论文标题
振荡信号的新型波浪分解
A novel wave decomposition for oscillatory signals
论文作者
论文摘要
振荡系统出现在不同的科学领域。已经提出了具有微分方程的复杂数学公式，以模拟这些系统的动力学。尽管它们具有具有直接生理意义的优势，但由于参数调整复杂性和噪声的存在，它们在实践中没有用。在本文中，提出了一个信号加上误差模型来分析振荡，其中信号是多组分$ fmm $，并且假定噪声为高斯。信号公式也是AM-FM组件中的一种新型分解方法，与傅立叶和其他分解竞争。得出了几种有趣的理论特性，包括描述信号的普通微分方程。此外，实际实践中的有用性是证明可以分析与神经元突触相关的信号，并通过解决神经科学中的其他问题。
Oscillatory systems arise in the different science fields. Complex mathematical formulations with differential equations have been proposed to model the dynamics of these systems. While they have the advantage of having a direct physiological meaning, they are not useful in practice as a result of the parameter adjustment complexity and the presence of noise. In this paper, a signal plus error model is proposed to analyze oscillations, where the signal is a multicomponent $FMM$ and the noise is assumed Gaussian. The signal formulation is also a novel decomposition approach in AM-FM components, competing with Fourier and other decompositions. Several interesting theoretical properties are derived including the Ordinary Differential Equations describing the signal. Furthermore, the usefulness in real practice is demonstrate to analyze signals associated to neuron synapses and by addressing other questions in Neuroscience.
