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Analysis of the adaptive filter algorithm for feedback-type active noise control

The feedback-type active noise control (ANC) system uses only one microphone to provide necessary signals for adjusting the adaptive filter. Due to the complicated nature of the whole adaptive filter structure there have been no theoretical results about its convergence properties. First a stationary point of the adaptive filter using the filtered-X LMS algorithm is obtained by the averaging method combined with the frequency domain technique. Then the local convergence condition is derived. This is a counterpart of the well-known 90/spl deg/ condition for the feedforward-type ANC. Finally, the convergence condition is explicitly given for a simple example and its validity is shown by some simulations.