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The multivariate empirical mode decomposition (MEMD) algorithm has been recently proposed in order to make empirical mode decomposition (EMD) suitable for processing of multichannel signals. To shed further light on its performance, we analyze the behavior of MEMD in the presence of white Gaussian noise. It is found that, similarly to EMD, MEMD also essentially acts as a dyadic filter bank on each channel of the multivariate input signal. However, unlike EMD, MEMD better aligns the corresponding intrinsic mode functions (IMFs) from different channels across the same frequency range which is crucial for real world applications. A noise-assisted MEMD (N-A MEMD) method is next proposed to help resolve the mode mixing problem in the existing EMD algorithms. Simulations on both synthetic signals and on artifact removal from real world electroencephalogram (EEG) support the analysis.