New Metrics Between Rational Spectra and their Connection to Optimal Transport

TL;DR

This paper introduces new metrics for rational spectra based on optimal transport, enabling efficient computation and applications in signal processing tasks like classification and clustering.

Contribution

It develops a novel class of metrics between rational spectra that leverage optimal transport and linear systems theory, with efficient computational methods and practical applications.

Findings

Metrics are computationally efficient and scalable.

Effective in signal classification, clustering, and detection.

Established connection to Wasserstein distance for rational spectra.

Abstract

We propose a series of metrics between pairs of signals, linear systems or rational spectra, based on optimal transport and linear-systems theory. The metrics operate on the locations of the poles of rational functions and admit very efficient computation of distances, barycenters, displacement interpolation and projections. We establish the connection to the Wasserstein distance between rational spectra, and demonstrate the use of the metrics in tasks such as signal classification, clustering, detection and approximation.