On partial realization and interpolation of models from orthogonal basis function expansions∗

In this paper we address the problem of computing a minimal state-space realization from partial knowledge of an expansion in terms of generalized rational orthogonal basis functions. The basis functions considered are generated by stable all-pass £lters. It is shown how a minimal state-space realization can be found on the basis of complete knowledge of the expansion coef£cients. Subsequently an algorithm is given that solves the partial realization problem, meaning that it computes a minimal realization on the basis of a £nite number of expansion coef£cients. The analysis also results in compact expressions for computing the Hambo transform underlying this basis expansion as well as its inverse. Finally it is shown how these realization problems are related to the interpolation problem of £nding a rational model of minimal degree that interpolates to the derivatives of a transfer function in a given set of points outside the unit disc.