Block Toeplitz matrix inversion using Levinson polynomials

This paper addresses the problem of inverting positive definite Hermitian block Toeplitz matrixes using the associated matrix Levinson polynomial coefficients. In this context, the problem is reviewed here from a spectral estimation viewpoint, and the inversion formula originally obtained Gohberg and Semencul are derived here in terms of the corresponding reflection coefficient matrices and the coefficients of the matrix Levinson polynomial(s).