In 1918 S. Ramanujan defined a family of trigonometric sum now known as Ramanujan sums. In the last few years, Ramanujan sums have inspired the signal processing community. In this paper, we have defined an operator termed here as Ramanujan operator. In this paper it has been proved that these operator possesses properties of first derivative and second derivative with a particular shift. Generalised multiplicative property and new method of computing Ramanujan sums are also derived in terms of interpolation.
Signal processing community has recently shown interest in Ramanujan sums which was defined by S.Ramanujan in 1918. In this paper we have proposed Orthogonal 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 special case.
In most of existing Internet of Things (IoT) applications, data compression, data encryption and error/erasure correction are implemented separately. To achieve reliable communication, in particular, in harsh wireless environment with strong interference, error/erasure correction codes with higher correction capability or Automatic repeat request (ARQ) scheme are desirable but at the cost of increasing complexity and energy consumption. Due to resource-constrained IoT device, it is often challenging to implement all of them. In this paper, we propose a novel lightweight efficient secure error-robust scheme, ENCRUST, which is able to achieve these three functions using simple matrix multiplication. ENCRUST is built on the new theoretical foundation of projection-based encoding presented in this paper, by leveraging the sparsity inherent in the signal. We perform theoretical analysis and experimental study of the proposed scheme in comparison with the conventional schemes. It shows that the proposed scheme can work in low SINR range and the reconstructed signal quality shows graceful degradation. Furthermore, we apply the proposed scheme on real-life electrocardiogram (ECG) dataset and images. The results demonstrate that ENCRUST achieves decent compression, information secrecy as well as strong error recovery in one go.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.