Skip to main content

Exploiting Narrowband Efficiency for Broadband Convolutive Blind Source Separation


Based on a recently presented generic broadband blind source separation (BSS) algorithm for convolutive mixtures, we propose in this paper a novel algorithm combining advantages of broadband algorithms with the computational efficiency of narrowband techniques. By selective application of the Szegö theorem which relates properties of Toeplitz and circulant matrices, a new normalization is derived as a special case of the generic broadband algorithm. This results in a computationally efficient and fast converging algorithm without introducing typical narrowband problems such as the internal permutation problem or circularity effects. Moreover, a novel regularization method for the generic broadband algorithm is proposed and subsequently also derived for the proposed algorithm. Experimental results in realistic acoustic environments show improved performance of the novel algorithm compared to previous approximations.


  1. Hyvaerinen A, Karhunen J, Oja E: Independent Component Analysis. John Wiley & Sons, New York, NY, USA; 2001.

    Book  Google Scholar 

  2. Buchner H, Aichner R, Kellermann W: TRINICON: a versatile framework for multichannel blind signal processing. Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP '04), May 2004, Montreal, Quebec, Canada 3: 889–892.

    Google Scholar 

  3. Buchner H, Aichner R, Kellermann W: A generalization of blind source separation algorithms for convolutive mixtures based on second-order statistics. IEEE Transactions on Speech and Audio Processing 2005,13(1):120-134.

    Article  Google Scholar 

  4. Buchner H, Aichner R, Kellermann W: Blind source separation for convolutive mixtures: a unified treatment. In Audio Signal Processing for Next-Generation Multimedia Communication Systems. Edited by: Huang Y, Benesty J. Kluwer Academic, Boston, Mass, USA; 2004:255-293.

    Chapter  Google Scholar 

  5. Aichner R, Buchner H, Yan F, Kellermann W: A real-time blind source separation scheme and its application to reverberant and noisy acoustic environments. Signal Processing 2006,86(6):1260-1277. 10.1016/j.sigpro.2005.06.022

    Article  Google Scholar 

  6. Haykin S: Adaptive Filter Theory. 4th edition. Prentice Hall, Englewood Cliffs, NJ, USA; 2002.

    MATH  Google Scholar 

  7. Markel JD, Gray AH: Linear Prediction of Speech. Springer, Berlin, Germany; 1976.

    Book  Google Scholar 

  8. Aichner R, Buchner H, Kellermann W: On the causality problem in time-domain blind source separation and deconvolution algorithms. Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP '05), March 2005, Philadelphia, Pa, USA 5: 181–184.

    Google Scholar 

  9. Parra L, Spence C: Convolutive blind separation of non-stationary sources. IEEE Transactions on Speech and Audio Processing 2000,8(3):320-327. 10.1109/89.841214

    Article  Google Scholar 

  10. Gray RM: On the asymptotic eigenvalue distribution of Toeplitz matrices. IEEE Transactions on Information Theory 1972,18(6):725-730. 10.1109/TIT.1972.1054924

    MathSciNet  Article  Google Scholar 

  11. Sherman PJ: Circulant approximations of the inverses of Toeplitz matrices and related quantities with applications to stationary random processes. IEEE Transactions on Acoustics, Speech, and Signal Processing 1985,33(6):1630-1632. 10.1109/TASSP.1985.1164723

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations


Corresponding author

Correspondence to Robert Aichner.

Rights and permissions

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

Reprints and Permissions

About this article

Cite this article

Aichner, R., Buchner, H. & Kellermann, W. Exploiting Narrowband Efficiency for Broadband Convolutive Blind Source Separation. EURASIP J. Adv. Signal Process. 2007, 016381 (2006).

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI:


  • Information Technology
  • Quantum Information
  • Computational Efficiency
  • Previous Approximation
  • Regularization Method