Background

Two measures of cross-frequency coupling are phase-amplitude coupling (PAC) and bicoherence. The estimation of PAC with meaningful bandwidth for the high-frequency amplitude is crucial in order to avoid misinterpretations. While recommendations on the bandwidth of PAC's amplitude component exist, there is no consensus yet. Theoretical relationships between PAC and bicoherence can provide insights on how to set PAC's filters.

New method

To illustrate this, PAC estimated from simulated and empirical data are compared to the bispectrum. We used simulations replicated from earlier studies and empirical data from human electro-encephalography and rat local field potentials. PAC's amplitude component was estimated using a filter bandwidth with a ratio of (1) 2:1, (2) 1:1, or (3) 0.5:1 relative to the phase frequency.

Results

For both simulated and empirical data, PAC was smeared over a broad frequency range and not present when the estimates comprised a 2:1- and 0.5:1-ratio, respectively. In contrast, the 1:1-ratio accurately avoids smearing and results in clear signals of cross-frequency coupling. Bicoherence estimates were found to be essentially identical to PAC calculated with the recommended frequency setting.

Comparison with existing method(s)

Earlier recommendations on filter settings of PAC lead to estimates which are smeared in the frequency domain, which makes it difficult to identify cross-frequency coupling of neural processes operating in narrow frequency bands.

Conclusions

We conclude that smearing of PAC estimates can be avoided with a different choice of filter settings by theoretically relating PAC to bicoherence.

中文翻译：

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从双光谱的角度定义用于相位-幅度耦合的滤波器参数

背景

跨频耦合的两种度量是相位幅度耦合（PAC）和双相干性。为了避免误解，估算具有有意义带宽的PAC对于高频幅度至关重要。尽管存在有关PAC幅度分量带宽的建议，但尚未达成共识。PAC和双相干之间的理论关系可以提供有关如何设置PAC滤波器的见解。

新方法

为了说明这一点，将根据模拟和经验数据估计的PAC与双谱进行了比较。我们使用从早期研究中复制的模拟以及来自人类脑电图和大鼠局部场电势的经验数据。PAC的幅度分量是使用滤波器带宽估算的，相对于相位频率，滤波器带宽的比例为（1）2：1，（2）1：1或（3）0.5：1。

结果

对于模拟数据和经验数据，PAC都在很宽的频率范围内被拖尾，并且当估计值分别包含2：1和0.5：1比率时，PAC不会出现。相反，1：1的比率可准确避免拖尾现象，并产生清晰的跨频耦合信号。发现双相干性估计与使用推荐频率设置计算出的PAC基本相同。

与现有方法的比较

较早的关于PAC滤波器设置的建议会导致在频域中模糊估计，这使得难以识别在狭窄频带中运行的神经过程的跨频耦合。

结论

我们得出结论，通过在理论上将PAC与双相干联系起来，可以通过使用不同的滤波器设置选择来避免PAC估计值的模糊。