基于锯齿变换的时间序列数据快速本征模态分解
Fast Intrinsic Mode Decomposition of Time Series Data with Sawtooth Transform
AI总结：
提出一种基于锯齿变换的快速本征模态分解方法，通过将数据转换为分段线性锯齿函数并直接构造包络，避免了EMD的迭代筛选过程，实现单次分解。
摘要：
本文介绍了一种高效的方法来寻找时间序列数据的本征模态函数（IMF）分量。该方法比希尔伯特-黄变换（HHT）作者提出的经验模态分解（EMD）方法更快且更具可预测性。该方法将原始数据函数转换为分段线性锯齿函数（或三角波函数），然后在锯齿空间中通过连接极大值点构造上包络、连接极小值点构造下包络，IMF计算为锯齿函数与上下包络均值之差。在锯齿空间中得到的结果被逆变换回原始数据空间，作为所需的IMF和包络均值。该分解方法通过一次处理数据获得唯一的IMF分量，无需EMD方法中耗时的重复筛选过程。还提出了一种基于锯齿函数展开的替代分解方法。
英文摘要：
An efficient method is introduced in this paper to find the intrinsic mode function (IMF) components of time series data. This method is faster and more predictable than the Empirical Mode Decomposition (EMD) method devised by the author of Hilbert Huang Transform (HHT). The approach is to transforms the original data function into a piecewise linear sawtooth function (or triangle wave function), then directly constructs the upper envelope by connecting the maxima and construct lower envelope by connecting minima with straight line segments in the sawtooth space, the IMF is calculated as the difference between the sawtooth function and the mean of the upper and lower envelopes. The results found in the sawtooth space are reversely transformed into the original data space as the required IMF and envelopes mean. This decomposition method process the data in one pass to obtain a unique IMF component without the time consuming repetitive sifting process of EMD method. An alternative decomposition method with sawtooth function expansion is also presented.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
