Period Determination in Cyclo-Stationary Signals by Autocorrelation and Ramanujan Subspaces

Abstract

Period determination in a periodic-like signal is a challenging process, if the signal is contaminated with a noise or noise-like interference signals. In this work, multiple period determination was considered in aforementioned signals. Recently, cyclostationary properties of the periodic-like signals were utilized to determine the time-varying autocorrelation function (TVAC). First we proved that TVAC can be expressed in terms of Ramanujan sums, then we used TVAC in the periodicity metric to identify the periods. Periodicity metric provides energy distribution of each periodic component as a function of block folding index and reaches a maximum at the points representing the hidden periods in the signal. Proposed method was verified by artificial signals and mean estimation errors versus signal to noise ratio were illustrated. Finally, hidden periods in the noisy respiration signals were estimated by the proposed method successfully.