A Criterion for Selecting Relevant Intrinsic Mode Functions in Empirical Mode Decomposition

Information extraction from time series has traditionally been done with Fourier analysis, which use stationary sines and cosines as basis functions. However, data that come from most natural phenomena are mostly nonstationary. A totally adaptive alternative method has been developed called the Hilbert–Huang transform (HHT), which involves generating basis functions called the intrinsic mode functions (IMFs) via the empirical mode decomposition (EMD). The EMD is a numerical procedure that is prone to numerical errors that may persist in the decomposition as extra IMFs. In this study, results of numerical experiments are presented, which would establish a stringent threshold by which relevant IMFs are distinguished from IMFs that may have been generated by numerical errors. The threshold is dependent on the correlation coefficient between the IMFs and the original signal. Finally, the threshold is applied to IMFs of earthquake signals from five accelerometers located in a building.

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