Shannon wavelets theory

Abstract

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 (ℝ;) 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 ℓ -functions.