分数导数与数字微分器设计

Fractional-Order Derivative and Design of FractionaI DigitaI Differentiators

从信号处理角度来考察分数阶导数和微分问题 .首先论述分数阶微积分的基本概念 ,评论分数阶导数的几种典型定义 ,并重点探讨分数阶导数的频域定义及其基本性质 .紧接着详细研究分数阶微分的实现 :理想分数阶数字微分滤波器和FIR分数阶数字微分滤波的基本性质和设计问题 ,并提出分数阶微分滤波器设计中遇到的新问题以及奇对称微分滤波器、偶对称微分滤波器等新概念 .最后给出一些值得进一步探讨的有趣问题 .

The topics of fractional (order) derivative and its digital implementations are studied from the view point of signal processing. A brief survey on fractional differentiation and integration is given, some basic concepts of the fractional calculus and some typical definitions of the fractional derivative are reviewed. Next the digital implementation approaches of fractional differentiators are discussed in detail. Some new problems, which would been encounted in the design of the fractional differentiators, and some new concepts, such as the odd symmetric differentiators and even symmetric differentiators are proposed. Finally, future works are reviewed in the concluding remarks.