Optimizing IIR Filter Design using Multi-Objective Genetic Algorithm: A Focus on Passband Ripple and Stopband Attenuation

This study focuses on the multi-objective optimization of Infinite Impulse Response (IIR) filters, with a particular emphasis on minimizing passband ripple and maximizing stopband attenuation, while constraining the filter order within a feasible range of 4 to 10. Traditional IIR filter design methods, such as Butterworth, Chebyshev, and Elliptic filters, often focus on optimizing a single performance criterion. However, this approach can lead to suboptimal designs when multiple objectives - such as ripple, attenuation, and filter order - need to be considered simultaneously in the design process. These classical methods typically face tradeoffs, where improving one aspect, such as sharper roll-off, results in drawbacks in another, like increased passband ripple or higher filter order, resulting in added computational complexity. To address these challenges, this research applies the Non-dominated Sorting Genetic Algorithm II (NSGA-II), which is a robust evolutionary algorithm designed for multi-objective optimization. NSGA-II is employed to balance the conflicting goals of minimizing ripple and maximizing stopband attenuation, with the filter order constrained within a feasible range of 4 to 10. By generating a set of Pareto-optimal solutions, the algorithm allows designers to explore the tradeoffs between different objectives and select filter configurations based on specific application needs. The experimental results show that the proposed approach not only enhances filter performance in terms of signal quality and computational efficiency but also offers greater flexibility in filter design. The research demonstrates that multi-objective optimization is a more comprehensive and effective methodology for designing IIR filters, especially in applications requiring a careful balance between performance and complexity. This study contributes to the advancement of digital filter design by providing a more adaptable and robust framework for optimizing filter performance.