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In this paper, recent results by Petersen and Ran on the J-spectral factorization problem to rational matrix functions with constant signature that are not necessarily analytic at infinity are extended. In particular, a full parametrization of all J-spectral factors that have the same pole pair as a given square J-spectral factor is given. In this case a special realization involving a quintet of matrices is used.

J-spectral factorization for rational matrix functions with alternative realization