Frequency dependent convergence rate of FXLMS in narrowband active noise control systems

Direct, parallel, and direct/parallel form narrowband active noise control (NANC) systems use single or multiple adaptive filters adapted by the filtered-x least mean square (FXLMS) algorithms to cancel narrowband noises at several distinct frequencies. This paper analyzes the effects of the narrowband noises’ frequencies on the convergence rates of the FXLMS algorithms used in the direct, parallel, and direct/parallel form NANC systems. Theoretical analysis shows that the convergence rates for the given filter lengths are frequency dependent. This paper also establishes the conditions to achieve fast convergence for the NANC systems. Computer simulations verify the theoretical analysis.