Physiol Meas. 2017 Nov 30;38(12):2141-2163. doi: 10.1088/1361-6579/aa93a1.
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 filter parameters and background noise level, especially in low analytical signal amplitudes. The objective of this study is to propose a robust statistical framework for EEG IP/IF estimation and analysis.
Herein, a Monte Carlo estimation scheme is proposed for the 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 analytically probability density functions of the instantaneous envelope (IE) and IP of EEG signals, which justify the proposed Monte Carlo scheme.
The instantaneous analytical envelope of the EEG, which has been empirically used in previous studies, is shown to have a fundamental impact on the accuracy of the EEG phase contents. 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.
脑电（EEG）的瞬时相位（IP）和瞬时频率（IF）被认为是 EEG 频谱的显著补充。这些参数的计算通常包括窄带滤波，然后计算信号的解析形式。这些参数的计算高度依赖于滤波器参数和背景噪声水平，尤其是在低分析信号幅度的情况下。本研究的目的是提出一种稳健的 EEG IP/IF 估计和分析统计框架。
本文提出了一种用于稳健估计 EEG IP 和 IF 的蒙特卡罗估计方案。建议任何与 EEG 相位相关的推断都应报告为平均值，并通过在算法参数（如滤波器带宽、中心频率和背景噪声水平）下重复 IP 和 IF 估计（由专家选择）来获得置信区间。在本文的第二部分，使用由窄带 foreground 和 background EEG 叠加组成的随机模型，推导出 EEG 信号瞬时包络（IE）和 IP 的解析概率密度函数，这证明了所提出的蒙特卡罗方案的合理性。
已在先前研究中经验使用的 EEG 瞬时分析包络被证明对 EEG 相位内容的准确性有根本影响。严格证明了 IP/IF 估计质量高度依赖于 IE，并且在低 IE 下的任何相位/频率解释在统计学上都是不可靠的，需要进行假设检验。
通过示例研究了该方法对先前研究的影响，包括时域相位同步、相位重置、锁相值和相位幅度耦合。这项研究的结果可以为 EEG 相位/频率估计和分析技术设定新的标准。
