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).
Download
Full text not available from this repository.
Description/Abstract
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 [1999] is only necessary to prevent an initial increase of the error in the adaptive filter coefficients (critical behavior).
| Item Type: | Article |
|---|---|
| Additional Information: | |
| ISSNs: | 1053-587X (print) |
| Related URLs: | |
| 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 |
| Item ID: | 49555 |
| Date Deposited: | 15 Nov 2007 |
| Last Modified: | 02 Mar 2012 11:30 |
| Contributors: | Fraanje, R. (Author) Verhaegen, M. (Author) Elliott, S.J. (Author) |
| Date: | August 2007 |
| Additional Information: | |
| Status: | Published |
| URI: | http://eprints.soton.ac.uk/id/eprint/49555 |
Actions (login required)
 |
View Item |
