Estimation of the coherence spectrum and its confidence interval using the fast Fourier transform

Correction factors were devised for correction of bias and computation of confidence intervals around estimates of coherence spectra computed upon Gaussian random time series. Using Monte Carlo methods to compute approximate sampling distributions for coherence, statistical descriptions of the bias and standard deviations were obtained. Correction factors were devised which extend the utility of coherence estimates to a value of coherence = 0. Previously coherence = 0.4 was a lower limit.