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Computation of the condition number of a nonsingular symmetric toeplitz matrix with the Levinson-durbin algorithm

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2 Author(s)
Benesty, J. ; INRS-EMT, Univ. du Quebec, Montreal, Que., Canada ; Gansler, Tomas

One well-known and widely used concept in signal processing is the optimal Wiener filtering, where a linear system (Wiener-Hopf equations) has to be solved. The symmetric Toeplitz matrix that naturally appears in this system is the covariance matrix. If this matrix is ill-conditioned and the data is perturbed, the accuracy of the solution will suffer a lot if the linear system is solved directly. One way to improve the accuracy is to regularize the covariance matrix. However, this regularization depends on the condition number: the higher the condition number, the larger the regularization. Therefore, it is important to be able to estimate this condition number in an efficient way, in order to use this information for improving the quality of the solution. Many other problems require the knowledge of this condition number for different reasons. Therefore, it is of great interest to find a practical algorithm to determine this condition number, which is the focus of this correspondence.

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Signal Processing, IEEE Transactions on  (Volume:54 ,  Issue: 6 )