Nonuniform Extrema Resampling and Empirical Mode Decomposition

Empirical mode decomposition (EMD) isan adaptive signal processing method. However, it stilllacks a rigorous mathematical foundation. This paper investigates the EMD method using the nonuniform sampling theory. The first step of the EMD algorithm, identifying all the local extrema, can be regarded as a process ofextrema resampling. The extrema resampling rate changeswith the extrema distribution, so the EMD method isadaptive. By comparing the average extrema resamplingrate of a composite two-tones signal with the EMD results, we conclude that EMD will work properly only whenextrema resampling satisfies the sampling theorem of thelow-frequency component. Therefore, extrema resamplingcan explain the nature of the resolution properties of theEMD. Consequently, we gain an in depth understanding ofthe EMD method.