Robustness of the filtered-x LMS algorithm: part 1: necessary conditions for convergence and the asymptotic pseudospectrum of Toeplitz matrices
Fraanje, R., Verhaegen, M. and Elliott, S.J. (2007) Robustness of the filtered-x LMS algorithm: part 1: necessary conditions for convergence and the asymptotic pseudospectrum of Toeplitz matrices. IEEE Transactions on Signal Processing, 55, (8), 4029-4037. (doi:10.1109/TSP.2007.896083).
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Errors in the secondary path model of the filtered-x LMS (FXLMS) algorithm will lead to its divergence when the eigenvalues of the cross-correlation matrix between the estimated filtered reference and the true filtered reference signals are not all located in the right half plane. This cross-correlation matrix has a (block) Toeplitz structure whose dimension is determined by the number of adaptive filter coefficients. Using results on the asymptotic pseudospectrum of Toeplitz matrices, a frequency-domain condition on the model is derived to ensure stability. The condition is sufficient and necessary for a large number of filter coefficients. A transient analysis shows that the sufficient condition given by Wang and Ren  is only necessary to prevent an initial increase of the error in the adaptive filter coefficients (critical behavior).
|Digital Object Identifier (DOI):||doi:10.1109/TSP.2007.896083|
|Keywords:||toeplitz matrices, adaptive filter coefficients, asymptotic, pseudospectrum, block Toeplitz structure, cross-correlation matrix eigenvalues, filtered-x LMS algorithm robustness, frequency-domain condition, secondary path model, transient analysis, true filtered, reference signals|
|Subjects:||Q Science > Q Science (General)
T Technology > TA Engineering (General). Civil engineering (General)
|Divisions :||University Structure - Pre August 2011 > Institute of Sound and Vibration Research > Signal Processing and Control
|Accepted Date and Publication Date:||
|Date Deposited:||15 Nov 2007|
|Last Modified:||31 Mar 2016 12:26|
|RDF:||RDF+N-Triples, RDF+N3, RDF+XML, Browse.|
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