Once a signal is added to this uniformly distributed white noise background, the components in different scales of the signal are automatically projected onto proper scales of reference established by the white noise in the background. Because each of the noise-added decompositions includes the signal and the added white noise, each individual trial may certainly generate a noisy result. But the noise in each trial is different in separate trials. Thus it can be decreased or even completely cancelled out in the ensemble mean of enough trails. The ensemble mean is treated as the true answer because finally, the only persistent component is the signal as more and more trials are added in the ensemble.Based on the principle mentioned above, the EEMD algorithm can be given as follows .
(1)Initialize the number of ensemble M, the amplitude of the added white noise, and m = 1.(2)Perform the mth trial on the signal added white noise.(a)Add a white noise series with the given amplitude to the investigated signal:xm(t)=x(t)+nm(t)(1)where nm(t) indicates the mth added white noise series, and xm(t) represents the noise-added signal of the mth trial.(b)Decompose the noise-added signal xm(t) into I IMFs ci (i = 1, 2, ��, I) using EMD, where ci,m denotes the ith IMF of the mth trial, and I is the number of IMFs.(c)If m < M then go to step (a) with m = m + 1. Repeat steps (a) and (b) again and again, but with different white noise series each time.(3)Calculate the ensemble mean ci of the M trials for each IMF.ci=1M��m=1Mci,m,i=1,2,��,I,m=1,2,��,M��(2)(4)Report the mean ci (i = 1, 2, ��, I) of each of the I IMFs as the final IMFs.
EEMD is an improved version of EMD and is supposed to eliminate the problem of mode mixing by adding noise to the signal to change the distribution of extrema. The improvement of EEMD, however, largely depends on the parameters adopted in the EEMD algorithms, Drug_discovery for example, the amplitude of the added noise. If the parameters vary, the decomposition results may change accordingly. To prove this statement, a simulation signal x(t) is considered here. It consists of three components: an impact component, a high-frequency sinusoidal wave and a low-frequency sinusoidal wave. The three components and the simulation signal are shown in Figure 1a�Cd, respectively.Figure 1.(a)�C(c) the three components, and (d) the simulation signal.
First, the signal is processed by EEMD with the added white noise amplitude of 0.001 of the standard deviation of the simulation signal. Correspondingly, four IMFs are generated and plotted in Figure 2a�Cd, respectively. It is obvious that the impact component and the high-frequency sinusoidal component are decomposed into the same IMF c1, i.e., the mode mixing is occurring between higher frequency components. It could be explained that the added noise is too small to change the extrema distribution of the signal.