论文标题
一种扩展的希尔伯特变换方法，用于从振荡信号中重建相位
An extended Hilbert transform method for reconstructing the phase from an oscillatory signal
论文作者
论文摘要
从细胞到生物水平的生物系统中，有节奏的活性无处不在。重建瞬时相是分析从观察到的信号导致同步状态的基本机制的第一步。一种流行的相重建方法是基于希尔伯特变换，该变换只能从有限的信号（例如狭窄的频段信号）中重建可解释的相位。为了解决这个问题，我们提出了一种扩展的希尔伯特变换方法，该方法可以准确地从各种振荡信号中重建该相。提出的方法是通过借助Bedrosian定理分析希尔伯特变换方法的重建误差来开发的。我们使用合成数据验证了所提出的方法，并显示了与常规希尔伯特变换方法相比，相对于准确重建阶段而言，其系统改善了性能。最后，我们证明所提出的方法可能对检测观察到的信号中的相位移位有用。所提出的方法有望促进从实验数据中研究同步现象。
Rhythmic activity is ubiquitous in biological systems from the cellular to organism level. Reconstructing the instantaneous phase is the first step in analyzing the essential mechanism leading to a synchronization state from the observed signals. A popular method of phase reconstruction is based on the Hilbert transform, which can only reconstruct the interpretable phase from a limited class of signals, e.g., narrow band signals. To address this issue, we propose an extended Hilbert transform method that accurately reconstructs the phase from various oscillatory signals. The proposed method is developed by analyzing the reconstruction error of the Hilbert transform method with the aid of Bedrosian's theorem. We validate the proposed method using synthetic data and show its systematically improved performance compared with the conventional Hilbert transform method with respect to accurately reconstructing the phase. Finally, we demonstrate that the proposed method is potentially useful for detecting the phase shift in an observed signal. The proposed method is expected to facilitate the study of synchronization phenomena from experimental data.
