# Conal Distances Between Rational Spectral Densities

arXiv: https://arxiv.org/abs/1708.02818 · HTML: https://mlsanity.com/paper/1708.02818/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Aug 2017.

## Built on by (most cited first, 2 of 2)

- [Differential geometry with extreme eigenvalues in the positive semidefinite cone](https://mlsanity.com/paper/2304.07347/) (2023)
- [Fisher-Rao distance and pullback SPD cone distances between multivariate normal distributions](https://mlsanity.com/paper/2307.10644/) (2023)

## Abstract (arXiv)

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.