The Hilbert transform of the LORETA time series was computed using complex demodulation to compute instantaneous coherence and phase-differences between each pair of the Brodmann area time series with Talaraich atlas coordinates described in Table 1 (Granger and Hatanka, 1964; Otnes and Enochson, 1978; Bloomfield, 2000). A total of 91 pairs of the LORETA Brodmann area time series were used to compute “instantaneous” phase differences. This method is an analytic linear shift-invariant transform that first multiplies a time series by the complex function of a sine and cosine at a specific center frequency (Center frequency = 2.5 Hz) followed by a low pass filter (6th order low-pass Butterworth, bandwidth = 1–4 Hz) which removes all but very low frequencies (shifts frequency to 0) and transforms the time series into instantaneous amplitude and phase and an “instantaneous” spectrum (Bloomfield, 2000). We place quotations around the term “instantaneous” to emphasize that there is always a trade-off between time resolution and frequency resolution. The broader the band width the higher the time resolution but the lower the frequency resolution and vice versa. Mathematical details are in Thatcher et al. (2008a).
