Related papers: Orthogonal Ramanujan Sums, its properties and Appl…
In this paper, the authors present sharp approximations in terms of sine function and polynomials for the so-called Ramanujan constant (or the Ramanujan $R$-function) $R(a)$, by showing some monotonicity, concavity and convexity properties…
Extracting a common robust signal from data divided into heterogeneous groups can be difficult when each group -- in addition to the signal -- can contain large, unique variation components. Previously, maximin estimation has been proposed…
Super-resolution (SR) aims to increase the resolution of imagery. Applications include security, medical imaging, and object recognition. We propose a deep learning-based SR system that takes a hexagonally sampled low-resolution image as an…
Let $K$ be a number field. This paper considers arithmetic functions over $K$, that are, complex valued functions on the set of nonzero integral ideals in $K$. Firstly we generalize some basic results on arithmetic functions. Next we define…
In this paper we present experimental ways of evaluating Ramanujan`s quantities which as someone can see are related with algebraic numbers. The good thing with algebraic numbers is that can be found in a closed form, from there…
In terms of the difference operators, we establish several curious transformation and summation formulas for basic hypergeometric series. When the parameters are specified, they produce $q$-analogues of Ramanujan's three series for 1/$\pi$…
The purpose of this paper is to introduce a very efficient algorithm for signal extrapolation. It can widely be used in many applications in image and video communication, e. g. for concealment of block errors caused by transmission errors…
The double-direction orthogonalization algorithm is applied to construct sequences of polynomials, which are orthogonal over the interval [0,1]with the weighting function 1. Functional and recurrent relations are derived for the sequences…
In this paper, we identify optical reconfigurable intelligent surfaces (ORISs) as key enablers of next-generation free-space optical (FSO) multiple access systems. By leveraging their beam steering and beam splitting capabilities, ORISs are…
We extend the results of Denisov-Rakhmanov, Szego-Shohat-Nevai, and Killip-Simon from asymptotically constant orthogonal polynomials on the real line (OPRL) and unit circle (OPUC) to asymptotically periodic OPRL and OPUC. The key tool is a…
The focus of this research is sensor applications including radar and sonar. Optimal sensing means achieving the best signal quality with the least time and energy cost, which allows processing more data. This paper presents novel work by…
To improve the sum-rate (SR) of the dual-hop relay system, a novel two-stage power allocation scheme with non-orthogonal multiple access (NOMA) is proposed. In this scheme, after the reception of the superposition coded symbol with a power…
This paper is a tribute to the genius of the legendary Indian mathematician Srinivasa Ramanujan (22 December 1887 - 26 April 1920) in the centenary year of his death. The life story of Ramanujan is so well known that it needs no elaboration…
Opportunistic Spatial Orthogonalization (OSO) is a cognitive radio scheme that allows the existence of secondary users and hence increases the system throughput, even if the primary user occupies all the frequency bands all the time.…
The tridiagonal representation approach is an algebraic method for solving second order differential wave equations. Using this approach in the solution of quantum mechanical problems, we encounter two new classes of orthogonal polynomials…
An identity by Ramanujan related to the multisection of Bernoulli numbers is revisited. Two alternative approaches are proposed, both relying on the multisection technique. A geometric approach reveals the role played by the symmetries of…
Polyspectral estimation is a problem of great importance in the analysis of nonlinear time series that has applications in biomedical signal processing, communications, geophysics, image, radar, sonar and speech processing, etc. Higher…
Super-Resolution (SR) is a technique that seeks to upscale the resolution of a set of measured signals. SR retrieves higher-frequency signal content by combining multiple lower resolution sampled data sets. SR is well known both in the…
Multiple-frequency periodograms -- based on time series models consisting of two or more independent sinusoids -- have long been discussed. What is new here is the presentation of a practical, simple-to-use computational framework…
The relation between Radon transform and orthogonal expansions of a function on the unit ball in $\RR^d$ is exploited. A compact formula for the partial sums of the expansion is given in terms of the Radon transform, which leads to…