数字分数微分器系数的快速算法

提出了一种理想数字分数微分器系数的快速算法。从理想数字分数微分器系数计算公式的特点考虑，利用变量代换把积分函数中的振荡因子转换成积分上限，避免高阶振荡函数积分计算，给出了计算分数微分器系数的递推公式。分析了快速算法的计算复杂度、稳定性和收敛性等问题。实验结果表明新算法具有运算量少，运算速度快并具有较好的稳定性和收敛性。
关 键 词 分数微分器; 振荡因子; 快速算法; 稳定性

Abstract A new fast algorithm for calculating the coefficients of ideal digital fractional differentiator is presented. It is difficult to compute directly the coefficients from the integral formula, since the integral function in the formula of the ideal digital fractional differentiator is a high-order oscillating function. Based on the properties of the integral formula, it’s easy to convert the oscillating factor to the integral upper limit. Therefore a set of recursive expressions for calculating coefficients of ideal digital fractional differentiator are introduced in this paper. The experimental result shows that the new algorithm decreases the amount of operation greatly, at the same time promotes the algorithm’s efficiency as well as avoid integral of high-order oscillating function.
Key words digital fractional differentiator; oscillating factor; fast algorithm; stability