Null or Linear-Phase Filters for the Derivation of a New Variant of the MSE

The multiscale entropy (MSE) is used in a wide range of applications, especially by physiologists with bio-signals for classification. It consists in estimating the sample entropies of the signal under study and its coarse-grained (CG) versions. The CG process amounts to filtering the signal with an average filter whose order is the scale and then to decimating the filter output by a factor also equal to the scale. In this paper, the novelty stands in the way to get the sequences at different scales, by avoiding distortions that can appear during the decimation step. If a low-pass filter is implemented, the cut-off frequency of which is well suited to the decimation factor, the phase distortions induced by the filter must be attenuated as much as possible. Two ways are considered in this paper: 1/ design a linear-phase finite- impulse-response filter with the window method or the Remez algorithm. 2/ design a zero-phase filter from any infinite impulse response filter. Simulations with white noises and 1/ $f$ processes are given. The way the sample entropy evolves with the scale is presented. Depending on the filter parameters, one can see how it differs from the evolution obtained with the CG.