Signal Periodic Decomposition Based On Ramanujan Subspace

The period estimation and the periodic decomposition of a signal are the long-standing problems in many application domains,including biomolecular sequence analysis and signal processing.To address such problems,this paper presents the Ramanujan subspace pursuit(RSP)algorithm based on the Ramanujan subspace.The RSP is a greedy iterative algorithm that can uniquely decompose any signal into a sum of exactly periodic components,by selecting and removing the most dominant periodic component from the residual signal in each iteration.In RSP,a novel periodicity metric is derived based on the energy of the periodic component obtained by orthogonally projecting the residual signal into each Ramanujan subspace,and is then used to select the most dominant periodic component in each iteration.To reduce the computational cost of the RSP,we also propose the fast RSP based on the relation between the periodic subspace and the exactly periodic subspace and the maximum likelihood estimation of the energy of the periodic component in the periodic subspace.The fast RSP has a lower computational cost and can decompose a signal into the sum of periodic components.In addition,our result shows that the RSP outperforms the current algorithms for period estimation.Several examples demonstrate that the proposed algorithm can be used in many applications such as the period detection in DNA sequence,period analysis for signals,and signal decomposition.