Comparison of Wavelet and RID-Rihaczek Based Methods for Phase-Amplitude Coupling

Abstract

Oscillatory phenomena and linear/nonlinear interactions across different oscillatory frequencies are commonly seen between the elements of complex systems. One particular form of interaction that is widely encountered is the modulation of the amplitude of broadband high-frequency oscillations by the phase of low-frequency oscillations, defined as phase-amplitude coupling (PAC). Conventional methods for assessing PAC mostly rely on the Hilbert transform. Previous studies have shown that this method produces biased or spurious PAC estimates as it is highly dependent on the parameters of the bandpass filter used to extract narrowband signals from broadband signals. Recently, wavelet-based methods have been proposed to address some of these limitations. In this letter, we provide a thorough comparison between wavelet-based PAC measures and our recently introduced Reduced Interference Rihaczek (RID-Rihaczek) distribution based PAC both analytically and through simulations. The proposed method is shown to yield higher frequency resolution PAC estimates compared to wavelet-based methods.