On Minimal Spectral Factors With Zeroes and Poles Lying on Prescribed Regions

Abstract

In this paper, we consider a general discrete-time spectral factorization problem for rational matrixvalued functions. We build on a recent result establishing existence of a spectral factor whose zeroes and poles lie in any pair of prescribed regions of the complex plane featuring a geometry compatible with symplectic symmetry. In this general setting, uniqueness of the spectral factor is not guaranteed. It was, however, conjectured that if we further impose stochastic minimality, uniqueness can be recovered.The main result of his paper is a proof of this conjecture.

Parametrization of Minimal Spectral Factors of Discrete-Time Rational Spectral Densities

“…These conditions, together with (5), guarantee that the right-hand side of ( 3) is all-pass [13, Theorem 2.1, point 3)]. As for (ii), by taking into account that…”

“…In [4], a general result on discrete-time spectral factorization was established and two conjectures were left to further investigation: one was answered in the affirmative in [5]. The other Giacomo Baggio is with the Dipartimento di Ingegneria dell'Informazione, Università di Padova, via Gradenigo, 6/B I-concerns the parametrization of the set of minimal spectral factors (i.e.…”

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