Orthogonal Ramanujan Sums, its properties and Applications in Multiresolution Analysis

2017/05/25 by Devendra Kumar Yadav, Yadav, Devendra Kumar, Gajraj Kuldeep +3
Biochemistry, Genetics and Molecular Biology · Computer Science · Physics and Astronomy · #Advanced Mathematical Theories and Applications #Blind Source Separation Techniques #FOS: Computer and information sciences #Fractal and DNA sequence analysis #Information Theory (cs.IT)

paper · pdf · doi:10.48550/arxiv.1707.06283

openalex publication_date 2017/05/25 · openalex created_date 2017/07/31 · openalex updated_date 2026/07/28

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.

Related

• Ramanujan Sums as Derivatives
• On near orthogonality of certain k-vectors involving generalized Ramanujan sums
• Ramanujan sums in signal recovery and uncertainty principle inequalities
• An Algebraic Generalization of the Ramanujan Sum
• Gauss-Ramanujan Functions: Constructions, Properties, and Applications in Communications and Signal Processing