Consistent kth-order time-frequency representations for (almost) cyclostationary signals

Abstract

Limitations of existing kth-order time-frequency representations (TFR) are discussed. It is emphasized that consistent estimation of TFRs is possible if the underlying nonstationarity is structured. The role of consistent and asymptotically normal cyclic-statistics in estimating the TFRs of cyclostationarity processes is elucidated, and relationships between cyclic-statistics, ambiguity functions, and Wigner-Ville distributions are discussed. Noise immunity of cyclic-statistics is shown. Conditions for consistent estimation of statistics of a class of nonstationary processes are given without assuming cyclostationarity.<>