Conal Distances Between Rational Spectral Densities

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 resulting 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.

24 pages, 4 figures. Revised version: title has been changed, several parts have been rewritten, two sections have been added (one illustrating some motivating examples, the other concerning a numerical example). Submitted for publication