A polynomial approach to the generalized Levinson algorithm based on the Toeplitz distance

A polynomial approach to the generalized Levinson algorithm based on the Toeplitz distance concept is given. It turns out that most properties of the standard Levinson algorithm admit natural generalizations, including the three-term recurrence relations, the Christoffel-Darboux formula, and the reflection coefficients (Schur-Szegö parameters) obtainable from the data via an extension of the Schur algorithm. The theory of∑-lossless transfer functions is shown to play the same illuminating role in the problem as the theory of Szegö orthogonal polynomials in the standard Levinson algorithm.