Distribution of the sample magnitude-squared coherence obtained using overlapped Fourier transforms

An approximate expression is derived for the probability density of the sample magnitude-squared coherence function obtained using overlapped Fourier transforms. For this approximation it is shown that the expression obtained with overlap is identical to the expression obtained without overlap but with a reduced number of degrees of freedom. In addition, it is shown that, regardless of the amount of overlap, the bias and variance of the sample statistic cannot be reduced to less than 2/3 of their no-overlap values. Numerical examples are presented to illustrate the accuracy of the approximate expression.