A Robust Statistical Framework for Instantaneous Electroencephalogram Phase and Frequency Estimation and Analysis

Overview & Synopsis

The instantaneous phase (IP) and instantaneous frequency (IF) of the electroencephalogram (EEG) are considered as notable complements for the EEG spectrum. The calculation of these parameters commonly includes narrow-band filtering, followed by the calculation of the signal's analytical form. The calculation of the IP and IF is highly susceptible to the filtering parameters and background noise level, especially in low analytical signal amplitudes. In this work, a Monte Carlo estimation scheme is proposed for robust estimation of the EEG IP and IF. It is proposed that any EEG phase-related inference should be reported as an average with confidence intervals obtained by repeating the IP and IF estimation under infinitesimal variations (selected by an expert), in algorithmic parameters such as the filter's bandwidth, center frequency and background noise level. In the second part of the paper, a stochastic model consisting of the superposition of narrow-band foreground and background EEG is used to derive probability density functions of the instantaneous envelope (IE) and IP of EEG signals, which justify the proposed Monte Carlo scheme. It is rigorously shown that the IP/IF estimation quality highly depends on the IE and any phase/frequency interpretations in low IE are statistically unreliable and require a hypothesis test. The impact of the proposed method on previous studies, including time-domain phase synchrony, phase resetting, phase locking value and phase amplitude coupling are studied with examples. The findings of this research can set forth new standards for EEG phase/frequency estimation and analysis techniques.