Extending the Concept of Analog Butterworth Filter for Fractional Order Systems
Abstract
This paper proposes the design of Fractional Order (FO) Butterworth filter in complex w-plane (w=sq; 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. Firstly, 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.
Keywords
Cite
@article{arxiv.1210.8194,
title = {Extending the Concept of Analog Butterworth Filter for Fractional Order Systems},
author = {Anish Acharya and Saptarshi Das and Indranil Pan and Shantanu Das},
journal= {arXiv preprint arXiv:1210.8194},
year = {2014}
}
Comments
21 pages, 5 figures