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

• Let MxMx be the average of a given signal xx, it has been proved that M(x−Mx)=0M(x−Mx)=0, at some extent.
• Do not need to predefined the class of functions, to calculate the average of a signal.
• The model we proposed can avoid the global influence and robust to noise perturbations.

The empirical mode decomposition (EMD) is an algorithm pioneered by 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 IMF 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.