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

Abstract

In this paper, the problem of providing a complete parametrization of the minimal spectral factors of a discrete-time rational spectral density is considered. The desired parametrization, given in terms of the all-pass divisors of a certain all-pass function, is established in the most general setting: after several partial results, mostly in the continuous-time case, this is indeed the first complete parametrization obtained without resorting to any facilitating assumption. This result provides a positive answer to a conjecture raised in [Baggio and Ferrante, 2016].

25 pages, no figures. Revised version: the introduction has been largely rewritten and a numerical example has been inserted. Extended version of manuscript submitted to IEEE Transactions on Automatic Control