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Matrix spectral factorization is traditionally described as finding spectralfactors having a fixed analytic pole configuration. The classification ofspectral factors then involves studying the solutions of a certain algebraicRiccati equation which parametrizes their zero structure. The pole structure ofthe spectral factors can be also parametrized in terms of solutions of anotherRiccati equation. We study the relation between the solution sets of these twoRiccati equations and describe the construction of general spectral factorswhich involve both zero- and pole-flipping on an arbitrary reference spectralfactor.

On the state space and dynamics selection in linear stochastic models: a spectral factorization approach