Shannon Wavelets Theory

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 Cℓ‐functions.