Extending the Concept of Analog Butterworth Filter for Fractional Order Systems
This work provides a novel design framework for fractional-order filters, which may benefit signal processing and control systems requiring non-integer order dynamics.
This paper proposes a method to design fractional-order Butterworth filters in the complex w-plane, extending the conventional integer-order Butterworth filter concept to fractional-order systems. The approach is validated through simulations and a practical example, demonstrating its feasibility for frequency-domain specifications.
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.