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Conal Distances Between Rational Spectral Densities

Accepted version
Peer-reviewed

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