On the analysis of signals in a permutation Lempel-Ziv complexity - permutation Shannon entropy plane

The aim of this paper is to introduce the Lempel–Ziv permutation complexity vs permutation entropy plane as a tool to analyze time series of different nature. This two quantities make use of the Bandt and Pompe representation to quantify continuous-state time series. The strength of this plane is to combine two different perspectives to analyze a signal, one being statistic (the permutation entropy) and the other being deterministic (the Lempel–Ziv complexity). This representation is applied (i) to characterize non-linear chaotic maps, (ii) to distinguish deterministic from stochastic processes and (iii) to analyze and differentiate fractional Brownian motion from fractional Gaussian noise and K-noise given a same (averaged) spectrum. The results allow to conclude that this plane is “robust” to distinguish chaotic signals from random signals, as well as to discriminate between different Gaussian and nonGaussian noises.