Recovery of rational functions via Hankel pencil method and sensitivities of the poles

In the paper, we develop a new method for the recovery of rational functions. Our idea is based on the property that Fourier coefficients of rational functions have the exponential structure and reconstruction of this exponential structure with the ESPRIT method in the frequency domain. Further we present sensitivity analysis for poles of rational functions reconstructed with our method in case of unstructured and structured perturbations. Finally, we consider several numerical experiments and, using sensitivities, explain the recovery errors for poles.