Hybrid FxRLS-FxNLMS Adaptive Algorithm for Active Noise Control in fMRI Application

A hybrid adaptive algorithm is developed for an active noise control system that leverages the stability of the filtered-input normalized least mean squares (FxNLMS) adaptive algorithm, with the high convergence speed of the filtered-input recursive least squares (FxRLS) adaptive algorithm. This algorithm is motivated by practical issues in implementing a real-time active noise control system. It leads to fast initial convergence with low, stable steady-state error while being limited by the computational capability of hardware. It gives better convergence speed than either the FxNLMS or FxRLS algorithm individually, lower residual error, and a lower overall computational complexity than the FxRLS algorithm, when appropriate filter lengths are chosen. Experimental results are presented for the implementation of the hybrid algorithm to cancel functional magnetic resonance imaging (fMRI) acoustic noise in an fMRI test-bed.