Imaginary coherency

Imaginary coherency is the imaginary part of the complex coherency (the normalized cross-spectrum). Its purpose is to be robust to volume conduction: a single source seen simultaneously by two sensors produces a zero-lag, purely real contribution to the cross-spectrum, so taking only the imaginary part discards that spurious instantaneous mixing and retains only interactions with a genuine time lag. A nonzero imaginary coherency therefore cannot be explained by a single instantaneously projected source.

The robustness comes at a price: because it responds only to lagged interactions, it is insensitive to true interactions that happen to occur at or near zero phase lag, and its magnitude depends on the phase-lag angle as well as the coupling strength, so it is not a pure measure of coupling strength. Related constructions, the phase-lag index and the weighted phase-lag index, pursue the same volume-conduction insensitivity with different bias and sensitivity profiles.