Signal Representation Using Ramanujan Subspaces Utilizing A Prior Signal Information

TLDR: This paper proposes a new signal representation to estimate the period and frequency information of a given signal with low computational complexity by representing a finite-length discrete-time signal as a linear combination of signals belongs to Ramanujan subspaces.

Abstract: In signal processing applications the information about the signal such as frequency (or) period is known a prior for most of the practical signals like ECG, EEG, speech, etc. Inspired by this, in this paper, we propose a new signal representation to estimate the period and frequency information of a given signal with low computational complexity. We achieve this by representing a finite-length discrete-time signal as a linear combination of signals belongs to Ramanujan subspaces. Further, we evaluate the performance of the proposed representation with a simulated example and also by addressing the problem of reducing Power Line Interference (PLI) in an ECG signal. Finally, for a given integer-valued signal, we show that the computational complexity of the proposed transform is quite low in comparison with the existing transforms, and it is quite comparable for a given real (or) complex-valued signal.