Table of Contents
ISRN Signal Processing
Volume 2013, Article ID 605035, 18 pages
http://dx.doi.org/10.1155/2013/605035
Research Article

About a Partial Differential Equation-Based Interpolator for Signal Envelope Computing: Existence Results and Applications

1Département Informatique et Télécommunications, Ecole Polytechnique de Thiès (EPT), Thiès BP A10, Senegal
2Laboratoire Images, Signaux et Systèmes Intelligents (LISSI-E.A.3956), Université Paris-Est Créteil Val-de-Marne, Créteil, France
3Laboratoire d’Analyse Numérique et d’Informatique (LANI), Université Gaston Berger (UGB), Saint-Louis BP 234, Senegal
4Département de Mathématique et Informatique, Faculté des Sciences et Technique, Université Cheikh Anta Diop de Dakar, Dakar BP 5005, Senegal

Received 6 November 2012; Accepted 3 December 2012

Academic Editors: H. Hu and S. Li

Copyright © 2013 Oumar Niang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper models and solves the mathematical problem of interpolating characteristic points of signals by a partial differential Equation-(PDE-) based approach. The existence and uniqueness results are established in an appropriate space whose regularity is similar to cubic spline one. We show how this space is suitable for the empirical mode decomposition (EMD) sifting process. Numerical schemes and computing applications are also presented for signal envelopes calculation. The test results show the usefulness of the new PDE interpolator in some pathological cases like input class functions that are not so regular as in the cubic splines case. Some image filtering tests strengthen the demonstration of PDE interpolator performance.