Algorithms for Analysis of Signals with Time-Warped Cyclostationarity

Two philosophically different approaches to the analysis of signals with imperfect cyclostationarity or polycyclostationarity of the autocorrelation function due to warping are presented. The first approach consists of directly estimating the time-warping function (or its inverse) in a manner that transforms data having an empirical autocorrelation with irregular cyclicity into data having regular cyclicity. The second approach consists of modeling the signal as a time-warped polycyclostationarity stochastic process, thereby providing a widesense probabilistic characterization–a time-varying probabilistic autocorrelation function–which is used to specify an estimator of the time-warping function that is intended to remove the impact of time-warping. From this estimate, an estimate of the autocorrelation function of the unwarped process is also obtained.