Analysis and design of narrowband active noise control systems

This paper presents an analysis and optimization of narrowband active noise control (ANC) systems using the filtered-X least mean-square (LMS) algorithm. First, we derive an upper bound for the eigenvalue spread of the filtered reference signal's covariance matrix, which provides insights into algorithm convergence speed. Amplitude of internally generated sinusoidal reference signal is optimized as the inverse of the secondary path's magnitude response at the corresponding frequency to improve the convergence speed. Second, we analyze the characteristic of asymmetric out-of-band overshoot. Based on the analysis result, the phase of sinusoidal reference signal is optimized to compensate for the phase shift of the secondary path. This phase optimization leads to the minimization of the out-of-band overshoot.