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Blind Separation of Nonstationary Sources Based on Spatial Time-Frequency Distributions

EURASIP Journal on Advances in Signal Processing20062006:064785

Received: 1 January 2006

Accepted: 13 August 2006

Published: 10 October 2006


Blind source separation (BSS) based on spatial time-frequency distributions (STFDs) provides improved performance over blind source separation methods based on second-order statistics, when dealing with signals that are localized in the time-frequency (t-f) domain. In this paper, we propose the use of STFD matrices for both whitening and recovery of the mixing matrix, which are two stages commonly required in many BSS methods, to provide robust BSS performance to noise. In addition, a simple method is proposed to select the auto- and cross-term regions of time-frequency distribution (TFD). To further improve the BSS performance, t-f grouping techniques are introduced to reduce the number of signals under consideration, and to allow the receiver array to separate more sources than the number of array sensors, provided that the sources have disjoint t-f signatures. With the use of one or more techniques proposed in this paper, improved performance of blind separation of nonstationary signals can be achieved.


Information TechnologyQuantum InformationSeparation MethodArray SensorSource Separation


Authors’ Affiliations

Wireless Communications and Positioning Lab, Center for Advanced Communications, Villanova University, Villanova, USA


  1. Tong L, Inouye Y, Liu R-W: Waveform-preserving blind estimation of multiple independent sources. IEEE Transactions on Signal Processing 1993, 41(7):2461-2470. 10.1109/78.224254View ArticleMATHGoogle Scholar
  2. Cardoso JF, Souloumiac A: Blind beamforming for non-Gaussian signals. IEE Proceedings, Part F: Radar and Signal Processing 1993, 140(6):362-370. 10.1049/ip-f-2.1993.0054Google Scholar
  3. Belouchrani A, Abed-Meraim K, Cardoso J-F, Moulines E: Blind source separation technique using second-order statistics. IEEE Transactions on Signal Processing 1997, 45(2):434-444. 10.1109/78.554307View ArticleGoogle Scholar
  4. Grellier O, Comon P: Blind separation of discrete sources. IEEE Signal Processing Letters 1998, 5(8):212-214. 10.1109/97.704975View ArticleGoogle Scholar
  5. Chen B, Petropulu AP: Frequency domain blind MIMO system identification based on second- and higher order statistics. IEEE Transactions on Signal Processing 2001, 49(8):1677-1688. 10.1109/78.934137View ArticleGoogle Scholar
  6. Hyvärinen A, Karhunen J, Oja E: Independent Component Analysis. John Wiley & Sons, New York, NY, USA; 2001.View ArticleGoogle Scholar
  7. Hyvärinen A: Survey on independent component analysis. Neural Computing Surveys 1999, 2: 94-128.Google Scholar
  8. O'Grady PD, Pearlmutter BA, Rickard ST: Survey of sparse and non-sparse methods in source separation. International Journal of Imaging Systems and Technology 2005, 15(1):18-33. special issue on Blind Source Separation and Deconvolution in Imaging and Image Processing 10.1002/ima.20035View ArticleGoogle Scholar
  9. Chen V, Ling H: Time-Frequency Transforms for Radar Imaging and Signal Analysis. Artech House, Boston, Mass, USA; 2002.MATHGoogle Scholar
  10. Boashash B (Ed): Time-Frequency Signal Analysis and Processing. Elsevier, Oxford, UK; 2003.MATHGoogle Scholar
  11. Debnath L (Ed): Wavelets and Signal Processing. Birkhäuser, Boston, Mass, USA; 2003.MATHGoogle Scholar
  12. Belouchrani A, Amin MG: Blind source separation based on time-frequency signal representations. IEEE Transactions on Signal Processing 1998, 46(11):2888-2897. 10.1109/78.726803View ArticleGoogle Scholar
  13. Leyman AR, Kamran ZM, Abed-Meraim K: Higher-order time frequency-based blind source separation technique. IEEE Signal Processing Letters 2000, 7(7):193-196. 10.1109/97.847366View ArticleGoogle Scholar
  14. Belouchrani A, Abed-Meraim K, Amin MG, Zoubir AM: Joint anti-diagonalization for blind source separation. Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP '01), May 2001, Salt Lake, Utah, USA 5: 2789-2792.Google Scholar
  15. Giulieri L, Thirion-Moreau N, Arquès P-Y: Blind sources separation based on bilinear time-frequency representations: a performance analysis. Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP '02), May 2002, Orlando, Fla, USA 2: 1649-1652.Google Scholar
