Design of Nearly Linear Phase IIR Fractional Order Digital Differentiators using Iterative Convex Optimization Algorithm

This paper introduces a methodology for the design of IIR fractional-order digital differentiators with near-linear phase properties. The primary objective is to minimize the maximum phase deviation from the ideal linear phase, subject to constraints on stability and relative magnitude response deviations. This design incorporates group delay as an optimization variable, leading to a nonconvex optimization problem. To resolve this, we propose an Iterative Convex Optimization algorithm that reformulates the nonconvex problem into a series of convex subproblems utilizing a Gauss-Newton strategy. Simulation experiments have substantiated the superiority of the proposed differentiator compared to methods in the field, demonstrating significantly reduced relative magnitude deviations and maximum phase errors.