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

The development of the theory of nonlinear processing of cyclostationa ry time-series that is initiated in the first part of this two-part pa per is continued here in the second part. A new type of cumulant for c omplex-valued variables is introduced and used to generalize the tempo ral 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 out puts of several signal processing operations are determined. Formulas for the temporal and spectral cumulants of complex-valued pulse-amplit ude-modulated time-series are derived. Estimators for the temporal mom ents and cumulants and for the cyclic polyspectra are presented and th eir properties are discussed. The performance of these estimators is i llustrated 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.