Generalizations of Cyclostationary Signal Processing: Spectral Analysis and Applications

2.4 Estimation of the Cyclic Cross-Correlation Function

Let x(t) and y(t) be jointly GACS stochastic processes with cross-correlation function (2.31a)–(2.31c). In Sections 2.4–2.8 and 3.4–3.13, when it does not create ambiguity, for notation simplification we will put

From (2.31b), it follows that the knowledge of the cyclic cross-correlation function , as a function of the two variables α and τ, completely characterizes the second-order cross-moments of jointly GACS processes. For each τ, is nonzero only for those values of α such that for some (see (2.39)). Moreover, for (α, τ) such that for some , the magnitude and phase of are the amplitude and phase of the finite-strength additive complex ...