e. components crossings and components ending/starting times) are obtained from the features of the entropy-based estimated number of components. The presented approach allows to resolve ambiguities in the case of local decrements of the number of components, and to obtain information on the time locations of components crossings [5]. When this information is combined with the entropy-based estimate of the number of components, a correct estimation of the total and local number of components present in a signal can be made. However, the results obtained by the Short-term Rényi entropy are highly biased by the amplitude ratio of the signal components present in the analyzed time slice of the TFD. Since in engineering applications one deals with real-life signals, being mixtures of dominant and weaker spectral components, a refined algorithm is proposed, especially well-suited to situations of unequal spectral amplitudes. This iterative method exhibits pronounced sensitivity to low energy components, and it is robust to moderate levels of additive noise. Also, the result obtained by the proposed algorithm is an integer valued function *The author is supported by the Croatian Ministry of Science and Education 2 which easies procedures for blind source separation based on &quot ; peak detection and tracking&quot ; techniques. In addition, the information on the time instants of the starts/ends of the signal components allows to estimate the total number of components. This information can turn advantageous from a computational optimization prospective, allowing dynamic memory allocation, and prevention of memory overflow. The main contribution of the presented study consists in proving that the Short-term Rényi entropy can estimate the local number of components in a nonstationary signal, without any prior information on the signal. Other future research directions will include implementation of the information on the local and total number of components, obtained by the Short-term Rényi entropy, in advanced blind source separation methods and clustering algorithms. This would lead to more efficient computing solutions and memory handling. Finally, the Short-term Rényi entropy information can be used in applications for signal denoising as a classifier of the output of the K-means algorithm.

Renyi entropy, complexity

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