All discrete-time positive real functions interpolating input-output characteristics

It is an important problem in signal processing, system realization and system identification to find linear discrete-time systems which are consistent with given covariance parameters. This problem is formulated as a problem of finding discrete-time positive real functions which interpolate given covariance parameters. Among Various solutions to the problem, a recent remarkable one is a parameterization of all the discrete-time strictly positive real functions that interpolate the covariance parameters and have a limited McMillan degree. In this paper, we use more general input-output characteristics than covariance parameters and consider finding discrete-time positive real functions which interpolate such characteristics. The input-output characteristics are given by the coefficients of the Taylor series at some complex points in the open unit disk. Based on our previous work, we present an algorithm to generate all the discrete-time positive real functions that interpolate the input-output characteristics and have a limited McMillan degree. The algorithm is more general and simpler than the previous one, and is an important practical supplement to the previous work. Moreover, the interpolation of the general input-output characteristics can be effectively applied to the frequency-weighted model reduction. Hence, the algorithm makes a contribution to the problem from the practical viewpoint as well as the theoretical viewpoint.