@article{Pacheco2025, 
author = {Julio César Ramírez Pacheco and Joel Antonio Trejo-Sánchez and Luis Rizo-Domínguez},
title = {The shifted wavelet    (  q  ,      q    ′    )-entropy and the classification of stationary fractal signals},
year = {2025},
journal = {Networks and Heterogeneous Media},
volume = {20},
number = {1},
pages = {89-103},
keywords = {fractals, fractal analysis, entropy, wavelet entropy, fractal signal classification},
url = {https://www.sciopen.com/article/10.3934/nhm.2025006},
doi = {10.3934/nhm.2025006},
abstract = {In this article, a wavelet entropy, which behaves as a shifted version of the standard wavelet    (  q  ,      q    ′    )-entropy of fractal signals, is presented. The shifted wavelet    (  q  ,      q    ′    )-entropy is obtained by computing the standard    (  q  ,      q    ′    )-entropy functional on a weighted relative-wavelet-energy (RWE) representation of fractal signals; it is shown that the weight within the RWE plays the role of a shifting factor in the characteristics of the standard wavelet    (  q  ,      q    ′    )-entropy. Therefore the shifted wavelet    (  q  ,      q    ′    )-entropy relocates the wavelet entropy values to any point of the fractality index range, which allows us to analyze a wide variety of fractal signal families thus improving on previously proposed entropies in the literature. Information planes for these entropies are obtained using different shifts and values of parameters    q and        q    ′  , which allow us to highlight the potential applications for a fractal signal analysis. Moreover, an experimental study using synthesized exact fractal signals shows that the shifted wavelet entropy can classify stationary long-memory signals from short-memory ones and can also be used to differentiate other fractal signal families.}
}