A Consistent Definition of Phase Resetting Using Hilbert Transform

Figure 3

Analytical signal from Hilbert Transform. (a) A typical membrane potential (real part of HT) plot versus its imaginary (phase shifted) part of HT shows a well-defined limit cycle. The arrow indicates the synaptic stimulus that transiently moved the figurative point outside the stable limit cycle. The plot is very similar (besides a phase shift) to the phase space plot shown in Figure 1(b). (b) The amplitude of HT shows the first two unperturbed limit cycles followed by the perturbed cycle and a few recovery cycles. The third cycle that contains the perturbation clearly shows a significant amplitude distortion due to the external stimulus. (c) The unwrapped phase of the analytical signal is also sensitive to external stimuli (although less obvious from the plot). (d) A full period of oscillation of Hilbert frequency (rate of change of Hilbert phase) measured one period before the stimulus (blue trace) clearly shows a permanent phase shift (resetting) when compared against a full period far away from the perturbation (red trace).

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