Resolving transient neurophysiological signals and their interactions with adaptive time-frequency analysis

Research of neural oscillations has shifted from studying individual frequency components to within-cycle modulation and interactions between components. Deciphering these complexities requires advanced methodological approaches capable of accurately capturing the dynamical nature of biological signals. Conventional methods such as event-related potentials and time-frequency spectral analyses assume stationarity, linearity, and additive processes, overlooking nonlinear and nonstationary features of brain activity. Cognitive insights from traditional techniques are therefore limited, potentially misrepresenting how transient oscillatory events contribute to cognition. Critical issues inherited from analytical methods include: First, predefined frequency bands obscure inter-individual and task-dependent variations, including shifts in individual alpha frequency. Second, focus on sinusoidal waveforms neglects functional relevance of nonsinusoidal oscillatory shapes encoding critical physiological information. Third, Fourier-based methods assume linear superposition of oscillations, but multiplicative interactions are prevalent in natural systems. Therefore, Fourier methods may overlook critical nonlinear interactions and misinterpret underlying mechanisms. To address these limitations, we propose Holo-Hilbert Spectral Analysis (HHSA) as a unified framework for analyzing neurophysiological signals. This approach utilizes empirical mode decomposition (EMD) to extract intrinsic mode functions (IMFs) directly from data. By applying additional EMD to envelope and instantaneous frequency functions, researchers can quantify energy from multiplicative and phase-based processes. The approach offers three advantages: First, IMF extraction provides objective signal analysis adapting to individual characteristics without predetermined frequency boundaries. Second, waveform shape and nonlinearity can be described with frequency modulation spectrum. Third, signal envelope modulation can be quantified using amplitude modulation spectrum, helping identify potential cross-frequency couplings.