Nonparametric polyspectral estimators for kth-order (almost) cyclostationary processes

Second- and higher-order almost cyclostationary processes are random signals with almost periodically time-varying statistics. The class includes stationary and cyclostationary processes as well as many real-life signals of interest. Cyclic and time-varying cumulants and polyspectra are defined for discrete-time real kth-order cyclostationary processes, and their interrelationships are explored. Smoothed polyperiodograms are proposed for cyclic polyspectral estimation and are shown to be consistent and asymptotically normal. Asymptotic covariance expressions are derived along with their computable forms. Higher than second-order cyclic cumulants and polyspectra convey time-varying phase information and are theoretically insensitive to any stationary (for nonzero cycles) as well as additive cyclostationary Gaussian noise (for all cycles)