Design of Nearly Linear Phase IIR Fractional Order Digital Integrators Using Iterative Convex Optimization Algorithm

We propose a novel design method for fractional digital integrators with infinite impulse response. Our research focuses on minimizing the maximum phase error while ensuring system stability and keeping the relative amplitude response error within an acceptable range under specific constraints. To achieve these objectives, we also introduce group delay as an optimization variable to further enhance system performance. To this end, we develop an iterative convex optimization algorithm based on the Gauss-Newton strategy to effectively address complex problems in the design process. Through the analysis of the provided examples, our results demonstrate that, compared to existing solutions, the proposed fractional-order integrator shows a significant improvement in maximum phase error.