IIR Digital Filter Implementation via Red-billed Blue Magpie Optimization Algorithm

Abstract

To overcome the insufficient stop-band attenuation and poor stability of conventional IIR filter design, this paper introduces the Red-billed Blue Magpie Optimization (RBMO) algorithm for the synthesis of 8th-order infinite-impulse-response digital filters. By emulating the collective intelligence of red-billed blue magpies, RBMO integrates a tri-modal “hop-walk-fly” search strategy with an “information-sharing & food-storing” cooperation mechanism, achieving an effective balance between global exploration and local exploitation. A pole-radius constraint is embedded to guarantee BIBO stability, while a unified fitness function that simultaneously penalizes pass-band magnitude error, peak stop-band ripple, and weighted transition-band deviation converts the design task into a single-objective optimization problem. Extensive simulations on low-pass, high-pass, band-pass and band-stop specifications demonstrate that the proposed scheme significantly reduces pass-band peak ripple, stop-band amplitude and transition-band error. The optimized coefficients, visualized through magnitude–frequency curves and pole-zero maps, corroborate the feasibility and practical potential of RBMO in high-performance IIR filter design.