Resource-Efficient Design of High-Speed FIR Filter: Fractional-Order Integrator/Differentiator on FPGAs

Abstract

Fractional calculus has increasingly become a robust framework for modeling complex systems in engineering, offering advantages over traditional integer-order methods through its ability to encapsulate memory and non-local dynamics. Fractional-order integrators, in particular, have found applications in control engineering, signal processing, and biomedical fields. Despite their theoretical benefits, the digital realization of such integrators-especially under real-time constraints-poses significant challenges. This paper presents a comparative analysis of three numerical approximation methods for the digital implementation of fractional-order integrators on Field-Programmable Gate Arrays (FPGAs): Simpson's method, Tustin's method, and the Gr & uuml;nwald-Letnikov method. By exploiting the parallelism and reconfigurability of FPGAs, the study evaluates these approaches in terms of numerical accuracy, convergence properties, and resource utilization, thereby providing insights into the trade-offs inherent in each method for real-time applications.