Electroencephalographic (EEG) recordings are often contaminated by artifacts, i.e. signals that have no-cerebral origin and therefore distort the EEG analysis. In this paper we propose a wavelet analysis useful to detect impulsive artifacts, like spike and eye blink; in particular we use two threshold's methods based on the discrete wavelet transform (DWT) and on the stationary wavelet transform (SWT), respectively. Both methods are equivalent in the identification of eye blink artifact, but we find a different behavior in the spikes detection. Using the DWT we observed that the spike detection is decimation-sensitive, in other words the even or odd decimation corrupts the artifact identification step. On the other hand, the translational invariance property of SWT allows to overcome this limitation improving the wavelet analysis for the EEG artifacts detection.