分数阶IIR和FIR滤波器及其逆系统的研究

The fractional IIR and FIR filter and their inverse systems

分数阶滤波器(FrF)是传统整数阶滤波器的推广,在控制和信号处理等领域有广泛的应用前景。本文对离散时间FrF的一般表达形式进行了讨论;研究了基于Taylor级数展开的分数阶递归和非递归型IIR滤波器及其逆系统的结构和频率特性;分析了多项式近似情况下,递归和非递归型FIR FrF的频率特性与滤波器参数的关系;研究了非递归型FIR逆FrF系统及滤波器参数对频率特性的影响。

Fractional order filter （FrF） is the extension of the traditional integral order filter, which has a bright prospect for applications in fields of control, signal processing and etc. The general description of the FrF is discussed in this paper. Structures and frequency characteristics of recursive and non-recursive IIR FrF based on the form of Taylor expansion and their inverse systems are studied. And relationships between the frequency characteristics of the recursive or non-recursive FIR FrF based on the polynomial approximation and filter parameters are analyzed in detail. System and its frequency characteristics of the non-recursive FIR FrF is also explored.