Understanding phase-amplitude coupling from bispectral analysis

Two measures of cross-frequency coupling (CFC) 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 PACs amplitude component exist, there is no consensus yet. Here, we show that the earlier recommendations on filter settings lead to estimates which are smeared in the frequency domain, which makes it difficult to distinguish higher harmonics from other types of CFC. We also show that smearing can be avoided with a different choice of filter settings by theoretically relating PAC to bicoherence. To illustrate this, PAC estimates of simulations and empirical data are compared to bispectral analyses. We used simulations replicated from an earlier study and empirical data from human electro-encephalography and rat local field potentials. PACs amplitude component was estimated using a bandwidth with a ratio of (1) 2:1, (2) 1:1, or (3) 0.5:1 relative to the frequency of the phase component. 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 CFC. Bicoherence estimates, which do not smear across frequencies by construction, were found to be essentially identical to PAC calculated with the recommended frequency setting.