分数阶微分滤波器及高斯分布参数估计

Fractional-Order Differentiation Filter and Estimation of Gaussian Distribution Parameters

摘要: 设计了一种分数阶微分滤波器．利用此滤波器可实现信号的分数阶微分，使得分数阶微分计算简单化．首先，采用此滤波器获得高斯分布的分数阶微分；然后，通过对高斯分布的分数阶微分的分析，建立了高斯分布的分数阶微分的过零点与微分阶数之间的关系和高斯分布的分数阶微分的最大值与微分阶数之间的关系；最后，得到了一种估计高斯分布参数的新方法．

Abstract: 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.