Convergence analysis of narrow-band active noise control system

This paper presents the convergence analysis of the filtered-X least mean square algorithm for narrow-band active noise control with direct-form realization. Theoretical bounds are established for the maximum eigenvalue and the eigenvalue spread of the reference signal's covariance matrix, which in turn provide insight into algorithm convergence and optimization. In order to improve the convergence speed, amplitudes of sinusoidal reference signals are chosen to be the inverse of the magnitude responses of the secondary path at the corresponding frequencies.