Convergence of a Convolution-Filtering-Based Algorithm for Empirical Mode Decomposition

In [?] Lin, Wang and Zhou propose the iterative Toeplitz filters algorithm as an alternative iterative algorithm for EMD. In this alternative algorithm, the average of the upper and lower envelopes is replaced by certain “moving average” obtained through a low-pass filter. Performing the tradition sifting algorithm with such moving averages is equivlalent to iterating certain convolution filters (finite length Toeplitz filters). This paper studies the convergence of this algorithm for signals of continuous variables, and proves that the limit function of this iterative algorithm is an ideal high-pass filtering process.