RECENT MATHEMATICAL DEVELOPMENTS ON EMPIRICAL MODE DECOMPOSITION

摘要

Building the mathematical foundation for the empirical mode decomposition is an important issue in adaptive data analysis. The task of building such a foundation consists of two stages. The first is to construct a large bank of basis functions for the time-frequency analysis of nonlinear and nonstationary signals. The second is to establish a fast adaptive decomposition algorithm. We survey recent mathematical progress on these two stages. Related results on piecewise linear spectral sequences and the Bedrosian identity are also reviewed.