On the convergence of iterative filtering empirical mode decomposition

Abstract

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 chapter we study this problem, namely for a banded Toeplitz operator T and x ∈ l^∞(Z) we study the convergence of Tⁿ(x). We also study some related spectral properties of these operators. Even though these operators don't have any eigenvalue in Hilbert space l²(Z), all eigenvalues and their associated eigenvectors are identified in l^∞(Z) by using the Fourier transform on tempered distributions. The convergence of Tⁿ(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.