Padé approximants and noise: rational functions

We continue a study of Padé approximants (PA) for a series perturbed by random noise – this time we consider more general rational functions. We begin with the simple case of a sum of two geometric series, and then show how these considerations can be extended to a general rational function. We do not study the most general case, but rather concentrate on demonstrating how our results for geometric series extend to new situations encountered when a general rational function is considered. We show that Froissart doublets are a universal feature and we construct an analog of the Froissart polynomial introduced in the earlier paper.