  In this paper we present a mathematical model of the Empirical Mode
Decomposition (EMD). Although EMD is a powerful tool for signal processing, the
algorithm itself lacks an appropriate theoretical basis. The interpolation and
iteration processes involved in the EMD method have been obstacles for
mathematical modelling. Here, we propose a novel forward heat equation approach
to represent the mean envelope and sifting process. This new model can provide
a better mathematical analysis of classical EMD as well as identifying its
limitations. Our approach achieves a better performance for a "mode-mixing"
signal as compared to the classical EMD approach and is more robust to noise.
Furthermore, we discuss the ability of EMD to separate signals and possible
improvements by adjusting parameters.
