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A multi-taper based method for detecting significant activation patterns in a time series of observations at a single voxel, as measured with functional magnetic resonance imaging, is presented in this paper. The method involves testing for relations between the action frequencies and the hemodynamic response via non-parametric estimation of the spectral density of the time series and is used to locate the activated areas. For comparison, the correlation coefficients analysis and Welch method are also introduced. Experimental results demonstrate that the proposed method is effective and is quite suitable for detecting activation in functional MRI when the stimulus action is presented in periodic sequence.