## Coherence

Other dynamic measures involve a combination of location and time measures. For example, the (normalized) covariance of two signals is a correlation coefficient expressed as a function of time delay for characteristic waveforms recorded at the two locations. Covariance is used in ERP studies of cognition. A measure similar to covariance is the coherence of two signals, which is also a correlation coefficient (squared). It measures the phase consistency between pairs of signals in each frequency band. Scalp potential (with respect to a reference) recorded at many scalp locations, for example, over 1-min record may be represented by Eq. (1). Consider any two locations with time-dependent voltages V(t) and Vj(t). The methods of Fourier analysis may be used to determine the phases f^i and fnj associated with each 1-sec period or epoch (indicated by superscript p) of the full 60-sec record. The frequency component is indicated by subscript n and the two electrode locations are indicated by subscripts i and j. If the voltage phase difference (fn—fnj) is fixed over successive epochs p (phase locked), the estimated EEG coherence between scalp locations i and j is equal to 1 at frequency n. On the other hand, if the phase difference varies randomly over epochs, estimated coherence will be small at this frequency.

An EEG record involving J recording electrodes will generally provide J(J—1)/2 coherence estimates for each frequency band. For example, with J = 64 electrodes and 1-sec epochs, coherence estimates may be obtained for all electrode pairs (2016) for each integer frequency between 1 and 15 Hz. The generally very complicated coherence picture may be called the coherence structure of EEG. This dynamic structure provides information about local versus global dynamic behavior. It provides one important measure of functional interactions between oscillating brain subsystems. EEG coherence is a different (but closely related) measure than EEG ''synchrony,'' which refers to sources oscillating approximately in phase so that their individual contributions to EEG add by superposition. Thus, desynchronization is often associated with amplitude reduction. Sources that are synchronous (small phase differences) over substantial times will also tend to be coherent. However, the converse need not be true; coherent sources may remain approximately 180° out of phase so their individual contributions to EEG tend to cancel.

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