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