  Using a maximum-likelihood criterion, we derive optimal correlation
strategies for signals with and without digitization. We assume that the
signals are drawn from zero-mean Gaussian distributions, as is expected in
radio-astronomical applications, and we present correlation estimators both
with and without a priori knowledge of the signal variances. We demonstrate
that traditional estimators of correlation, which rely on averaging products,
exhibit large and paradoxical noise when the correlation is strong. However, we
also show that these estimators are fully optimal in the limit of vanishing
correlation. We calculate the bias and noise in each of these estimators and
discuss their suitability for implementation in modern digital correlators.
