Phase analyses

The phase locking analyses methods have been described previously in detail (Park et al., 2010a; Ahn et al., 2014). Briefly, signals were Kaiser windowed and digitally filtered using a FIR filter in the θ frequency band (5–11 Hz) at the sampling rate of 1017 Hz. Zero phase filtering was used to avoid phase distortions. Phase was extracted via Hilbert transform resulting in two signals; φ1t and φ2t (Pikovsky et al., 2001; Hurtado et al., 2004). To clarify, let x(t) be the filtered signal at the given frequency band. Then the complex analytic extension of x(t) is given by Eqn. 1

where x¯t is given by the Hilbert transform of the signal (Eqn. 2)

Then the analytic signal is projected on the unit circle (Eqn. 3)

where ζt is the modulus of ζt. The phase φ(t) was then extracted through the argument (angle) of zt.