基于循环平稳特性的时频分析法欠定盲源分离
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摘要
基于二次时频分布的算法是解决欠定盲源分离问题的一种有效方法。不同于传统算法,针对循环平稳信号,借助分段平均的周期图法求解谱相关密度函数,并利用其实现Wigner-Ville时频分布的重构。计算信号时频分布矩阵并找出自源时频点,利用自源时频点对应的时频分布矩阵构建新的3阶张量模型。利用平行因子分解,直接实现源信号的分离。该算法不需要假设任意时频点的源数目,不大于混合信号数目。仿真实验结果表明,所提出的方法可以有效地抑制噪声,并且只需要一步即可实现源信号的恢复,避免"两步法"造成的误差叠加,提高了盲源分离的效率和性能。
Quadratic time-frequency distribution(TFD) is an effective method to solve the underdetermined blind source separation problems.In the proposed method,the cyclic spectrum density(CSD) is calculated using the piecewise average periodogram method,which is used to reconstruct the Wigner-Ville distribution(WVD).The auto-term TF points are detected after computing the matrixes of TFDs,and a new three-order tensor is folded by the chosen TFD matrixes.At last,PARAFAC decomposition is applied to separate the sources directly,which does not assume that the number of active sources at any TF point is not larger than the sensor number.Simulation results demonstrate that the proposed method can suppress die noise effectively and separate the sources directly with only one step,avoiding the superposition of error of "two-step" methods,which improves the performance and efficiency of separation.
Quadratic time-frequency distribution(TFD) is an effective method to solve the underdetermined blind source separation problems.In the proposed method,the cyclic spectrum density(CSD) is calculated using the piecewise average periodogram method,which is used to reconstruct the Wigner-Ville distribution(WVD).The auto-term TF points are detected after computing the matrixes of TFDs,and a new three-order tensor is folded by the chosen TFD matrixes.At last,PARAFAC decomposition is applied to separate the sources directly,which does not assume that the number of active sources at any TF point is not larger than the sensor number.Simulation results demonstrate that the proposed method can suppress die noise effectively and separate the sources directly with only one step,avoiding the superposition of error of "two-step" methods,which improves the performance and efficiency of separation.
引文
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[14]De Lathauwer L.A link between the canonical decomposition in multilinear algebra and simultaneous matrix diagonalization[J].SIAM Journal on Matrix Analysis and Application,2006,28(3):642-666.
[15]Nion D,De Lathauwer L.An enhanced line search scheme for complex-valued tensor decompositions application in DS-CDMA[J].Signal Processing,2008,88(3):749-755.
[16]Nion D,Sidiropoulos N D.Tensor algebra and multidimensional harmonic retrieval in signal processing for MIMO radar[J].IEEE Transactions on Signal Processing,2010,58(11):5693-5705.
[17]Lu F,Huang Z,Jiang W.Underdetermined blind separation of non-disjoint signals in time-frequency domain based on matrix diagonalization[J].Signal Processing,2011,91(7):1568-1577.
[2]邓兵,陶然.尹德强.分数阶傅里叶域的阵列信号盲分离方法[J].兵工学报,2009,30(11):1451-1456.DENG Bing,TAO Ran,YIN De-qiang.Blind source separation of the array signal in the franctional fourier domain[J].Acta Armamentarii,2009,30(11):1451-1456.(in Chinese)
[3]Bofill P,Zibulevsky M.Underdetermined blind source separation using sparse representations[J].Signal Processing,2001,81(11):2353-2362.
[4]Belouchrani A,Amin M G,Nadege T M,et al.Source separation and localization using time-frequency distributions:an overview[J].IEEE Signal Processing Magazine,2013,30(6):97-107.
[5]Linh-Trung N,Belouchrani A,Abed-Meraim K,et al.Separating more sources than sensors using time-frequency distributions[J].EURASIP Journal on Applied Signal Processing,2005,2005(17):2828-2847.
[6]Aissa-El-Bey A,Linh-Trung N,Abed-Meraim K,et al.Underdetermind blind separation of nondisjoint sources in the time-frequency domain[J].IEEE Transaction on Signal Process,2007,55(3):897-907.
[7]Peng D Z,Xiang Y.Underdetermined blind source separation based on relaxed sparsity condition of sources[J].IEEE Transaction on Signal Process,2009,57(2):809-814.
[8]Peng D Z,Xiang Y.Underdetermined blind separation of nonsparse sources using spatial time-frequency distributions[J].Digital Signal Processing,2010,20(2):581-596.
[9]Xie S L,Yang L,Yang J M,et al.Time-frequency approach to underdetermined blind source separation[J].IEEE Transaction on Neural Network and Learning System,2012,23(2):306-316.
[10]Guo J,Zeng X P,She Z S.Blind source separation based on high-resolution time-frequency distributions[J].Computer and Electrical Engineering,2012,38(1):175-184.
[11]Ghaderi F,Makkiabadi B,McWhirter J G,et al.Blind source extraction of cyclostationary sources with common cyclic frequencies[C]//Proceedings of International conference on Acoustics,Speech and Signal Processing.Dallas,Texas,US:IEEE,2010:4146-4149.
[12]Lu F,Zhang B,Huang Z,et al.Blind identification of underdetermined mixtures using second-order cyclostationary statistics[J].Chinese Journal of Electronics,2013,22(1):31-35.
[13]Zhou Y,Chen J,Dong G M,et al.Wigner-Ville distribution based on cyclic spectral density and the application in rolling element bearing diagnosis[J].Proceedings of the Institution of Mechanical Engineers Part C-Journal of Mechanical Engineering Science,2011,225(12):2831-2847.
[14]De Lathauwer L.A link between the canonical decomposition in multilinear algebra and simultaneous matrix diagonalization[J].SIAM Journal on Matrix Analysis and Application,2006,28(3):642-666.
[15]Nion D,De Lathauwer L.An enhanced line search scheme for complex-valued tensor decompositions application in DS-CDMA[J].Signal Processing,2008,88(3):749-755.
[16]Nion D,Sidiropoulos N D.Tensor algebra and multidimensional harmonic retrieval in signal processing for MIMO radar[J].IEEE Transactions on Signal Processing,2010,58(11):5693-5705.
[17]Lu F,Huang Z,Jiang W.Underdetermined blind separation of non-disjoint signals in time-frequency domain based on matrix diagonalization[J].Signal Processing,2011,91(7):1568-1577.