Padé approximations in noise filtering

Résumé st recall the results on the distribution of poles and zeros of Padé approximations to noisy Taylor series around a point. We then report the numerical experiment on noisy data coming from inelastic electron-scattering cross-sections on rare gases, as functions of the momentum transfer at fixed energy. We apply the Thiele algorithm (Padé approximations of type II) to those data, which are known to belong to an analytic function in a cut plane from −∞ to 0. In this case, the poles and zeros split into three families: 1. ublet pole-zero at a distance of the order of the computer roundoff. oublet pole-zero at a distance of the order of the noise in the experimental data. Remaining poles and zeros compatible with the analytic structure of the experimentally measured function. owing away the first two families of poles and zeros (noisy ones), we were able to obtain an excellent filtering of the data compatible with the analytic structure of the analyzed function.