Shannon Wavelets Theory
By Carlo Cattani. 2008
109 citations recorded by the source corpus.
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 functions. The differential properties of Shannon wavelets are also studied through the connection coefficients. It is shown that Shannon wavelets are -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 -functions.
Subfields: Applied Mathematics, Computer Vision and Pattern Recognition, Signal Processing
View Paper: https://www.semanticscholar.org/paper/2af35aeb2d54b5568dcb57e51d8e42a2a473c1b9
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In Applied Mathematics
In Computer Vision and Pattern Recognition
In Signal Processing
Citations in the corpus
- Multifocus and multispectral image fusion based on pixel significance using discrete cosine harmonic wavelet transform (2012, background): “The Shannon scaling function is nothing but a sinc function and is given by Sincethesincfunctionisassociatedwithsamplingtheory,the scaling function is called as Shannon scaling function, and the wavelet is called as Shannon wavelet in honor of Claude Shannon [44,46].”