Analysis for the reconstruction of a noisy signal based on orthogonal moments

摘要

Suppose that we have a set of discrete data of a noisy signal and we reconstruct the original signal from its orthogonal moments based on Legendre polynomials. In this paper we derive a new error estimation of the reconstruction, which reveals the relationships between the number of moments, the signal smoothness and sampling rate. Numerical simulations provided are consistent with our analysis.