On the factorization of rational discrete-time spectral densities
G Baggio, A Ferrante - IEEE Transactions on Automatic Control, 2015 - ieeexplore.ieee.org
G Baggio, A Ferrante
IEEE Transactions on Automatic Control, 2015•ieeexplore.ieee.orgIn 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)= WT (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 be viewed as the discrete-time counterpart of the …
show with a constructive proof that Φ (z) admits a factorization of the form Φ (z)= WT (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 be viewed as the discrete-time counterpart of the …
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 T (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 be viewed as the discrete-time counterpart of the matrix factorization method devised by Youla in his celebrated work [48].
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