2.4. Electrophysiological data analysis

Phase Locking Value (PLV) and n:m Phase Synchronization Index (nmPSI) are bivariate time-series measures that quantify the degree of phase synchronization between two oscillators or time series. PLV computes the phase synchrony of two time series (e.g., acoustic and EEG signals) at a singular frequency (^{Assaneo & Poeppel, 2018; He et al., 2023; Lachaux et al., 1999}). In contrast, nmPSI evaluates the cross-frequency phase coupling between two oscillators with distinct frequencies described by n and m (e.g., delta and theta frequency bands of EEG signals), where n:m is an integer relation (^{Leong et al., 2017; Rosenblum et al., 1998; Schack & Weiss, 2005}). Conceptually, both PLV and nmPSI capture the temporal consistency in phase difference (and, conversely, the coherence) between two signals. Their resulting values range from 0 (no synchronization) to 1 (complete synchronization). PLV and nmPSI were computed using the following formulas:

Here, t denotes the discretized time, T is the total number of time points, and θ1(t) and θ2(t) are the Hilbert phases of the first and second signals, respectively.

The current study assessed synchronization between neural and acoustic speech signals using PLV at frequencies corresponding to stress rhythm (i.e., 1, 2, and 3 Hz) and syllable rhythm (i.e., 2, 4, and 6 Hz), respectively. This results in PLV_Stress representing brain-acoustic synchronization at the stress level and PLV_Syllable reflecting brain-acoustic synchronization at the syllable level. We measured nmPSI to quantify the cross-frequency coupling within the brain`s theta and delta frequency bands, corresponding to the alignment of nested syllable and stress rhythms unfolding at a 2:1 ratio. Specifically, frequency-specific neural signals and acoustic inputs were computed by applying passband filters around the frequencies of interest (± 0.5 Hz) (see Fig. 2). The phase was extracted as the imaginary part of the signal’s Hilbert transform. PLV was then computed between the EEG signal and acoustic stimulus waveform within each narrow frequency band and averaged over time per individual according to Equation 1. In contrast, nmPSI was computed by bandpass filtering the EEG data into two separate bands (i.e., m = 1, 2, 3 ± 0.5 Hz; n = 2, 4, 6 ± 0.5 Hz) to isolate phase-locked responses to the stress (m) and syllable (n) rhythm in the brain at a 2:1 ratio. To reduce noise in the metric, we quantified nmPSI in a moving window (6 sec; overlap ratio of 0.3) and averaged across windows for each condition according to Equation 2. To establish the noise floor of our PSI metric, we applied this identical analysis to our previous EEG data evoked by similar syllable trains but devoid of any stress patterns (e.g., ‘ba-ba-ba…’) (^{He et al., 2023}).