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The problem of estimating time delay by cross correlation methods is reexamined for the whole class of stationary signals. Expressions are derived for the estimation mean square error (MSE) by the cross correlation method, and are shown to be identical to previously published results for Gaussian signals. The generalized cross correlation method is also analyzed, and the optimal weight function for this method is derived. It is shown to be identical to that derived for Gaussian signals by the maximum likelihood method. For the cross correlation method a simplified MSE expression is derived, which is to be used instead of a previously published result.