Influence of the signal to noise ratio for the estimation of Permutation Entropy

Abstract

In this paper, the influence of signal to noise ratio in the estimation of Permutation Entropy was studied upon signals obtained by simulations of a chaoticdeterministic system. Then, using a bootstrap scheme, we applied hypothesistests to detect noise in a signal computing the Permutation Entropy. Similarly to recent publications, we found that as the content of noise increases (i.e. the signal to noise ratio decreases), three clearly different dynamics appear: dominant deterministic, deterministic noisy and dominant noisy. To discriminate the limits of these zones, another hypothesis test was applied. Finally, we also show that if a hypothesis test detects changes in the value of Permutation Entropy, it is due to changes in the actual dynamics of the system and not due to thepresence of noise in the signal.