Skip to main content

Subband Affine Projection Algorithm for Acoustic Echo Cancellation System

Abstract

We present a new subband affine projection (SAP) algorithm for the adaptive acoustic echo cancellation with long echo path delay. Generally, the acoustic echo canceller suffers from the long echo path and large computational complexity. To solve this problem, the proposed algorithm combines merits of the affine projection (AP) algorithm and the subband filtering. Convergence speed of the proposed algorithm is improved by the signal-decorrelating property of the orthogonal subband filtering and the weight updating with the prewhitened input signal of the AP algorithm. Moreover, in the proposed algorithms, as applying the polyphase decomposition, the noble identity, and the critical decimation to subband the adaptive filter, the sufficiently decomposed SAP updates the weights of adaptive subfilters without a matrix inversion. Therefore, computational complexity of the proposed method is considerably reduced. In the SAP, the derived weight updating formula for the subband adaptive filter has a simple form as ever compared with the normalized least-mean-square (NLMS) algorithm. The efficiency of the proposed algorithm for the colored signal and speech signal was evaluated experimentally.

References

  1. 1.

    Widrow B, Stearns SD: Adaptive Signal Processing. Prentice-Hall, Englewood Cliffs, NJ, USA; 1985.

    Google Scholar 

  2. 2.

    Haykin S: Adaptive Filter Theory. 4th edition. Prentice-Hall, Upper Saddle River, NJ, USA; 2002.

    Google Scholar 

  3. 3.

    Ozeki K, Umeda T: An adaptive filtering algorithm using an orthogonal projection to an affine subspace and its properties. Electronics & Communications in Japan 1984,67(5):19–27.

    MathSciNet  Article  Google Scholar 

  4. 4.

    Sankaran SG, Beex AA: Convergence behavior of affine projection algorithms. IEEE Transactions on Signal Processing 2000,48(4):1086–1096. 10.1109/78.827542

    MathSciNet  Article  Google Scholar 

  5. 5.

    Gay SL, Benesty J: Acoustic Signal Processing for Telecommunication. Kluwer Academic, Boston, Mass, USA; 2000.

    Google Scholar 

  6. 6.

    Rupp M: A family of adaptive filter algorithms with decorrelating properties. IEEE Transactions on Signal Processing 1998,46(3):771–775. 10.1109/78.661344

    Article  Google Scholar 

  7. 7.

    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 

  8. 8.

    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

    MathSciNet  Article  Google Scholar 

  9. 9.

    Gay SL, Tavathia S: The fast affine projection algorithm. Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP '95), May 1995, Detroit, Mich, USA 5: 3023–3026.

    Google Scholar 

  10. 10.

    Tanaka M, Makino S, Kojima J: A block exact fast affine projection algorithm. IEEE Transactions on Speech and Audio Processing 1999,7(1):79–86. 10.1109/89.736333

    Article  Google Scholar 

  11. 11.

    Albu F, Kwan HK: Fast block exact Gauss-Seidel pseudo affine projection algorithm. Electronics Letters 2004,40(22):1451-1453. 10.1049/el:20046320

    Article  Google Scholar 

  12. 12.

    Vaidyanathan PP: Multirate Systems and Filter Banks. Prentice-Hall, Englewood Cliffs, NJ, USA; 1993.

    Google Scholar 

  13. 13.

    Pradhan SS, Reddy VU: A new approach to subband adaptive filtering. IEEE Transactions on Signal Processing 1999,47(3):655–664. 10.1109/78.747773

    Article  Google Scholar 

  14. 14.

    Petraglia MR, Alves RG, Diniz PSR: New structures for adaptive filtering in subbands with critical sampling. IEEE Transactions on Signal Processing 2000,48(12):3316–3327. 10.1109/78.886995

    MathSciNet  Article  Google Scholar 

  15. 15.

    Miyagi S, Sakai H: Convergence analysis of alias-free subband adaptive filters based on a frequency domain technique. IEEE Transactions on Signal Processing 2004,52(1):79–89. 10.1109/TSP.2003.820076

    MathSciNet  Article  Google Scholar 

  16. 16.

    Makino S, Strauss K, Shimauchi S, Haneda Y, Nakagawa A: Subband streo echo canceller using the projection algorithm with convergence to the true echo path. Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP '97), April 1997, Munich, Germany 1: 299–302.

    Google Scholar 

  17. 17.

    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 

  18. 18.

    Liu QG, Champagne B, Ho KC: On the use of a modified fast affine projection algorithm in subbands for acoustic echo cancelation. Proceedings of the IEEE Digital Signal Processing Workshop, September 1996, Loen, Norway 354–357.

    Google Scholar 

  19. 19.

    Chau E, Sheikhzadeh H, Brennan RL: Complexity reduction and regularization of a fast affine projection algorithm for oversampled subband adaptive filters. Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP '04), May 2004, Montreal, Quebec, Canada 5: 109–112.

    Google Scholar 

  20. 20.

    Nishikawa K, Kiya H: New structure of affine projection algorithm using a novel subband adaptive system. Proceedings of the 3rd IEEE Workshop on Signal Processing Advances in Wireless Communications (SPAWC '01), March 2001, Taoyuan, Taiwan 364–367.

    Google Scholar 

  21. 21.

    Abutalebi HR, Sheikhzadeh H, Brennan RL, Freeman GH: Affine projection algorithm for oversampled subband adaptive filters. Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP '03), April 2003, Hong Kong 6: 209–212.

    Google Scholar 

  22. 22.

    Chong EKP, Zak SH: An Introduction to Optimization. John Wiley & Sons, New York, NY, USA; 1996.

    Google Scholar 

  23. 23.

    Moon TK, Stirling WC: Mathematical Methods and Algorithms. Prentice-Hall, Englewood Cliffs, NJ, USA; 2000.

    Google Scholar 

  24. 24.

    de Almeida SJM, Bermudez JCM, Bershad NJ, Costa MH: A statistical analysis of the affine projection algorithm for unity step size and autoregressive inputs. IEEE Transactions on Circuits and Systems I: Regular Papers 2005,52(7):1394–1405.

    MathSciNet  Article  Google Scholar 

  25. 25.

    Lin Y-P, Vaidyanathan PP: A kaiser window approach for the design of prototype filters of cosine modulated filterbanks. IEEE Signal Processing Letters 1998,5(6):132–134. 10.1109/97.681427

    Article  Google Scholar 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to Hun Choi.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Choi, H., Bae, H. Subband Affine Projection Algorithm for Acoustic Echo Cancellation System. EURASIP J. Adv. Signal Process. 2007, 075621 (2006). https://doi.org/10.1155/2007/75621

Download citation

Keywords

  • Computational Complexity
  • Quantum Information
  • Speech Signal
  • Convergence Speed
  • Adaptive Filter