Wavelet q-extropies of fractal signals

Abstract

The standard Tsallis and R´enyi extropies of parameter q are extended to the time-scale domain, and closed-form expressions of these extropies for fractal signals of parameter α are obtained. Wavelet extropy planes are computed for a range of the fractality parameter α and signal length N which allows an unveiling of the properties and potential applications of wavelet q-extropies on fractals. Results indicate that wavelet q-extropies allow accurate description of the complexities of fractals since they are maximum for completely random samples, decreasing for correlated fractals and increasing for uncorrelated fractals. Unlike Shannon and R´enyi, Tsallis extropies display a constant region, symmetric on α, which allows classification of fractals based on a simple heuristic of wavelet extropy values. Finally, the application of wavelet Tsallis extropies allows the differentiation of electroencephalogram (EEG) times series from volunteers with eyes closed and eyes open.