ABSTRACT
This chapter begins with a review of Szego polynomials, which provide orthonormal basis functions that prove convenient when working with weighted inner products. It examines to what extent the rational least-squares approximation problem can be converted to an equivalent unweighted rational least-squares problem, of interest since the unweighted approximation problem is generically easier to understand. The chapter explores the interaction between Hankel singular values and spectral weighting functions, in order to expose different approaches to introducing spectrally weighted Hankel singular values. It indicates how a Grammian of the weighted Hankel form arises from a covariance matrix constructed from input and output processes. The chapter generalizes some notions of shift operations over Szego polynomials. It examines some potential tools for studying convergence properties of a given adaptation algorithm for the undermodelled case. The chapter suggests that the overall transfer function so realized is unaltered by the transposition operation.
