The significance threshold for coherence when using the Welch's periodogram method: Effect of overlapping segments

A classical tool to identify coupling mechanisms between two biological signals is transfer function (TF) analysis, commonly estimated by the Welch's periodogram method. However, the reliability of TF estimation depends on the coherence function, an index of linear coupling in the frequency domain. Thus, a threshold value has to be determined before assuming a coupling between two signals at a given frequency.Koopmans (The spectral analysis of time series) proposed a theoretical expression in the case of non-overlapping segments. Overlapping segments, however, improves the estimation of TF.In the present study, a modification of the expression by Koopmans is proposed for taking into account the effect of the overlapping procedure, including the most common case of a 50% overlapping ratio. Simulation tests were done on non-coherent signals (using the Hanning window), and a Kolmogorov–Smirnov test was used to check for the adequacy with the proposed threshold formula. The results showed that for an overlapping ratio of 50%, no statistical difference could be found (P > 0.05), except when using less than seven segments.The method has been applied to the computation of the transfer function between systolic blood pressure and heart rate.