In this paper, we consider an arbitrary matrix-valued, rational spectral density Φ(z). We show with a constructive proof that Φ(z) admits a factorization of the form Φ(z)=W^ (z^-1)W(z), where W(z) is stochastically minimal. Moreover, W(z) and its right inverse are analytic in regions that may be selected with the only constraint that they satisfy some symplectic-type conditions. By suitably selecting the analyticity regions, this extremely general result particularizes into a corollary that may

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... be viewed as the discrete-time counterpart of the matrix factorization method devised by Youla in his celebrated work (Youla, 1961).