Orthogonal Ramanujan Sums, its properties and Applications in Multiresolution Analysis
Information Theory
2017-07-21 v1 math.IT
Abstract
Signal processing community has recently shown interest in Ramanujan sums which was defined by S.Ramanujan in 1918. In this paper we have proposed Orthog- onal Ramanujan Sums (ORS) based on Ramanujan sums. In this paper we present two novel application of ORS. Firstly a new representation of a finite length signal is given using ORS which is defined as Orthogonal Ramanujan Periodic Transform.Secondly ORS has been applied to multiresolution analysis and it is shown that Haar transform is a spe- cial case.
Cite
@article{arxiv.1707.06283,
title = {Orthogonal Ramanujan Sums, its properties and Applications in Multiresolution Analysis},
author = {Devendra Kumar Yadav and Gajraj Kuldeep and S. D. Joshi},
journal= {arXiv preprint arXiv:1707.06283},
year = {2017}
}