Trend extraction based on separations of consecutive empirical mode decomposition components in Hilbert marginal spectrum

Extracting the underlying trends is an important tool for the analysis of signals. This paper presents a novel methodology for extracting the underlying trends of signals based on the separations of consecutive empirical mode decomposition (EMD) components in the Hilbert marginal spectrum. A signal is initially represented as a sum of intrinsic mode functions (IMFs) obtained via the EMD. The Hilbert marginal spectrum of each IMF is then calculated. The separations of two consecutive IMFs in the Hilbert marginal spectrum are estimated based on their correlation coefficients. The group of the last several IMFs in which the IMFs are close to each other in the Hilbert marginal spectrum will be used for the representation of the underlying trend of the signal. Extensive experimental results are presented to illustrate the rationale and the effectiveness of the proposed method.