Sparse Signal Analysis Using Ramanujan Sums

Abstract

In this paper, we perform sparse signal analysis by using the Ramanujan Sums (RS). The RS are orthogonal in nature and therefore offer excellent energy conservation. Our analysis shows that the RS can compress the energy of a periodic impulse chain signal into fewer number of RS coefficients than the Fourier transform (FT). In addition, the RS are faster than the FT in computation time because we can calculate the RS basis functions only once and save them to a file. We can retrieve these RS basis functions for our calculation instead of computing them online. To process a signal of 128 samples, we spend 1.0 millisecond for the RS and 5.82 milliseconds for the FT by using our unoptimized Matlab code.