  16. Févotte C, Doncarli C: Two contributions to blind source separation using time-frequency distributions. IEEE Signal Processing Letters 2004, 11(3):386-389. 10.1109/LSP.2003.819343View ArticleGoogle Scholar
  17. Linh-Trung N, Belouchrani A, Abed-Meraim K, Boashash B: Separating more sources than sensors using time-frequency distributions. EURASIP Journal on Applied Signal Processing 2005, 2005(17):2828-2847. 10.1155/ASP.2005.2828View ArticleMATHGoogle Scholar
  18. Mu W, Amin MG, Zhang Y: Bilinear signal synthesis in array processing. IEEE Transactions on Signal Processing 2003, 51(1):90-100. 10.1109/TSP.2002.806577MathSciNetView ArticleGoogle Scholar
  19. Yilmaz Ö, Rickard S: Blind separation of speech mixtures via time-frequency masking. IEEE Transactions on Signal Processing 2004, 52(7):1830-1847. 10.1109/TSP.2004.828896MathSciNetView ArticleGoogle Scholar
  20. Yeredor A: Non-orthogonal joint diagonalization in the least-squares sense with application in blind source separation. IEEE Transactions on Signal Processing 2002, 50(7):1545-1553. 10.1109/TSP.2002.1011195MathSciNetView ArticleGoogle Scholar
  21. Giulieri L, Thirion-Moreau N, Arquès P-Y: Blind sources separation based on quadratic time-frequency representations: a method without pre-whitening. Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP '03), April 2003, Hong Kong 5: 289-292.Google Scholar
  22. Bofill P, Zibulevsky M: Blind separation of more sources than mixtures using sparsity of their short-time Fourier transform. Proceedings of the 2nd International Workshop on Independent Component Analysis and Blind Signal Separation, June 2000, Helsinki, Finland 87-92.Google Scholar
  23. Aïssa-El-Bey A, Abed-Meraim K, Grenier Y: Underdetermined blind source separation of audio sources in time-frequency domain. Proceedings of the Signal Processing with Adaptive Sparse Structured Representations (SPARS '05), November 2005, Rennes, FranceGoogle Scholar
  24. Rickard S, Melia T, Fearon C: DESPRIT—histogram based blind source separation of more sources than sensors using subspace methods. Proceedings of IEEE Workshop on Applications of Signal Processing to Audio and Acoustics (WASPAA '05), October 2005, New Paltz, NY, USA 5-8.Google Scholar
  25. Cirillo LA, Amin MG: Auto-term detection using time-frequency array processing. Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP '03), April 2003, Hong Kong 6: 465-468.Google Scholar
  26. Zhang Y, Mu W, Amin MG: Subspace analysis of spatial time-frequency distribution matrices. IEEE Transactions on Signal Processing 2001, 49(4):747-759. 10.1109/78.912919View ArticleGoogle Scholar
  27. Holobar A, Fevotte C, Doncarli C, Zazula D: Single autoterms selection for blind source separation in time-frequency plane. Proceedings of 11th European Signal Processing Conference (EUSIPCO '02), September 2002, Toulouse, France 565-568.Google Scholar
  28. Zhang Y, Amin MG: Spatial averaging of time-frequency distributions for signal recovery in uniform linear arrays. IEEE Transactions on Signal Processing 2000, 48(10):2892-2902. 10.1109/78.869043MathSciNetView ArticleGoogle Scholar
  29. Amin MG, Zhang Y: Direction finding based on spatial time-frequency distribution matrices. Digital Signal Processing 2000, 10(4):325-339. 10.1006/dspr.2000.0374View ArticleGoogle Scholar
  30. Zhang Y, Amin MG: Blind separation of sources based on their time-frequency signatures. Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP '00), June 2000, Istanbul, Turkey 5: 3132-3135.Google Scholar
  31. Zhang Y, Amin MG, Frazer GJ: A new approach to FM jammer suppression for digital communications. Proceedings of IEEE Sensor Array and Multichannel Signal Processing Workshop, August 2002, Rosslyn, Va, USAGoogle Scholar
  32. Boudreaux-Bartels GF, Parks TW: Time-varying filtering and signal estimation using Wigner distribution synthesis techniques. IEEE Transactions on Acoustics, Speech, and Signal Processing 1986, 34(3):442-451. 10.1109/TASSP.1986.1164833MathSciNetView ArticleGoogle Scholar
  33. Krattenthaler W, Hlawatsch F: Time-frequency design and processing of signals via smoothed Wigner distributions. IEEE Transactions on Signal Processing 1993, 41(1):278-287. 10.1109/TSP.1993.193145View ArticleMATHGoogle Scholar
  34. Hlawatsch F, Krattenthaler W: Bilinear signal synthesis. IEEE Transactions on Signal Processing 1992, 40(2):352-363. 10.1109/78.124945View ArticleMATHGoogle Scholar


© Zhang and Amin 2006

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.