Extending The Concept of Analog Butterworth Filter For Fractional Domain
Signal Processing (Elsevier), 2014
Designs fractional-order Butterworth filters in the complex w-plane, including under-, hyper-, and ultra-damped poles, and demonstrates the formulation in simulations and a frequency-domain design example.
Abstract
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.