Analysis of an adaptive filter algorithm for hybrid ANC system

The hybrid active noise control (ANC) system consists of the combination of feedforward and feedback type ANCs. The filtered-X LMS algorithm is used to adapt the controllers.. The averaging method is applied to the hybrid ANC system with the frequency domain expression to derive a stationary point of the adaptive algorithm. Then, it is found that though the adaptive filters of both ANCs are operating simultaneously, the stationary point of each adaptive filter is same with that for the case where each ANC system is operating separately. Then the local convergence condition is derived. Finally, the convergence condition is explicitly examined for a simple case and its validity is shown by some simulations.