NONPARAMETRIC POLYSPECTRAL ESTIMATORS FOR KTH-ORDER (ALMOST) CYCLOSTATIONARY PROCESSES

Second- and higher-order almost cyclostationary processes are random s ignals with almost periodically time-varying statistics. The class inc ludes stationary and cyclostationary processes as well as many real-li fe signals of interest. Cyclic and time-varying cumulants and polyspec tra are defined for discrete-time real kth-order cyclostationary proce sses, and their interrelationships are explored. Smoothed polyperiodog rams are proposed for cyclic polyspectral estimation and are shown to be consistent and asymptotically normal. Asymptotic covariance express ions are derived along with their computable forms. Higher than second -order cyclic cumulants and polyspectra convey time-varying phase info rmation and are theoretically insensitive to any stationary (for nonze ro cycles) as well as additive cyclostationary Gaussian noise (for all cycles).