Using filter bank property to simplify the calculations of Empirical Mode Decomposition

Abstract

The Empirical Mode Decomposition (EMD) is a method to analyze non-linear non-stationary signals. EMD was proved to behave like a dyadic filter bank when operating on a broadband signal. This means that the frequency content of the Intrinsic Mode Functions (IMFs) calculated decreases from one IMF to the following one. As the frequency contents of the signal decreases, the number of points needed to represent them and the calculations they require should decrease similar to what happens in the Fast Wavelet Transform. The sifting operation of the original EMD algorithm does not benefit from this property. It evaluates the upper and lower envelopes for all data points regardless of the decrease in frequency content that occurs from one IMF to the other. In this work, we present the Computationally Adaptive Empirical Mode Decomposition (CAEMD). This method approximates data using a piecewise-cubic polynomial (PCP) having a minimal number of knots. The sifting and all the steps of the EMD are modified to be applicable to a PCP. After the calculation of each IMF, the PCP is reapproximated to one with fewer knots. Hence, this method benefits from the frequency decrease between IMFs and simplifies the required calculations and reduces the memory needed to store the IMFs. The proposed method was implemented and has demonstrated an improvement in execution time and required storage when compared to EMD. This method, although it involves approximation, can be set to produce a negligible reconstruction error comparable to the rounding error obtained from the EMD method.