Mathematical Problems in Engineering
Volume 2008 (2008), Article ID 164808, 24 pages
Research Article

Shannon Wavelets Theory

Carlo Cattani

Department of Pharmaceutical Sciences (DiFarma), University of Salerno, Via Ponte don Melillo, Fisciano, 84084 Salerno, Italy

Received 30 May 2008; Accepted 13 June 2008

Academic Editor: Cristian Toma

Copyright © 2009 Carlo Cattani. 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.


Shannon wavelets are studied together with their differential properties (known as connection coefficients). It is shown that the Shannon sampling theorem can be considered in a more general approach suitable for analyzing functions ranging in multifrequency bands. This generalization coincides with the Shannon wavelet reconstruction of L2() functions. The differential properties of Shannon wavelets are also studied through the connection coefficients. It is shown that Shannon wavelets are C-functions and their any order derivatives can be analytically defined by some kind of a finite hypergeometric series. These coefficients make it possible to define the wavelet reconstruction of the derivatives of the C-functions.