Extending the concept of analog Butterworth filter for fractional order systems

被引：63

作者：

Acharya, Anish ^{[1
]}

Das, Saptarshi ^{[2
]}

Pan, Indranil ^{[3
]}

Das, Shantanu ^{[4
]}

机构：

[1] Jadavpur Univ, Dept Instrumentat & Elect Engn, Kolkata 700098, W Bengal, India

[2] Univ Southampton, Sch Elect & Comp Sci, Commun Signal Proc & Control Grp, Southampton SO17 1BJ, Hants, England

[3] UCL, MERG, Energy Environm Modelling & Minerals E2M2 Res Stn, Dept Earth Sci & Engn, London SW7 2AZ, England

[4] Bhabha Atom Res Ctr, Reactor Control Div, Bombay 400085, Maharashtra, India

来源：

SIGNAL PROCESSING | 2014年 / 94卷

关键词：

Butterworth filter; Fractional order filter; Fractional order linear system; w-plane stability; Analog filter design; SINUSOIDAL OSCILLATORS; DESIGN;

D O I：

10.1016/j.sigpro.2013.07.012

中图分类号：

TM [电工技术]; TN [电子技术、通信技术];

学科分类号：

0808 ; 0809 ;

摘要：

This paper proposes the design of fractional order (FO) Butterworth filter in complex w-plane (w=s(q); q being any real number) considering the presence of under-damped, hyper-damped, ultra-damped poles. This is the first attempt to design such fractional Butterworth filters in complex w-plane instead of complex s-plane, as conventionally done for integer order filters. First, the concept of fractional derivatives and w-plane stability of linear fractional order systems are discussed. Detailed mathematical formulation for the design of fractional Butterworth-like filter (FBWF) in w-plane is then presented. Simulation examples are given along with a practical example to design the FO Butterworth filter with given specifications in frequency domain to show the practicability of the proposed formulation. (C) 2013 Elsevier B.V. All rights reserved.

引用

页码：409 / 420

页数：12

共 29 条

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