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

2016/09/09 by Giacomo Baggio, Baggio, Giacomo, Augusto Ferrante +1
Mathematics · #Advanced Topics in Algebra #FOS: Mathematics #Numerical methods for differential equations #Optimization and Control (math.OC) #math.OC

paper · pdf · doi:10.48550/arxiv.1609.02711

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

openalex publication_date 2016/09/09 · arxiv created 2017/11/29 · arxiv updated 2017/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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].

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