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

Authors:
Jiahong Yin;Alvaro Rodolfo De Pierro;Musheng Wei
Affiliations:
Departamento de Matemá/tica, Centro Polité/cnico, CP: 19.081, Universidade Federal do Paraná/, Curitiba 81531-990 PR, Paraná/ Brazil;Department of Applied Mathametics, State University of Campinas, 13083-970 SP, Brazil;Department of Mathematics, East China Normal University, Shanghai 200062, China
Venue:
Applied Mathematics and Computation
Year:
2002

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Abstract

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.