  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.
