THE CUMULANT THEORY OF CYCLOSTATIONARY TIME-SERIES .2. DEVELOPMENT AND APPLICATIONS

The development of the theory of nonlinear processing of cyclostationary time-series that is initiated in the first part of this two-part paper is continued here in the second part. A new type of cumulant for complex-valued variables is introduced and used to generalize the temporal and spectral moments and cumulants for cyclostationary time-series from real-valued to complex-valued time-series. The relations between the temporal and spectral moments and cumulants at the inputs and outputs of several signal processing operations are determined. Formulas for the temporal and spectral cumulants of complex-valued pulse-amplitude-modulated time-series are derived. Estimators for the temporal moments and cumulants and for the cyclic polyspectra are presented and their properties are discussed. The performance of these estimators is illustrated by several computer simulation examples for pulse-amplitude-modulated time-series. The theory is applied to the problems of weak-signal detection and interference-tolerant time-delay estimation.