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

This is an instantaneous cosine and sine representation of a time series from
which the time series of the “cospectrum” and “quadspectrum” are
computed from the cross-spectrum (see Appendix B for the mathematical
details of complex demodulation). As described in section 9 the results of
the CDF is the creation of a new real valued time series. The CDF real
valued time series is then used as the input to spectral analyses for the
computation of bi-coherence and bi-phase.
25- What is the physiological meaning of EEG Auto-Frequency
Coherence (AFC) and Auto-Frequency Phase (AFP)?
Cross-channel Auto-Frequency Coherence and Auto-frequency phase
measure the spatial and temporal relations between EEG “spindles” or “burst
activity” and “rhythmic episodes” as well as the frequency structure of EEG
bursts between two channels but at the same frequency (i.e., autofrequency).
Complex demodulation of a EEG time series at a given center
frequency measures the instantaneous power (uV 2 ) of activity at each instant
of time in a frequency band, similar to a filter except that the time series is
represented in the complex domain. The frequency spectrum of “spindle
activity” at a given frequency measures spindle duration and inter-spindle
intervals or how common spindles are within a record and auto bi-coherence
shows the phase synchrony of spindle activity at different frequencies within
a channel. Cross bi-coherence measures the phase synchrony of spindle or
burst activity at the same or different frequency in different channels.
The FFT of the complex demodulation time series (x’ t ) computes the
inter-burst frequency and average burst duration and burst rise times because
x’ t is the envelope of the spindle structure of EEG events. For example,
long duration bursts result in high power in the lower frequencies of the FFT
spectrum. Short inter-burst intervals result in high power at higher
frequencies of the FFT spectrum.