Asymptotic analysis of estimated cyclic cross-correlation function between stationary and cyclostationary processes

The cyclic cross-correlation between a stationary process and a cyclosrationary process at cycle frequency α(≠ 0) is identically zero under an ideal condition, which indicates that a cyclic cross-correlation method performs much better than the conventional cross-correlation method in suppressing the stationary noise orinterference. But unfortunately, the cyclic cross-correlation will not really approach zero due to the limited data length in some real conditions. In this paper, the quantitative relation between the data length and the estimated cyclic cross-correlation is deduced, and some useful conclusions are drawn, which are proven by some computer simulations. The conclusion in this paper is really useful for the practical application of cyclostationary signal processing.