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A new proof of the minimum phase property of the unit delay prediction error operator-revisited

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2 Author(s)
Ulrych, T.J. ; PPPG/UFBa, Salvador, Brazil ; Treitel, Sven

It is shown, using the properties of the eigenvectors of doubly symmetric matrices, that the prediction error operator which is computed from normal equations of Toeplitz form is minimum phase. A requirement is that the Toeplitz matrix be positive definite. It is interesting to note that the special properties of the eigenvectors which correspond to the minimum and maximum eigenvalues, namely, that the zeros of these eigenvectors lie on the unit circle, are not required in the proof. A correct proof based on spectral decomposition is presented

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Signal Processing, IEEE Transactions on  (Volume:39 ,  Issue: 1 )