The Impact of Linear Filter Preprocessing in the Interpretation of Permutation Entropy

Area of Science:

• Complexity Science
• Signal Processing
• Information Theory

Background:

• Permutation Entropy (PE) quantifies information in time series.
• Linear filtering is a common preprocessing step for PE analysis.
• The impact of linear filters on PE values is not well understood.

Purpose of the Study:

• To theoretically characterize the effect of linear filters on Permutation Entropy.
• To separate the contribution of linear filters from the signal's ordinal information.
• To improve the interpretation of PE by identifying filter-induced artifacts.

Main Methods:

• Theoretical analysis using the Wiener-Khinchin theorem.
• Simulation of time series data subjected to various linear filters (moving average, Butterworth, Chebyshev Type I).
• Validation of theoretical predictions against simulation results.

Main Results:

• A theoretical framework was developed to characterize the intrinsic PE of linear filters.
• The contribution of linear filters to PE was successfully separated from the signal's information.
• Simulation results closely matched theoretical predictions for all tested filters.

Conclusions:

• Linear filter preprocessing significantly influences Permutation Entropy values.
• The proposed framework allows for the decoupling of filter-induced information from signal-specific information.
• This work enhances the reliability of PE analysis by identifying and accounting for preprocessing artifacts.