Conal Distances Between Rational Spectral Densities


Type
Article
Change log
Authors
Baggio, Giacomo 
Ferrante, Augusto 
Sepulchre, Rodolphe  ORCID logo  https://orcid.org/0000-0002-7047-3124
Abstract

The paper generalizes Thompson and Hilbert metric to the space of spectral densities. The resulting complete metric space has the differentiable structure of a Finsler manifold with explicit geodesics. The corresponding distances are filtering invariant, can be computed efficiently, and admit geodesic paths that preserve rationality; these are properties of fundamental importance in many engineering applications.

Description
Keywords
Conal distances, Finsler geometry, Hilbert metric, linear filtering, rational spectral densities, spectral estimation, speech morphing, Thompson metric
Journal Title
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
Conference Name
Journal ISSN
0018-9286
1558-2523
Volume Title
64
Publisher
IEEE
Sponsorship
European Research Council (670645)
ERC