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  • Research Article
  • Open Access

Wavelet-Based MPNLMS Adaptive Algorithm for Network Echo Cancellation

EURASIP Journal on Audio, Speech, and Music Processing20072007:096101

  • Received: 30 June 2006
  • Accepted: 24 January 2007
  • Published:


The μ-law proportionate normalized least mean square (MPNLMS) algorithm has been proposed recently to solve the slow convergence problem of the proportionate normalized least mean square (PNLMS) algorithm after its initial fast converging period. But for the color input, it may become slow in the case of the big eigenvalue spread of the input signal's autocorrelation matrix. In this paper, we use the wavelet transform to whiten the input signal. Due to the good time-frequency localization property of the wavelet transform, a sparse impulse response in the time domain is also sparse in the wavelet domain. By applying the MPNLMS technique in the wavelet domain, fast convergence for the color input is observed. Furthermore, we show that some nonsparse impulse responses may become sparse in the wavelet domain. This motivates the usage of the wavelet-based MPNLMS algorithm. Advantages of this approach are documented.


  • Autocorrelation
  • Input Signal
  • Impulse Response
  • Acoustics
  • Adaptive Algorithm


Authors’ Affiliations

Freescale Semiconductor, 7700 W. Parmer Lane, Austin, TX 78729, USA
Department of Electrical and Computer Engineering, The George Washington University, 801 22nd Street, N.W. Washington, DC 20052, USA


  1. Duttweiler DL: Proportionate normalized least-mean-squares adaptation in echo cancelers. IEEE Transactions on Speech and Audio Processing 2000,8(5):508-518. 10.1109/89.861368View ArticleGoogle Scholar
  2. Gay SL: An efficient, fast converging adaptive filter for network echo cancellation. Proceedings of the 32nd Asilomar Conference on Signals, Systems & Computers (ACSSC '98), November 1998, Pacific Grove, Calif, USA 1: 394-398.Google Scholar
  3. Deng H, Doroslovački M: Modified PNLMS adaptive algorithm for sparse echo path estimation. Proceedings of the Conference on Information Sciences and Systems, March 2004, Princeton, NJ, USA 1072-1077.Google Scholar
  4. Deng H, Doroslovački M: Improving convergence of the PNLMS algorithm for sparse impulse response identification. IEEE Signal Processing Letters 2005,12(3):181-184.View ArticleGoogle Scholar
  5. Deng H, Doroslovački M: Proportionate adaptive algorithms for network echo cancellation. IEEE Transactions on Signal Processing 2006,54(5):1794-1803.View ArticleGoogle Scholar
  6. Doroslovački M, Deng H: On convergence of proportionate-type NLMS adaptive algorithms. Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP '06), May 2006, Toulouse, France 3: 105-108.Google Scholar
  7. Haykin S: Adaptive Filter Theory. 4th edition. Prentice-Hall, Upper Saddle River, NJ, USA; 2002.MATHGoogle Scholar
  8. Doroslovački M, Fan H: Wavelet-based linear system modeling and adaptive filtering. IEEE Transactions on Signal Processing 1996,44(5):1156-1167. 10.1109/78.502328View ArticleGoogle Scholar
  9. Strang G, Nguyen T: Wavelets and Filter Banks. Wellesley-Cambridge Press, Wellesley, Mass, USA; 1996.MATHGoogle Scholar
  10. Shamma M, Doroslovački M: Comparison of wavelet and other transform based LMS adaptive algorithms for colored inputs. Proceedings of the Conference on Information Sciences and Systems, March 2000, Princeton, NJ, USA 2: FP5 17-FP5 20.Google Scholar
  11. Doroslovački M, Fan H: On-line identification of echo-path impulse responses by Haar-wavelet-based adaptive filter. Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP '95), May 1995, Detroit, Mich, USA 2: 1065-1068.Google Scholar


© H. Deng and M. Doroslovački. 2007

This article is published under license to BioMed Central Ltd. 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.