Oversampling and reconstruction functions with compact support

Authors:
A. G. García;M. A. Hernández-Medina;G. Pérez-Villalón
Affiliations:
Departamento de Matemáticas, Universidad Carlos III de Madrid, Avda. de la Universidad 30, 28911 Leganés-Madrid, Spain;Departamento de Matemática Aplicada, E.T.S.I.T., U.P.M., Avda. Complutense s/n, 28040 Madrid, Spain;Departamento de Matemática Aplicada, E.U.I.T.T., U.P.M., Carret. Valencia km. 7, 28031 Madrid, Spain
Venue:
Journal of Computational and Applied Mathematics
Year:
2009

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Abstract

Assume that a sequence of samples of a filtered version of a function in a shift-invariant space is given. This paper deals with the existence of a sampling formula involving these samples and having reconstruction functions with compact support. This is done in the light of the generalized sampling theory by using the oversampling technique. A necessary and sufficient condition is given in terms of the Smith canonical form of a polynomial matrix. Finally, we prove that the aforesaid oversampled formulas provide nice approximation schemes with respect to the uniform norm.