Mean square analysis of a fast filtered-x affine projection algorithm

This paper provides an analysis of the steady-state behavior of the filtered-x affine projection algorithm (FXAP). This efficient affine projection (AP) algorithm for active noise control (ANC) applications is based on the filtered-x scheme, unlike most AP algorithms based on the more computationally demanding modified filtered-x scheme. This study depends on energy conservation arguments and does not require an specific signal distribution. The theoretical expressions derived for the mean square error (MSE) allowed to accurately predict the steady-state performance of the FXAP for meaningful practical cases. Simulation results of a single-channel ANC system validate the analysis and the theoretical expressions derived.

[1]  Alberto González,et al.  Fast Filtered-X Affine Projection Algorithm with Efficient Computation of Coefficient Update , 2006, 2006 IEEE International Conference on Acoustics Speech and Signal Processing Proceedings.

[2]  G. Pinero,et al.  Fast filtered-x affine projection algorithm for active noise control , 2005, IEEE Workshop on Applications of Signal Processing to Audio and Acoustics, 2005..

[3]  Ali H. Sayed,et al.  Mean-square performance of a family of affine projection algorithms , 2004, IEEE Transactions on Signal Processing.

[4]  M. Bellanger.  Adaptive filter theory: by Simon Haykin, McMaster University, Hamilton, Ontario L8S 4LB, Canada, in: Prentice-Hall Information and System Sciences Series, published by Prentice-Hall, Englewood Cliffs, NJ 07632, U.S.A., 1986, xvii+590 pp., ISBN 0-13-004052-5 025 , 1987 .

[5]  Giovanni L. Sicuranza,et al.  Transient and steady-state analysis of filtered-x affine projection algorithms with imperfect secondary path estimate , 2005, ISPA 2005. Proceedings of the 4th International Symposium on Image and Signal Processing and Analysis, 2005..

[6]  S. Haykin,et al.  Adaptive Filter Theory , 1986 .

[7]  S. Douglas.  The fast affine projection algorithm for active noise control , 1995, Conference Record of The Twenty-Ninth Asilomar Conference on Signals, Systems and Computers.

[8]  Martin Bouchard.  Multichannel affine and fast affine projection algorithms for active noise control and acoustic equalization systems , 2003, IEEE Trans. Speech Audio Process..