New Metrics Between Rational Spectra and their Connection to Optimal Transport
This work addresses the problem of comparing rational spectra in signal processing and control theory, offering a novel computational approach.
The authors introduced new metrics for comparing signals, linear systems, or rational spectra by combining optimal transport with linear-systems theory, focusing on pole locations for efficient computation of distances and related operations. They demonstrated applications in signal classification, clustering, detection, and approximation, though no specific performance numbers were provided.
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.