Spectral phase estimates in the setting of multidirectional coupling.

In this paper we explore conventional techniques for estimating the time lag between two signals, using both time and frequency domain measures. We generate test signals to illustrate that in general, estimated temporal relationships between neural sites connected by multiple pathways are ambiguous except in special cases where multidirectional flow of information can be ruled out a priori. Signals are analyzed using the cross correlogram in the time domain, and coherence, phase and directed transfer function (DTF) in the frequency domain. In particular, we show how similar phase and DTF measures can be obtained from qualitatively different dynamical situations (uni and bi-directional flow), and argue that although the phase and DTF combined provide more directionality information than phase alone, one still needs to observe caution if one suspects multidirectional flow.