Linear prediction in the singular case and the stability of eigen models

The paper gives some insight on the use of Levinson´s recursion on non positive Toeplitz matrices. The critical case, where a principal minor is zero, leads to define a new lossless lattice structure with zeros on the unit circle, also useful in the standard case. The stability of the AR models built on the eigen vectors of a Toeplitz is also examined, most of the corresponding zeros are shown to lie on the unit circle. The results apply to noise cancellation, spectral line analysis and computation of eigenvectors of correlation matrices.