Approximation of statistical distribution of magnitude squared coherence estimated with segment overlapping

Abstract

This paper suggests an approximation to the statistical distribution of a magnitude squared coherence (MSC) function estimated with segment overlapping. So far, the statistical distribution is known for an MSC computed without segment overlapping only. However, as the overlapped segmentation provides a more accurate MSC estimate, its statistical distribution is desired to allow its evaluation. This paper provides an approximation of the cumulative density function, probability density function, confidence limit formula, confidence interval computation and a procedure for the comparison of two MSC estimates, all for an MSC accurately estimated with the segment overlapping. Additionally, the benefits of the knowledge of the approximated statistics are illustrated on EEG–EMG (i.e. cortico-muscular) MSC estimates.