Analysis on frequency resolution of EMD based on B-spline interpolation

Empirical mode decomposition (EMD) is an algorithm to split composite signals into narrow subbands termed intrinsic mode functions (IMFs) to obtain a meaningful instantaneous frequency. However, numerical experiments are still the dominant approach adopted to investigate the EMD algorithm. In this paper, the concrete form of IMFs is first discussed. Two simple criteria do not need to count the number of extrema and zero-crossings which are used to define IMFs are presented to identify IMFs. These criteria show that narrow-band signals with non-zero extrema, frequency modulation (FM) signals, and monocomponent signals are all IMFs. The EMD resolution is then analyzed from the digital signal processing perspective. Based on B-spline interpolation, the filtering characteristics of iterative B-spline filters developed to describe IMFs are analyzed. For the first time, a theoretical proof is presented to demonstrate that the EMD method cannot obtain narrow-band IMFs. Nevertheless, a theoretical proof is given to show that the frequency resolution of EMD can be improved in some extent with more sifting iterations.