Some properties of the asymptotic location of poles of Pade approximants to noisy rational functions, relevant for modal analysis

The modal analysis model, made up by a linear combination of complex exponential functions, is considered. Pade approximants to the Z-transform of a noisy sample are then considered, and the asymptotic locus of their poles is studied. It turns out that this locus is strongly related to the complex exponentials of the model. By exploiting these properties, powerful methods for estimating the model parameters can be devised, which have both denoising and super-resolution capabilities.