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

EURASIP Journal on Audio, Speech, and Music Processing volume 2007, Article number: 031314 (2007) Cite this article

Abstract

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.

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References

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

    Google Scholar 

  2. Douglas SC: Fast implementations of the filtered-X LMS and LMS algorithms for multichannel active noise control. IEEE Transactions on Speech and Audio Processing 1999,7(4):454-465. 10.1109/89.771315

    Article  Google Scholar 

  3. Bouchard M: Multichannel affine and fast affine projection algorithms for active noise control and acoustic equalization systems. IEEE Transactions on Speech and Audio Processing 2003,11(1):54-60. 10.1109/TSA.2002.805642

    Article  Google Scholar 

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

    Article  Google Scholar 

  5. Neuvo Y, Dong C-Y, Mitra SK: Interpolated finite impulse response filters. IEEE Transactions on Acoustics, Speech, and Signal Processing 1984,32(3):563-570. 10.1109/TASSP.1984.1164348

    Article  Google Scholar 

  6. Werner S, Diniz PSR: Set-membership affine projection algorithm. IEEE Signal Processing Letters 2001,8(8):231-235. 10.1109/97.935739

    Article  Google Scholar 

  7. Douglas SC: Adaptive filters employing partial updates. IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing 1997,44(3):209-216. 10.1109/82.558455

    Article  Google Scholar 

  8. Doğançay K, Tanrikulu O: Adaptive filtering algorithms with selective partial updates. IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing 2001,48(8):762-769. 10.1109/82.959866

    Article  MATH  Google Scholar 

  9. Sicuranza GL, Carini A: 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.

    Google Scholar 

  10. Bjarnason E: Analysis of the filtered-X LMS algorithm. IEEE Transactions on Speech and Audio Processing 1995,3(6):504-514. 10.1109/89.482218

    Article  Google Scholar 

  11. Tobias OJ, Bermudez JCM, Bershad NJ: Mean weight behavior of the filtered-X LMS algorithm. IEEE Transactions on Signal Processing 2000,48(4):1061-1075. 10.1109/78.827540

    Article  Google Scholar 

  12. Shin H-C, Sayed AH: Mean-square performance of a family of affine projection algorithms. IEEE Transactions on Signal Processing 2004,52(1):90-102. 10.1109/TSP.2003.820077

    Article  MathSciNet  Google Scholar 

  13. Bouchard M, Quednau S: 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 2000,8(5):606-618. 10.1109/89.861382

    Article  Google Scholar 

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

    Google Scholar 

  15. Strauch P, Mulgrew B: Active control of nonlinear noise processes in a linear duct. IEEE Transactions on Signal Processing 1998,46(9):2404-2412. 10.1109/78.709529

    Article  Google Scholar 

  16. Das DP, Panda G: Active mitigation of nonlinear noise processes using a novel filtered-s LMS algorithm. IEEE Transactions on Speech and Audio Processing 2004,12(3):313-322. 10.1109/TSA.2003.822741

    Article  Google Scholar 

  17. Elliott SJ, Stothers I, Nelson PA: A multiple error LMS algorithm and its application to the active control of sound and vibration. IEEE Transactions on Acoustics, Speech, and Signal Processing 1987,35(10):1423-1434. 10.1109/TASSP.1987.1165044

    Article  Google Scholar 

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

    Google Scholar 

  19. Al-Naffouri TY, Sayed AH: Transient analysis of data-normalized adaptive filters. IEEE Transactions on Signal Processing 2003,51(3):639-652. 10.1109/TSP.2002.808106

    Article  Google Scholar 

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

    MATH  Google Scholar 

  21. Tan L, Jiang J: Adaptive Volterra filters for active control of nonlinear noise processes. IEEE Transactions on Signal Processing 2001,49(8):1667-1676. 10.1109/78.934136

    Article  Google Scholar 

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Authors and Affiliations

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

    Alberto Carini

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

    Giovanni L Sicuranza

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  1. Alberto Carini
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  2. Giovanni L Sicuranza
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Correspondence to Alberto Carini.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Carini, A., Sicuranza, G.L. Analysis of Transient and Steady-State Behavior of a Multichannel Filtered-x Partial-Error Affine Projection Algorithm. J AUDIO SPEECH MUSIC PROC. 2007, 031314 (2007). https://doi.org/10.1155/2007/31314

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  • DOI: https://doi.org/10.1155/2007/31314

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