<![CDATA[Digital elliptic filters, as a type of infinite impulse response (IIR) digital filter, play a crucial role in signal processing applications. Despite their widespread use, there remains a significant research gap in optimizing their frequency response to better approximate desired magnitude responses. This study addresses this gap by introducing an innovative optimization technique that leverages the DS-PSO (Dynamic & Static-Particle Swarm Optimization) algorithm. Based on artificial intelligence, the DS-PSO method uniquely integrates topologies (dynamic and static) into particle swarm optimization (PSO), enabling more precise analysis of pole positions derived from a filter's transfer function coefficients. The primary research problem lies in approximating the frequency response of digital IIR elliptic filters to match a desired magnitude response. Traditional methods often fail to achieve this due to limitations in their optimization techniques. The proposed DS-PSO algorithm addresses this by setting a slightly more significant maximum pole radius (Rmax) than 1.0, surpassing the pre-established pole radius (R). This approach allows for a more accurate approximation of the frequency response. This feature distinguishes it from previous studies that employed genetic algorithms (GA) and semi-definite programming (SDP) techniques, which reported lower Rmax values. The results of this study demonstrate the effectiveness of the DS-PSO algorithm in improving the frequency response of digital IIR elliptic filters. The proposed method successfully approximates the desired magnitude response by designing 4th and 12th-order lowpass digital IIR elliptic filters while maintaining stability at a high average. This makes the technique particularly suitable for determining frequency response boundaries in electronics or communications systems. The contribution of this research extends beyond the immediate results. By introducing and validating the DS-PSO algorithm, this study provides a robust framework for future research in optimizing digital IIR filters. The findings not only enhance the design of digital elliptic filters but also open new avenues for improving other types of IIR filters and signal processing applications. This paper establishes a foundation for further research in signal processing and other fields, with significant theoretical and practical implications.]]>
