Department of Physics and Astronomy, University of Potsdam, Karl-Liebknecht-Str. 24/25, 14476, Potsdam-Golm, Germany.
Movement Disorders and Neuromodulation Unit, Department of Neurology, Charité - Universitätsmedizin Berlin, Charitéplatz 1, 10117, Berlin, Germany.
Sci Rep. 2021 Sep 10;11(1):18037. doi: 10.1038/s41598-021-97560-5.
Computation of the instantaneous phase and amplitude via the Hilbert Transform is a powerful tool of data analysis. This approach finds many applications in various science and engineering branches but is not proper for causal estimation because it requires knowledge of the signal's past and future. However, several problems require real-time estimation of phase and amplitude; an illustrative example is phase-locked or amplitude-dependent stimulation in neuroscience. In this paper, we discuss and compare three causal algorithms that do not rely on the Hilbert Transform but exploit well-known physical phenomena, the synchronization and the resonance. After testing the algorithms on a synthetic data set, we illustrate their performance computing phase and amplitude for the accelerometer tremor measurements and a Parkinsonian patient's beta-band brain activity.
通过希尔伯特变换计算瞬时相位和幅度是数据分析的有力工具。这种方法在各个科学和工程分支中都有许多应用，但不适合因果估计，因为它需要了解信号的过去和未来。然而，有几个问题需要实时估计相位和幅度；神经科学中相位锁定或幅度相关刺激就是一个说明性的例子。在本文中，我们讨论并比较了三种不依赖希尔伯特变换但利用众所周知的物理现象（同步和共振）的因果算法。在对合成数据集进行测试后，我们说明了它们在计算加速度计震颤测量和帕金森病患者β波段脑活动的相位和幅度方面的性能。
