Analysis of Intrinsic Mode Functions: A PDE Approach

The empirical mode decomposition is a powerful tool for signal processing. Because of its original algorithmic, recent works have contributed to its theoretical framework. Following these works, some mathematical contributions on its comprehension and formalism are provided. In this paper, the so called local mean is computed in such a way that it allows the use of differential calculus on envelopes. This new formulation makes us prove that iterations of the sifting process are well approximated by the resolution of partial differential equations (PDE). Intrinsic mode functions are originally defined in a intuitive way. Herein, a mathematical characterization of modes is given with the proposed PDE-based approach.