Novel low-pass filter with adjustable parameters of~exponential-type forgetting

TL;DR

This paper introduces the Mittag-Leffler filter, a new low-pass filter utilizing a Mittag-Leffler distribution with adjustable parameters, offering enhanced flexibility over classical Gaussian filters.

Contribution

The paper proposes a novel Gaussian filter variant based on Mittag-Leffler functions, allowing parameter tuning for improved filtering performance.

Findings

The filter's parameters effectively adjust the curve shape.

Illustrative examples demonstrate advantages over classical Gaussian filters.

Implementation details and MATLAB code are provided.

Abstract

In this paper, a novel form of Gaussian filter, the Mittag-Leffler filter, is presented. This new filter uses a Mittag-Leffler function in the probability density function. Such Mittag-Leffler distribution is used in the convolution kernel of the filter. The filter has three parameters that may adjust the curve shape due to the filter forgetting factor. Illustrative examples present the main advantages of the proposed filter as compared to classical Gaussian filtering techniques. Some implementation notes, together with the Matlab function, are also presented.