Cm. Spooner et Wa. Gardner, THE CUMULANT THEORY OF CYCLOSTATIONARY TIME-SERIES .2. DEVELOPMENT AND APPLICATIONS, IEEE transactions on signal processing, 42(12), 1994, pp. 3409-3429
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.