Iterative Filtering as an Alternative Algorithm for Empirical Mode Decomposition

The empirical mode decomposition (EMD) was a method pioneered by (N. Huang et al., The empirical mode decomposition and the Hilbert spectrum for nonlinear nonstationary time series analysis, Proc. Roy. Soc. Lond. A454 (1998) 903–995) as an alternative technique to the traditional Fourier and wavelet techniques for studying signals. It decomposes a signal into several components called intrinsic mode functions (IMFs), which have shown to admit better behaved instantaneous frequencies via Hilbert transforms. In this paper, we propose an alternative algorithm for EMD based on iterating certain filters, such as Toeplitz filters. This approach yields similar results as the more traditional sifting algorithm for EMD. In many cases the convergence can be rigorously proved.