Reference-Based Extraction of Phase Synchronous Components

Phase synchronisation is a phenomenon observed in measurements of dynamic systems, composed of several interacting oscillators. It can be quantified by the phase locking factor (plf), which requires knowledge of the instantaneous phase of an observed signal. Linear sources separation methods treat scenarios in which measurements do not represent direct observations of the dynamics, but rather superpositions of underlying latent processes. Such a mixing process can cause spuriously high plfs between the measurements, and camouflage the phase locking to a provided reference signal. The plf between a linear projection of the data and a reference can be maximised as an optimisation criterion revealing the most synchronous source component present in the data, with its corresponding amplitude. This is possible despite the amplitude distributions being Gaussian, or the signals being statistically dependent, common assumptions in blind sources separation techniques without a-priori knowledge, e.g. in form of a reference signal.