Ramanujan Sums-Wavelet Transform: A New Approach to Signal Processing

Ramanujan Sum is a trigonometric summation introduced by Srinivasa Ramanujan in 1918. Recently, this summation technique is widely used in digital signal processing applications like pattern recognition, feature extraction, signal analysis, image compression, etc. Ramanujan Sums-Wavelet Transform (RSWT) is a signal analysis tool introduced by Chen et al. in 2013, in which the multiresolution representation nature of the wavelet transform and the energy conservation property of the Ramanujan Sums transform are blended to extract more useful information from the signal. Ordinary wavelet transform can be obtained as a special case of RSWT and hence it provides us with a multitude of ways to analyze signals under consideration. In this paper, we discuss RSWT in one-dimensional signal analysis, especially in time series analysis.