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.

翻译：本文提出了一种新的有理函数恢复方法。我们的思路基于有理函数傅里叶系数具有指数结构的特性，并利用频域中的ESPRIT方法重建该指数结构。进一步，我们针对非结构扰动和结构扰动两种情况，对通过本方法重建的有理函数极点进行了灵敏度分析。最后，我们通过若干数值实验，并利用灵敏度分析解释了极点恢复误差的产生原因。