FIR Filter System Modeling Using Metaheuristic Approaches: Applications of PSO, ABC, qABC, and MA

This study addresses the modeling of high-order FIR (Finite Impulse Response) systems using lower-order FIR filters, which is a significant challenge in digital filter design and system identification. The primary objective is to approximate the amplitude frequency response of a fifth-order FIR system with a fourth-order FIR model while minimizing the modeling error. To achieve this, four metaheuristic optimization algorithms—Particle Swarm Optimization (PSO), Artificial Bee Colony (ABC), Quick ABC (qABC), and Memetic Algorithm (MA)—are employed. Each algorithm is executed in 30 independent trials to assess its robustness and performance.The modeling task is formulated as an optimization problem where the mean squared error (MSE) between the reference system’s frequency response and the approximated model’s response is minimized. The performance of each algorithm is evaluated not only by their convergence behavior over iterations but also by detailed frequency-domain analyses, including both amplitude response and power spectrum comparisons. Furthermore, the statistical properties of each algorithm’s output—such as mean, standard deviation, minimum and maximum MSE values—are used to evaluate consistency and accuracy.The results show that the ABC algorithm achieves the best overall balance, providing the lowest average MSE and smallest variance, indicating strong stability and accuracy. The MA algorithm, while achieving the lowest minimum MSE in some runs, exhibits higher variability, suggesting less consistency. The qABC algorithm demonstrates fast convergence and high potential for accurate modeling, but its relatively high standard deviation points to a lack of solution stability. The PSO algorithm, although able to reach low error values in some runs, generally produces more dispersed and inconsistent solutions due to its broader error range.In conclusion, this work presents a comprehensive comparative evaluation of metaheuristic algorithms for low-order FIR filter modeling. The findings highlight the superiority of ABC and MA algorithms in terms of accuracy and stability, and point toward the potential of hybrid or adaptive versions of these algorithms for future filter design and system identification problems.Keywords: FIR filter, system modeling, PSO, ABC, Quick ABC, MA.