Fractional Proportionate Normalized Filtered Input Least Mean Square Algorithm for Active Noise Control Systems

This study presents an adaptive methodology for the purpose of eliminating narrow-band and broadband noise in active noise control systems. Due to its remarkable durability and simplicity, the Filtered Input Least Mean Square (FXLMS) algorithm is the most frequently employed approach for noise reduction. First, a Fractional Proportionate Normalized FXLMS (FPN-FXLMS), a fractional Taylor series-based noise reduction algorithm, is proposed for noise control. The fractional Taylor series-derived algorithm exclusively employs fractional derivatives and guarantees the convergence of mean square errors given that the step size is suitably selected. The proposed approach is then compared with existing methods for narrow-band and broadband noise cancelation. Furthermore, comparative simulations are performed, suggesting that the FPN-FXLMS algorithm exhibits faster convergence in mitigating noise levels compared to the Normalized FXLMS and Proportionate Normalized FXLMS algorithms.