Within-cycle instantaneous frequency profiles report oscillatory waveform dynamics

The nonsinusoidal waveform is emerging as an important feature of neuronal oscillations. However, the role of single-cycle shape dynamics in rapidly unfolding brain activity remains unclear. Here, we develop an analytical framework that isolates oscillatory signals from time series using masked empirical mode decomposition to quantify dynamical changes in the shape of individual cycles (along with amplitude, frequency, and phase) with instantaneous frequency. We show how phase-alignment, a process of projecting cycles into a regularly sampled phase grid space, makes it possible to compare cycles of different durations and shapes. "Normalized shapes" can then be constructed with high temporal detail while accounting for differences in both duration and amplitude. We find that the instantaneous frequency tracks nonsinusoidal shapes in both simulated and real data. Notably, in local field potential recordings of mouse hippocampal CA1, we find that theta oscillations have a stereotyped slow-descending slope in the cycle-wise average yet exhibit high variability on a cycle-by-cycle basis. We show how principal component analysis allows identification of motifs of theta cycle waveform that have distinct associations to cycle amplitude, cycle duration, and animal movement speed. By allowing investigation into oscillation shape at high temporal resolution, this analytical framework will open new lines of inquiry into how neuronal oscillations support moment-by-moment information processing and integration in brain networks.NEW & NOTEWORTHY We propose a novel analysis approach quantifying nonsinusoidal waveform shape. The approach isolates oscillations with empirical mode decomposition before waveform shape is quantified using phase-aligned instantaneous frequency. This characterizes the full shape profile of individual cycles while accounting for between-cycle differences in duration, amplitude, and timing. We validated in simulations before applying to identify a range of data-driven nonsinusoidal shape motifs in hippocampal theta oscillations.