On a generalized Szegö- Levinson realization algorithm for optimal linear predictors based on a network synthesis approach

We show the correspondence between the following: i) the Darlington synthesis procedure, well known in the network theory literature; ii)J-coprime (MFD) representations of transfer functions; iii) the Szegö-Levinson theory of orthogonal polynomials on the unit circle; iv) the theory of generalized Schur indices; and v) the theory of NevanlinnaPick approximations. More specifically: i) and ii) are equivalent, ii) and iv) are also equivalent for a subclass of i) and ii), while v) provides a nice framework for the study of convergence properties. The paper produces also an exact and an approximate construction procedure of prediction and modeling filters of a general (ARMA) type, for stationary processes, and shows its convergence.