Design of IIR Fractional Order Digital Differentiators Using Iterative Convex Optimization Algorithm

This paper introduces a new approach for the design of IIR fractional-order digital differentiators exhibiting near-linear phase characteristics. The methodology focuses on minimizing the maximum phase deviation from an ideal linear phase under stability-triangle and relative magnitude response error constraints. The formulated design problem is inherently nonconvex. To address this, an iterative convex optimization algorithm is proposed, leveraging a Gauss-Newton strategy to transform the nonconvex problem into a sequence of convex subproblems. Empirical design examples demonstrate that the proposed differentiators achieve superior performance in terms of both maximum phase error and maximum relative magnitude error compared to existing counterparts in the literature.