Multi-scale parameterization of neural rhythmicity with lagged Hilbert autocoherence

Analysis of neural activity in different frequency bands is ubiquitous in systems and cognitive neuroscience. Recent analytical breakthroughs and theoretical developments rely on phase maintenance of oscillatory signals without considering whether or not this assumption is met. Lagged (auto)coherence, the coherence between a signal and itself at increasing temporal delays, has been proposed as a way to quantify the rhythmicity, or periodicity, of a signal. However, current Fourier-based lagged autocoherence algorithms suffer from poor spectral accuracy and resolution, aliasing effects that become more pronounced at higher frequencies, and conflation with amplitude covariation, especially in frequency ranges in which the signal-to-noise ratio is low. We introduce a continuous estimator, lagged Hilbert autocoherence (LHaC), which addresses these limitations by using multiplication in the frequency domain for precise bandpass filtering, computing instantaneous analytic signals via the Hilbert transform, and thresholding using the amplitude covariation of phase-shuffled surrogate data. While LHaC and lagged Fourier autocoherence (LFaC) estimate distinct theoretical quantities, we compare their empirical behavior in simulations with controlled rhythmic structure. These analyses show that LHaC provides more spectrally resolved estimates of rhythmicity and is more sensitive to the duration of transient, short-lived oscillatory events. We further demonstrate the utility of LHaC for identifying frequency-specific differences in rhythmicity between conditions and tracking learning-related changes in neural oscillations. Lagged Hilbert autocoherence thus offers a refined and practically useful approach to characterizing neurophysiological rhythmicity.