  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.
