On the Convergence of Iterative Filtering Empirical Mode Decomposition

Empirical Mode Decomposition (EMD), an adaptive technique for data and signal decomposition, is a valuable tool for many applications in data and signal processing. One approach to EMD is the iterative filtering EMD, which iterates certain banded Toeplitz operators in l∞(Z). The convergence of iterative filtering is a challenging mathematical problem. In this paper we study this problem, namely for a banded Toeplitz operator T and x ∈ l∞(Z) we study the convergence of T(x). We also study some related spectral properties of these operators. Even though these operators don’t have any eigenvalue in Hilbert space l(Z), all eigenvalues and their associated eigenvectors are identified in l∞(Z) by using the Fourier transform on tempered distributions. The convergence of T(x) relies on a careful localization of the generating function for T around their maximal points and detailed estimates on the contribution from the tails of x.