Time-Frequency Analysis via Ramanujan Sums

Abstract

Research in signal processing shows that a variety of transforms have been introduced to map the data from the original space into the feature space, in order to efficiently analyze a signal. These techniques differ in their basis functions, that is used for projecting the signal into a higher dimensional space. One of the widely used schemes for quasi-stationary and non-stationary signals is the time-frequency (TF) transforms, characterized by specific kernel functions. This work introduces a novel class of Ramanujan Fourier Transform (RFT) based TF transform functions, constituted by Ramanujan sums (RS) basis. The proposed special class of transforms offer high immunity to noise interference, since the computation is carried out only on co-resonant components, during analysis of signals. Further, we also provide a 2-D formulation of the RFT function. Experimental validation using synthetic examples, indicates that this technique shows potential for obtaining relatively sparse TF-equivalent representation and can be optimized for characterization of certain real-life signals.