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For a given spectral density $\Psi(s)$, the globally-minimal degree is the smallest degree of all its spectral factors $\mW(s)$.  \end{mydef}  Any system of globally-minimal degree is said to be \emph{globally minimal}. Anderson \cite{anderson} \cite{Anderson_1982}  provides an algebraic characterization of all realizations of all spectral factors as follows. Minimal realizations of $\mS$ are related to globally-minimal realizations of spectral factors of $\Psi$ by the following lemma. \begin{lemma}[\cite{anderson}] \begin{lemma}[\cite{Anderson_1982}]  \label{lemma:andlem}  Let $(A,B_s,C,D_s)$ be a minimal realization of the positive-real matrix $\mS(s)$ of \eqref{Zdef}, then the system $(A,B,C,D)$ is a globally-minimal realization of a spectral factor of $\Psi(s)$, i.e., $\mW(s)$ if and only if the following equations hold: