Adaptive signal processing algorithms: stability and performance
Adaptive signal processing algorithms: stability and performance
Adaptive filter theory (3rd ed.)
Adaptive filter theory (3rd ed.)
Time series: data analysis and theory
Time series: data analysis and theory
ICASSP '00 Proceedings of the Acoustics, Speech, and Signal Processing, 2000. on IEEE International Conference - Volume 01
Frequency-domain adaptation of causal digital filters
IEEE Transactions on Signal Processing
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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. In this paper, 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° 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.