A time-domain analysis of multiple periodic signals

Periodic signal analysis is important in many areas such as communications systems, bio-medicine, sonar and radar. Many modelling schemes are used in this analysis and for a real system a period estimation technique must be able to estimate either single or multiple periodicities from sensor data. This estimation process may be constrained by the fact that the periods, periodic waveforms and number of periodicities present are unknown a-priori. It is also reasonable to assume that the sampling rate will not be synchronised to the replication rate of any of the periodic waveforms and that the period and shape of the periodic components will vary with time. We propose a time-domain estimator, for such a scenario. Our time domain estimator is based on a modified incremental multi-parameter (IMP) algorithm. It is able to detect and track several periodic components in a single time series. Two aspects of our method are discussed: (a) a detection and acquisition stage that includes a novel track-before-detect method, to estimate the period and amplitude profile (state variables) of each detected periodic component and (b) a recursive mode for updating the state variables in a real-time practical situation