End-effect, stopping criterion, mode mixing and confidence limit for the Hilbert-Huang transform

Abstract

The Hilbert-Huang transform is a new and powerful signal-processing technique, which has greater capability than all other methods in analysing nonlinear and non-stationary signals. Firstly, the problem of end-effect is studied and four solutions are developed in the algorithm. Secondly, the stopping criterion of the sifting process is investigated. Thirdly, an intermittency test preventing mode mixing is provided. These three points are discussed throughout a systematic study of length-of-day data. Moreover, a method evaluating the performances of the algorithm is described. It makes use of five indicators: the index of energy conservation, the index of orthogonality, the number of intrinsic mode functions (IMFs), the number of iterations per IMFs and the index of component separation. Finally, the efficiency of the intermittency test is demonstrated through the study of vortex-shedding signals, and a nonlinear phenomenon of intra-wave frequency modulation is found and interpreted.