This article is part of the series Adaptive Partial-Update and Sparse System Identification.

Open Access Research Article

Analysis of Transient and Steady-State Behavior of a Multichannel Filtered-x Partial-Error Affine Projection Algorithm

Alberto Carini1* and Giovanni L Sicuranza2

Author Affiliations

1 Information Science and Technology Institute, University of Urbino "Carlo Bo", Urbino 61029, Italy

2 Department of Electrical, Electronic and Computer Engineering, University of Trieste, Trieste 34127, Italy

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EURASIP Journal on Audio, Speech, and Music Processing 2007, 2007:031314  doi:10.1155/2007/31314


The electronic version of this article is the complete one and can be found online at: http://asmp.eurasipjournals.com/content/2007/1/031314


Received: 28 April 2006
Revisions received: 24 November 2006
Accepted: 27 November 2006
Published: 18 January 2007

© 2007 A. Carini and G. L. Sicuranza.

This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

The paper provides an analysis of the transient and the steady-state behavior of a filtered-x partial-error affine projection algorithm suitable for multichannel active noise control. The analysis relies on energy conservation arguments, it does not apply the independence theory nor does it impose any restriction to the signal distributions. The paper shows that the partial-error filtered-x affine projection algorithm in presence of stationary input signals converges to a cyclostationary process, that is, the mean value of the coefficient vector, the mean-square error and the mean-square deviation tend to periodic functions of the sample time.

References

  1. PA Nelson, SJ Elliott, Active Control of Sound (Academic Press, London, UK, 1995)

  2. SC Douglas, Fast implementations of the filtered-X LMS and LMS algorithms for multichannel active noise control. IEEE Transactions on Speech and Audio Processing 7(4), 454–465 (1999). Publisher Full Text OpenURL

  3. M Bouchard, Multichannel affine and fast affine projection algorithms for active noise control and acoustic equalization systems. IEEE Transactions on Speech and Audio Processing 11(1), 54–60 (2003). Publisher Full Text OpenURL

  4. A Carini, GL Sicuranza, Transient and steady-state analysis of filtered-x affine projection algorithms. IEEE Transactions on Signal Processing 54(2), 665–678 (2006)

  5. Y Neuvo, C-Y Dong, SK Mitra, Interpolated finite impulse response filters. IEEE Transactions on Acoustics, Speech, and Signal Processing 32(3), 563–570 (1984). Publisher Full Text OpenURL

  6. S Werner, PSR Diniz, Set-membership affine projection algorithm. IEEE Signal Processing Letters 8(8), 231–235 (2001). Publisher Full Text OpenURL

  7. SC Douglas, Adaptive filters employing partial updates. IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing 44(3), 209–216 (1997). Publisher Full Text OpenURL

  8. K Doğançay, O Tanrikulu, Adaptive filtering algorithms with selective partial updates. IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing 48(8), 762–769 (2001). Publisher Full Text OpenURL

  9. GL Sicuranza, A Carini, Nonlinear multichannel active noise control using partial updates. Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP '05), March 2005, Philadelphia, Pa, USA 3, 109–112

  10. E Bjarnason, Analysis of the filtered-X LMS algorithm. IEEE Transactions on Speech and Audio Processing 3(6), 504–514 (1995). Publisher Full Text OpenURL

  11. OJ Tobias, JCM Bermudez, NJ Bershad, Mean weight behavior of the filtered-X LMS algorithm. IEEE Transactions on Signal Processing 48(4), 1061–1075 (2000). Publisher Full Text OpenURL

  12. H-C Shin, AH Sayed, Mean-square performance of a family of affine projection algorithms. IEEE Transactions on Signal Processing 52(1), 90–102 (2004). Publisher Full Text OpenURL

  13. M Bouchard, S Quednau, Multichannel recursive-least-squares algorithms and fast-transversal-filter algorithms for active noise control and sound reproduction systems. IEEE Transactions on Speech and Audio Processing 8(5), 606–618 (2000). Publisher Full Text OpenURL

  14. VJ Mathews, GL Sicuranza, Polynomial Signal Processing (John Wiley & Sons, New York, NY, USA, 2000)

  15. P Strauch, B Mulgrew, Active control of nonlinear noise processes in a linear duct. IEEE Transactions on Signal Processing 46(9), 2404–2412 (1998). Publisher Full Text OpenURL

  16. DP Das, G Panda, Active mitigation of nonlinear noise processes using a novel filtered-s LMS algorithm. IEEE Transactions on Speech and Audio Processing 12(3), 313–322 (2004). Publisher Full Text OpenURL

  17. SJ Elliott, I Stothers, PA Nelson, A multiple error LMS algorithm and its application to the active control of sound and vibration. IEEE Transactions on Acoustics, Speech, and Signal Processing 35(10), 1423–1434 (1987). Publisher Full Text OpenURL

  18. AH Sayed, Fundamentals of Adaptive Filtering (John Wiley & Sons, New York, NY, USA, 2003)

  19. TY Al-Naffouri, AH Sayed, Transient analysis of data-normalized adaptive filters. IEEE Transactions on Signal Processing 51(3), 639–652 (2003). Publisher Full Text OpenURL

  20. S Haykin, Adaptive Filter Theory (Prentice-Hall, Englewood Cliffs, NJ, USA, 2002)

  21. L Tan, J Jiang, Adaptive Volterra filters for active control of nonlinear noise processes. IEEE Transactions on Signal Processing 49(8), 1667–1676 (2001). Publisher Full Text OpenURL