Multiscale entropy rates: a study on different stochastic processes
GRIVEL, Eric
Laboratoire de l'intégration, du matériau au système [IMS]
Institut Polytechnique de Bordeaux [Bordeaux INP]
Laboratoire de l'intégration, du matériau au système [IMS]
Institut Polytechnique de Bordeaux [Bordeaux INP]
LEGRAND, Pierrick
Institut de Mathématiques de Bordeaux [IMB]
Centre Inria de l'Université de Bordeaux
Méthodes avancées d’apprentissage statistique et de contrôle [ASTRAL]
Institut de Mathématiques de Bordeaux [IMB]
Centre Inria de l'Université de Bordeaux
Méthodes avancées d’apprentissage statistique et de contrôle [ASTRAL]
GRIVEL, Eric
Laboratoire de l'intégration, du matériau au système [IMS]
Institut Polytechnique de Bordeaux [Bordeaux INP]
Laboratoire de l'intégration, du matériau au système [IMS]
Institut Polytechnique de Bordeaux [Bordeaux INP]
LEGRAND, Pierrick
Institut de Mathématiques de Bordeaux [IMB]
Centre Inria de l'Université de Bordeaux
Méthodes avancées d’apprentissage statistique et de contrôle [ASTRAL]
< Reduce
Institut de Mathématiques de Bordeaux [IMB]
Centre Inria de l'Université de Bordeaux
Méthodes avancées d’apprentissage statistique et de contrôle [ASTRAL]
Language
EN
Article de revue
This item was published in
Digital Signal Processing. 2025-05-09
English Abstract
In this paper, we propose to analyze the behavior of the entropy rate (ER) when applied to a signal and its coarse-grained versions. The “multiscale entropy rate” (MSER) is deduced by storing in a vector the resulting ERs. ...Read more >
In this paper, we propose to analyze the behavior of the entropy rate (ER) when applied to a signal and its coarse-grained versions. The “multiscale entropy rate” (MSER) is deduced by storing in a vector the resulting ERs. Our contribution consists in studying the MSER calculated on different stochastic processes. When dealing with Gaussian complex or real moving average (MA) processes or autoregressive (AR) processes, which can be seen as the filtering of a white Gaussian driving process, the MSER depends on the variances of the driving processes of the corresponding minimum-phase ARMA process at each scale. More particularly, we derive the analytical expression of the MSER for -order MA or AR processes using different approaches. This study allows us to better understand what each scale brings in and to describe the behavior of the MSER for these types of processes. We also show that there is a mapping between the stochastic-process parameters and the ER computed at different scales. Finally, we show that the multiscale procedure is not relevant for a sum of complex exponentials disturbed by an additive white Gaussian noise.Read less <
English Keywords
Multiscale entropy
Entropy rates
Sum of complex exponentials
Autoregressive with moving average processes