1,041 research outputs found
Matrix-Based Ramanujan-Sums Transforms
In this letter, we study the Ramanujan Sums (RS) transform by means of matrix multiplication. The RS are orthogonal in nature and therefore offer excellent energy conservation capability. The 1-D and 2-D forward RS transforms are easy to calculate, but their inverse transforms are not defined in the literature for non-even function . We solved this problem by using matrix multiplication in this letter
Orthogonal Ramanujan Sums, its properties and Applications in Multiresolution Analysis
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
A-D-E Polynomial and Rogers--Ramanujan Identities
We conjecture polynomial identities which imply Rogers--Ramanujan type
identities for branching functions associated with the cosets , with
=A \mbox{}, D ,
E . In support of our conjectures we establish the correct
behaviour under level-rank duality for =A and show that the
A-D-E Rogers--Ramanujan identities have the expected asymptotics
in terms of dilogarithm identities. Possible generalizations to arbitrary
cosets are also discussed briefly.Comment: 19 pages, Latex, 1 Postscript figur
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