Meta-heuristic-based design of high-order stable digital filters using pole-zero placement

Abstract

This study presents a meta-heuristic optimization approach for digital IIR filter design that addresses fundamental limitations of conventional coefficient-based methods. Rather than optimizing filter coefficients directly, the proposed method identifies optimal locations of zeros, poles, and gain in the z-plane for a given frequency response. This pole-zero formulation provides an intuitive framework for managing filter characteristics, particularly stability constraints. The fitness function simultaneously optimizes magnitude and phase responses, enabling frequency response shaping for a wide range of applications. Extensive simulations across four complex design scenarios – including low-order filter, low-pass filters, curved frequency responses, and stabilized inverse systems – demonstrate the algorithm’s superior performance compared to related work for high-order implementations. Results show that the proposed approach maintains strong exploration capability even in high-dimensional optimization landscapes while guaranteeing stable filter realizations. This methodology provides engineers with a flexible and reliable tool for prototyping digital filters that accommodate specific operational requirements beyond conventional filter designs.