On the Construction of Orthonormal Basis Functions for System Identification

Abstract

In this paper we present an alternative derivation of orthonormal rational families in H2, based on previous work by Roberts and Mullis. The construction is based on balanced state space realizations of all-pass transfer functions, and generalizes recent work of Heuberger et al. The emphasis is put on the simplicity of this approach compared with traditional methods. We also present some historical remarks concerning earlier approaches to this problem, as well as completeness ami uniform boundedness conditions for this family of orthonormal functions.