Fractional-Order Differentiation Filter and Estimation of Gaussian Distribution Parameters

A fractional-order differentiation filter is designed to obtain fractional-order differential of a given signal and to simplify computation of the fractional-order differential.Firstly,a fractional-order differential of Gaussian distribution is obtained with the proposed filter.Secondly,the relationship between the differential order and the zero-crossing point of fractional-order differential of the Gaussian distribution is developed by analyzing the fractional-order differential of Gaussian distribution.Also,the relationship between the differential order and the maximum of the fractional-order differential of Gaussian distribution is developed.Finally,a novel method is presented to estimate the parameters of Gaussian distribution.