Padé Approximants for Noise Filtering for Experimental Data

Abstract: We present a method for exploring the presence of noise, which may mimic systematic errors in experimental datasets, particularly when such errors introduce inconsistencies. The method is based on Padé approximants designed for Stieltjes functions, with extensions to holomorphic functions in the region covered by the data. It uses the known analytic properties of these functions to identify noise and systematically adjust data points that deviate from expected behavior, preserving the full information content of the dataset while maintaining physical and mathematical coherence. Its effectiveness and robustness are illustrated through simple examples, highlighting its advantages as a practical tool  compared to conventional data-removal procedures.