基于IFFT的Lubich数字分数微分器系数的快速算法

Fast algorithm based on IFFT for computing fractional Lubich coefficient of digital fractional differentiator

摘要:

从信号处理角度考察Lubich系数，分析了Lubich系数的频域特性。设计了一种基于快速傅里叶逆变换(IFFT)的Lubich系数的快速算法。IFFT算法直接求解的Lubich系数不准确，在甚低阶运算时频域存在吉布斯效应，新算法利用零频赋值可有效减弱该效应。数值仿真结果表明，与Lubich准确系数相比，在一定真分数运算阶范围内，新算法求得的Lubich近似系数构建数字分数微分器有更好的效果，且新算法计算复杂度低，运算效率高。

Abstract:

The Lubich coefficient is investigated from the point of view of signal processing, and the frequency characteristics of Lubich coefficient are analyzed. A fast algorithm based on Inverse Fast Fourier Transform (IFFT) for computing Lubich coefficient is designed. The Lubich coefficient directly solved by IFFT algorithm is not accurate. The Gibbs effect exists in the frequency domain with low order operations, and the new algorithm can reduce this effect effectively by zero-frequency assignment. The numerical simulation results show that, compared with Lubich accuracy coefficient, the Lubich approximation coefficients computed by the new algorithm have better performance in constructing the digital fractional differentiator with a certain proper fraction operation order range, and the new algorithm has low computational complexity and high efficiency.