On the influence of time-series length in EMD to extract frequency content: Simulations and models in biomedical signals

In this paper, fractional Gaussian noise (fGn) was used to simulate a homogeneously spreading broadband signal without any dominant frequency band, and to perform a simulation study about the influence of time-series length in the number of intrinsic mode functions (IMFs) obtained after empirical mode decomposition (EMD). In this context three models are presented. The first two models depend on the Hurst exponent H, and the last one is designed for small data lengths, in which the number of IMFs after EMD is obtained based on the regularity of the signal, and depends on an index measure of regularity. These models contribute to a better understanding of the EMD decomposition through the evaluation of its performance in fGn signals. Since an analytical formulation to evaluate the EMD performance is not available, using well-known signals allows for a better insight into the process. The last model presented is meant for application to real data. Its purpose is to predict, in function of the regularity signal, the time-series length that should be used when one wants to divide the spectrum into a pre-determined number of modes, corresponding to different frequency bands, using EMD. This is the case, e.g., in heart rate and blood pressure signals, used to assess sympathovagal balance in the central nervous system.