A parametrization of discrete-time positive real functions interpolating input-output characteristics

We consider a problem of finding discrete-time positive real functions which interpolate the given input-output characteristics. The input-output characteristics are given by the coefficients of the Taylor series at some complex points in the open unit disk. The problem is a generalization of the interpolation problem of covariance parameters, which is important in signal processing, system realization and system identification. We present an algorithm to parametrize all the discrete-time positive real functions that interpolate the input-output characteristics and have a limited McMillan degree