[R] spectral coherence & non-overlapping windows: confidence intervals?

[Martin Ivanov]

Dear R users,

The confidence intervals for the squared coherence and phase, plotted by plot.spec.coherence() and plot.spec.phase, respectively,
use the formulae 10.14 and 10.11 from Bloomfield, P. (1976) Fourier Analysis of Time Series: An Introduction. Wiley:

gg <- 2/x$df
se <- sqrt(gg/2)
 z <- -qnorm((1 - ci)/2)
coh <- sqrt(x$coh);
(tanh(atanh(coh) + z * se))^2; # this is the 95% line for the coherence
cl <- asin(pmin(0.9999, qt(ci, 2/gg - 2) * sqrt(gg *  (coh^{ -2 } - 1)/(2 * (1 - gg))))); # this is for the phase

Does somebody know how these formulae extend in case of calculating the cross-spectrum via 
K non-overlapping windows, i.e. via the Welch method? I would be very thankful if you could direct 
me to some literature. I tried finding something on the topic myself, but the information is only
for the case when one smooths with spectral windows.

Best regards,
Martin