Perfect Reconstructable Decimated One-Dimensional Empirical Mode Decomposition Filter Banks

This paper introduces decimated filter banks for the one-dimensional empirical mode decomposition(1D-EMD).These filter banks can provide perfect reconstruction and allow for an arbitrary tree structure.Since the EMD is a data driven decomposition,it is a very useful analysis instrument for non-stationary and non-linear signals.However,the traditional 1D-EMD has the disadvantage of expanding the data.Large data sets can be generated as the amount of data to be stored increases with every decomposition level.The 1D-EMD can be thought as having the structure of a single dyadic filter.However,a methodology to incorporate the decomposition into any arbitrary tree structure has not been reported yet in the literature.This paper shows how to extend the 1D-EMD into any arbitrary tree structure while maintaining the perfect reconstruction property.Furthermore,the technique allows for downsampling the decomposed signals.This paper,thus,presents a method to minimize the data-expansion drawback of the 1D-EMD by using decimation and merging the EMD coefficients.The proposed algorithm is applicable for any arbitrary tree structure including a full binary tree structure.