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For a better and faster method of extracting EPs, we study the difference between the EP signal singularities and the EEG noise singularities. The ensemble-averaging operation is based on the fact that the EEG can be looked upon as white noise. The singularity detection (SD) technique that we discuss can adequately remove white noise from the signal. We found that there was a very large difference between the EP signal singularities and the EEG noise singularities. The local maxima of the wavelet-transform modulus provide enough information to analyze these singularities. We can extract the EP signal components from the EEG noise by selecting the wavelet-transform modulus maxima that correspond to the EP signal singularities. After removing the modulus maxima of the EEG noise fluctuations, we are able to reconstruct a denoised EP signal.