Spurious cross-frequency amplitude–amplitude coupling in nonstationary, nonlinear signals

• Nonstationary oscillations can induce spurious amplitude–amplitude coupling (AAC).
• Nonlinear waveform can induce spurious AAC.
• The EMD-based AAC method performs better than the Fourier-based AAC method.

Recent studies of brain activities show that cross-frequency coupling (CFC) plays an important role in memory and learning. Many measures have been proposed to investigate the CFC phenomenon, including the correlation between the amplitude envelopes of two brain waves at different frequencies — cross-frequency amplitude–amplitude coupling (AAC). In this short communication, we describe how nonstationary, nonlinear oscillatory signals may produce spurious cross-frequency AAC. Utilizing the empirical mode decomposition, we also propose a new method for assessment of AAC that can potentially reduce the effects of nonlinearity and nonstationarity and, thus, help to avoid the detection of artificial AACs. We compare the performances of this new method and the traditional Fourier-based AAC method. We also discuss the strategies to identify potential spurious AACs.