A method of estimating the magnitude-squared coherence function spectrum for zero-mean processes that are wide-sense stationary and random is presented. The estimation technique uses the weighted overlapped segmentation fast Fourier transform FFT approach. Analytical and empirical results for statistics of the estimator are presented for the processes. Analytical expressions are derived in the non overlapped case. Empirical results show a decrease in bias and variance of the estimator with increasing overlap and suggest that a 50-percent overlap is highly desirable when cosine Hanning weighting is used.