Optimal Design of Digital IIR Filters Using Robust Group Search Optimization

This paper presents a novel approach to designing the optimal lowest-order serial digital Infinite Impulse Response (IIR) filters using robust group search optimization (R-GSO), where the structures of IIR filters are specified in advance. The R-GSO algorithm integrates the GSO algorithm and the Taguchi method. The number of producers of the original GSO algorithm is fixed to one, which makes it easy to fall into the local optimal solution. The R-GSO algorithm selects three producers and applies the Taguchi method to determine the optimal producer for each iteration to enhance the robustness of the search process and the performance of the global search optima. The Taguchi method not only considers the solutions with the highest fitness but also evaluates the robustness of the solutions. Digital IIR filter design is a complex, multi-parameter, multi-objective optimization problem, and the objectives are often at odds. The performance of a digital IIR filter can be evaluated by the Lp-norm error, the ripple size of the passband, and the ripple size of the stopband. Thus, this paper considers the L1-norm, L2-norm, and the ripple size of the passband and the stopband to search for a flatter and closer to the target of the lowest order of the digital IIR filter. From the experimental results, the R-GSO algorithm effectively optimizes the digital low-pass (LP), high-pass (HP), band-pass (BP), and band-stop (BS) filters. It outperforms the hybrid Taguchi genetic algorithm (HTGA) and original GSO algorithm. The RGSO algorithm also has fewer function evaluations than HTGA, making it possible to optimize these four filters more efficiently and apply them to real-world engineering applications where high-performance digital filters are required.