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

TLDR

The study proposes a method to assign statistical significance to IMF components in noisy data. The authors illustrate this method by applying it to Southern Oscillation Index data. Numerical experiments show that EMD behaves as a dyadic filter, producing normally distributed IMF components with identical Fourier spectra, and that the product of IMF energy density and averaged period is constant, with the energy‑density function following a chi‑squared distribution.

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.