Optimal averages for nonlinear signal decompositions - Another alternative for empirical mode decomposition

The empirical mode decomposition (EMD) is an algorithm pioneered by N. Huang et. al. as an alternative technique to the traditional Fourier and wavelet methods for analyzing nonlinear and non-stationary signals. It aims at decomposing a signal, via an iterative sifting procedure, into several intrinsic mode functions (IMFs), and each of the IMFs has better behaved instantaneous frequency analysis. This paper presents an alternative approach for EMD. The main idea is to replace the average of upper and lower envelopes in the sifting procedure of EMD by a local average obtained by variational optimization framework. Therefore, an IMF can be produced by simply subtracting the average from the signal without iteration. Our numerical examples illustrate that the resulting decomposition is convergent and robust against noise. ∗This research was partially supported by NSF Faculty Early Career Development (CAREER) Award DMS0645266, DMS-1042998, and DMS-1419027, ONR Award (N000141310408), NSFC (Nos. 11371017, 91130009), RFDP (No. 20130171110016), and the “Computational Science Innovative Research Team” program and Guangdong Province Key Laboratory of Computational Science at the Sun Yat-sen University. †The corresponding author. E-mail: [email protected], Tel: (8620)84115508