Estimation of coherences between complicated processes

Considers the problem of estimating coherences and transfer functions between processes that individually have complicated spectral densities and for which limited data is available. These processes are assumed to have a continuous spectrum that varies significantly on a frequency scale commensurate with the Rayleigh resolution but the transfer function between the processes does not vary as rapidly. For such calculations the author proposes a variant of the multiple-taper method were the vectors of eigencoefficients are augmented to include derivative terms and the coherences computed as canonical correlations between the blocks. A short simulation study between correlated processes with moderately severe delay within the analysis band shows that the variance of the smoothed canonical correlation estimate is about 20% of the standard multiple window estimate.<>