Filtered-X Affine Projection Algorithms for Active Noise Control Using Volterra Filters

We consider the use of adaptive Volterra filters, implemented in the form of multichannel filter banks, as nonlinear active noise controllers. In particular, we discuss the derivation of filtered-X affine projection algorithms for homogeneous quadratic filters. According to the multichannel approach, it is then easy to pass from these algorithms to those of a generic Volterra filter. It is shown in the paper that the AP technique offers better convergence and tracking capabilities than the classical LMS and NLMS algorithms usually applied in nonlinear active noise controllers, with a limited complexity increase. This paper extends in two ways the content of a previous contribution published in Proc. IEEE-EURASIP Workshop on Nonlinear Signal and Image Processing (NSIP '03), Grado, Italy, June 2003. First of all, a general adaptation algorithm valid for any order of affine projections is presented. Secondly, a more complete set of experiments is reported. In particular, the effects of using multichannel filter banks with a reduced number of channels are investigated and relevant results are shown.

[1]  Henning Puder,et al.  Acoustic echo and noise control — A long lasting challenge , 1998, 9th European Signal Processing Conference (EUSIPCO 1998).

[2]  H. Itoh,et al.  Active noise control by using prediction of time series data with a neural network , 1995, 1995 IEEE International Conference on Systems, Man and Cybernetics. Intelligent Systems for the 21st Century.

[3]  Kazuhiko Ozeki,et al.  An adaptive filtering algorithm using an orthogonal projection to an affine subspace and its properties , 1984 .

[4]  Jean Jiang,et al.  Filtered-X second-order Volterra adaptive algorithms , 1997 .

[5]  P. Grognot,et al.  [Electronic sound absorber]. , 1955, La Medecine aeronautique.

[6]  Martin Bouchard,et al.  Improved training of neural networks for the nonlinear active control of sound and vibration , 1999, IEEE Trans. Neural Networks.

[7]  Philip A. Nelson,et al.  Active Control of Sound , 1992 .

[8]  Giovanni L. Sicuranza,et al.  Simplified volterra filters for acoustic echo cancellation in GSM receivers , 2000, 2000 10th European Signal Processing Conference.

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

[10]  Scott C. Douglas.  Fast implementations of the filtered-X LMS and LMS algorithms for multichannel active noise control , 1999, IEEE Trans. Speech Audio Process..

[11]  V. J. Mathews,et al.  Polynomial Signal Processing , 2000 .

[12]  José Carlos M. Bermudez,et al.  Stochastic analysis of the filtered-X LMS algorithm in systems with nonlinear secondary paths , 2002, IEEE Trans. Signal Process..

[13]  Rui Seara,et al.  Performance comparison of the FXLMS, nonlinear FXLMS and leaky FXLMS algorithms in nonlinear active control applications , 2002, 2002 11th European Signal Processing Conference.

[14]  Barry D. Van Veen,et al.  Baseband Volterra filters for implementing carrier based nonlinearities , 1998, IEEE Trans. Signal Process..

[15]  Giovanni L. Sicuranza,et al.  Filtered-X affine projection algorithm for multichannel active noise control using second-order Volterra filters , 2004, IEEE Signal Processing Letters.

[16]  Giovanni L. Sicuranza,et al.  Low-complexity nonlinear adaptive filters for acoustic echo cancellation in GSM handset receivers , 2003, Eur. Trans. Telecommun..

[17]  Li Tan,et al.  Adaptive Volterra filters for active control of nonlinear noise processes , 2001, IEEE Trans. Signal Process..

[18]  Elias Bjarnason,et al.  Analysis of the filtered-X LMS algorithm , 1993, 1993 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[19]  Glenn E. Warnaka,et al.  Active Attenuation of Noise: The State of the Art , 1982 .

[20]  Pierre Chapelle,et al.  Active noise control with dynamic recurrent neural networks , 1995, ESANN.

[21]  Sen M. Kuo,et al.  Active Noise Control Systems: Algorithms and DSP Implementations , 1996 .

[22]  Joao M. C. Sousa,et al.  ACTIVE NOISE CONTROL BASED ON FUZZY MODELS , 2000 .

[23]  Paul Strauch,et al.  Active control of nonlinear noise processes in a linear duct , 1998, IEEE Trans. Signal Process..

[24]  S.J. Elliott,et al.  Active noise control , 1993, IEEE Signal Processing Magazine.