Spectral estimation at the edge

Cognitive functions depend on neuronal communication, which is subserved by the synchronization of neuronal rhythms. Rhythms are characterized by their frequency, power and phase. If the phase of a rhythm just preceding an input is predictive of the neuronal or behavioral response to the input, this provides strong evidence for a functional role of the rhythm. Yet, this requires estimating the phase of a rhythm at the edge of the epoch. This is challenging, because any phase estimation that is spectrally specific requires a finite window length often combined with tapers that de-emphasize the signal close to the edge. To overcome this, we propose a method that builds on previously described approaches based on autoregressive modeling of the data and corresponding extrapolation beyond the edge. In contrast to related previous approaches, the modeling is based on the broadband signals, avoiding filtering-related group delays, and the extrapolation is performed multiple times, allowing averaging and thereby the reduction of extrapolation noise. The new method provided more accurate phase estimation at the edge for most simulated datasets, and for an empirical dataset from awake macaque area V4. We propose that the enhanced phase estimation accuracy at the edge might help to investigate the functional roles of brain rhythms and potentially also to improve phase-specific stimulation for clinical applications.