دانلود رایگان مقاله آنالیز وضوح فرکانس EMD بر اساس انترپولاسیون B-Spline

abstract

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.

5. Conclusion

We have proposed two practical criteria to identify IMFs based on the definition. One criterion is only based on the envelopes of signals and the other is associated with the envelopes and extrema of signals. These criteria provide a proof for the EMD sifting stopping criterion which does not count the number of the zerocrossings and extrema of signals. By using these criteria, we deduce that narrow-band signals with non-zero extrema, FM signals, and monocomponent signals are all IMFs. We have further analyzed the frequency resolution of EMD from a digital signal processing perspective based on the B-spline interpolation. We have shown that the filtering characteristics of iterative B-spline filters have been improved as increasing iterations. Based on analysis on the characteristics of iterative B-spline filters, we have proved theoretically that the frequency resolution of EMD can be improved with more sifting times without considering the influence of noise generated in the EMD sifting process. We have then shown that the noise generated in the course of extracting IMFs will affect the frequency resolution of EMD. The EMD method cannot obtain narrow-band IMFs considering the influence of noise. More sifting iteration only can in some extent to improve the frequency resolution of EMD. In the practical application, it needs to limit the excessive EMD sifting iterations.