Design and Analysis of Fractional Filters with Complex Orders

This paper focuses on designing a complex fractional differentiator for the order $\alpha+j\beta$. An approximation technique using curve fitting based iterative algorithm is proposed for the implementation of these differentiators. Furthermore, the development of various complex fractional-order filters, namely low-pass, high-pass, band-pass, and all-pass, is presented. Bode diagrams from the results show that the proposed filters have produced a similar behavior to the conventional and fractional filter. Similarly, Bode diagrams of approximated filters using the proposed technique also confirms the achievement of similar behavior to the traditional and fractional filter. The step response on the process plant also proved that the fractional low-pass filter with complex order accomplished well on filtering the noise signal.