Ramanujan sums-wavelet transform for signal analysis

Abstract

The wavelet transform is a very useful tool for a number of real-life applications. This is due to its multiresolution representation of signals and its localized time-frequency property. The Ramanujan sums (RS) were introduced to signal processing recently. The RS are orthogonal in nature and therefore offer excellent energy conservation. The RS operate on integers and hence can obtain a reduced quantization error implementation. In this paper, we combine the wavelet transform with the RS transform in order to create a new representation of signals. We are trying to combine the merits of the both transforms and at the same time overcome their shortcomings. Our proposed transform contains much richer features than the wavelet transform, so it could be useful for such applications as time-frequency analysis, pattern recognition and image analysis.