A study of the characteristics of white noise using the empirical mode decomposition method

Zhaohua Wu, N. Huang
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引用次数: 1639

Abstract

Based on numerical experiments on white noise using the empirical mode decomposition (EMD) method, we find empirically that the EMD is effectively a dyadic filter, the intrinsic mode function (IMF) components are all normally distributed, and the Fourier spectra of the IMF components are all identical and cover the same area on a semi–logarithmic period scale. Expanding from these empirical findings, we further deduce that the product of the energy density of IMF and its corresponding averaged period is a constant, and that the energy–density function is chi–squared distributed. Furthermore, we derive the energy–density spread function of the IMF components. Through these results, we establish a method of assigning statistical significance of information content for IMF components from any noisy data. Southern Oscillation Index data are used to illustrate the methodology developed here.
利用经验模态分解方法研究白噪声的特性
利用经验模态分解(EMD)方法对白噪声进行了数值实验,结果表明EMD是一个有效的二进滤波器,其本征模态函数(IMF)分量均为正态分布,各本征模态函数分量的傅里叶谱在半对数周期尺度上均相同且覆盖相同的面积。从这些实证结果展开,我们进一步推导出IMF的能量密度与其对应的平均周期的乘积是一个常数,并且能量密度函数是卡方分布的。进一步推导了IMF分量的能量密度扩散函数。通过这些结果,我们建立了一种从任何噪声数据中分配IMF成分信息内容统计显著性的方法。南方涛动指数的数据被用来说明这里开发的方法。
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期刊介绍: Proceedings A publishes articles across the chemical, computational, Earth, engineering, mathematical, and physical sciences. The articles published are high-quality, original, fundamental articles of interest to a wide range of scientists, and often have long citation half-lives. As well as established disciplines, we encourage emerging and interdisciplinary areas.
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