Improving of the interpretation of linear filtering preprocessing-based multiscale permutation entropy.

Multi-scale permutation entropy (MPE) is an interesting tool for analyzing signal internal structures and quantifying complexity. The most commonly used MPEs involve a linear preprocessing step applied to the original signal prior to the evaluation of the permutation entropy (PE). However, recent research done by Davalos et al has demonstrated that linear filtering preprocessing significantly modifies the PE of Gaussian processes. To build on this work, we conducted a study to investigate the MPE's behavior across a variety of signal generation models including sinusoidal signals, frequency modulated signals, and colored Gaussian noise. Our findings indicate that the MPE mainly reflects changes in the center frequency of the signal spectrum, independent of signal generation models. It's important to note that the linear preprocessing step used in MPE calculations can lead to misinterpretation of the results. Therefore, we suggest that a proper interpretation of the MPE values should be done in conjunction with a spectral analysis or a time-frequency representation.