On the EMD Sifting Property and Instantaneous Parameters

Abstract

Recently proposed Hilbert–Huang transform (HHT), consisting of empirical mode decomposition (EMD) and Hilbert spectrum analysis (HSA), has been proved to be an effective approach in both scientific researches and engineering applications. However, this method is still empirical because of lacking rigorously mathematical foundation. This paper primarily focuses on providing a mathematical contribution on its sifting characteristics and instantaneous features. Firstly, the theory of the original methods as well as their advantages and restrictions are briefly reviewed. Secondly, we conduct in-depth investigations of the instantaneous parameters (IPs) and sifting ability. Thirdly, we proposed a new EMD stopping criterion, determined an optimal number of sifting iterations, employed a new masking signal to fix the mode mixing problem and investigated into the sifting property according to the extremum distribution. Finally, comparative studies, simulations and real data analyses depending on the proposed method are presented to demonstrate the validity of the novel research. The simulations illustrate that the typically defined intrinsic mode functions (IMFs) are not perfectly symmetric with zero-mean, there is still no rigorous mathematical standard to determine the “watershed” between mono and multi-component IMFs. The comparative researches indicate that unlike the prism property of the Fourier transform (FT) and the mathematical microscope property of the wavelet transform (WT), the ultimate goal of the HHT is to work as raindrops.