EEG and Brain Connectivity: A Tutorial - Bio-Medical Instruments, Inc.

That is, the cross-spectrum power is the absolute value of the complexvalued
cross-spectrum. The cross-spectrum power is a measure of
connectivity based on the total shared energy between two locations at a
specific frequency and it is a mixture of in-phase and out-of-phase activity
(i.e., local and distant). The cross-spectrum power is a real number because
a complex number times the complex conjugate is a real number.
Coherence is a normalization of the cross-spectral power by dividing by the
autospectra or the in-phase component and, therefore, coherence is
independent of autospectral amplitude or power and varies from 0 to 1.
Table III is an illustration of the computational details of coherence based
on the FFT auto and cross-spectra in Table II:
Table III
Hand Calculator Example
Cospectrum, Quaspectrum and Ensemble Smoothing
F (Hz)
Record 1
Record 2
Record 3
Average
Cospectrum
1.25 2.50 3.75 5.00
0.128 -0.875 4.375 0.938
-0.272 13.00 4.147 1.094
0.363 14.50 7.012 1.891
0.073 8.875 5.176 1.307
Quaspectrum
1.25 2.50 3.75 5.00
0.204 3.25 -1.795 0.000
-0.22 -21.125 0.541 0.000
0.108 4.563 -1.156 0.000
0.031 -4.438 -0.803 0.000
Cospectrum (1.25 Hz) = 0.634(-0.073) + 0.737(0.237) = 0.128
Quadspectrum (1.25 Hz) = 0.634(0.237) – 0.737(-0.073) = 0.204
Cross-spectrum (1.25 Hz) = 0.128 + sq. root -1 (0.204) and
Cross-spectrum power (1.25 Hz) = (0.128 2 + 0.204 2 ) ½ = 0.241
This computation is repeated for each frequency component to yield the
complete cross-spectrum.
As mentioned previously in section 3, the cross-spectrum is the sum
of the in-phase potentials (i.e., cospectrum) and out-of-phase potentials (i.e.,