Lommel函数与数字分数微分器系数的快速算法

利用Lommel函数表示理想数字分数微分器的系数，根据两类Lommel函数之间的关系和它们各自的基本性质给出理想数字分数微分器系数的一种新的快速算法.从理论上比较了新算法和其它几种现有算法的计算复杂度并对它们的运行时间进行仿真验证，所得结论证明，由这种新算法设计的微分器不但能够很好地完成分数阶微分运算，而且可以极大地缩短运算时间.

Lommel function and fast algorithm for coefficients of digital fractional differentiators

Lommel functions was used to represent the coefficients of ideal digital fractional differentiator, according to the relationship between two kinds of Lommel functions and the basic properties they each has, a new fast algorithm for coefficients of ideal digital fractional differentiator was presented. The computational complexity of the new algorithm was compared with other existing algorithms theoretically and simulation was carried out, the results showed that filters designed by this new algorithm can not only be of good performance in fractional differentiating, but also greatly shortened time that used for computation.