Well-Posedness of the Rational Covariance Extension Problem

摘要

In this paper, the authors give a new proof of the solution of the rationalcovariance extension problem, an interpolation problem with historical roots in potential theory, and with recent application in speech synthesis, spectral estimation, stochastic systems theory, and systems identification. The heart of this problem is to parameterize, in useful systems theoretical terms, all rational, (strictly) positive real functions having a specified window of Laurent coefficients and a bounded degree. After giving an historical motivation and a survey of the rational covariance extension problem, the authors give a proof that the rational covariance extension problem is well-posed in the sense of Hadamard, i.e. a proof of existence, uniqueness and continuity of solutions with respect to the problem data. The paper concludes with a discussion of open problems.