Generalized Approach for Fractional-Order Low-Pass Butterworth Filter Realization with an Inverse Follow the Leader Filter (IFLF) Topology

This research presents a generalized approach to determine the coefficients to realize any <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$(N+\alpha)$</tex> fractional-order low-pass Butterworth response using transfer function forms based on the Inverse Follow the Leader Filter (IFLF) topology. This approach automates the process to create and assemble the required transfer function (based on user specified values) and then apply a numerical optimization to estimate the necessary coefficients to achieve the target filter magnitude response. MATLAB simulations of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$(2+\alpha)$</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$(10+\alpha)$</tex> order filters using the generalized approach validate the process. Further, an experimental 2.5-order low-pass filter is experimentally realized (using an approximated fractional-order capacitor) to validate the characteristics of a low-pass filter designed using this process.