Ramanujan subspace pursuit for signal periodic decomposition

摘要

The period estimation and periodic decomposition of a signal are thelong-standing problems in the field of signal processing and biomolecularsequence analysis. To address such problems, we introduce the Ramanujansubspace pursuit (RSP) based on the Ramanujan subspace. As a greedy iterativealgorithm, the RSP can uniquely decompose any signal into a sum of exactlyperiodic components, by selecting and removing the most dominant periodiccomponent from the residual signal in each iteration. In the RSP, a novelperiodicity metric is derived based on the energy of the exactly periodiccomponent obtained by orthogonally projecting the residual signal into theRamanujan subspace, and is then used to select the most dominant periodiccomponent in each iteration. To reduce the computational cost of the RSP, wealso propose the fast RSP (FRSP) based on the relationship between the periodicsubspace and the Ramanujan subspace, and based on the maximum likelihoodestimation of the energy of the periodic component in the periodic subspace.The fast RSP has a lower computational cost and can decompose a signal oflength $N$ into the sum of $K$ exactly periodic components in $ \mathcal{O}(KN\log N)$. In addition, our results show that the RSP outperforms the currentalgorithms for period estimation.