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Near infrared spectroscopy (NIRS) is an effective technique for examining functional brain activity during cognitive tasks by enabling the measurement of the concentration changes of oxy-hemoglobin and deoxy-hemoglobin. In NIRS data analysis, accurate estimation of the hemodynamic response function (HRF) is still under investigation. Most existing methods assume that the shape of the HRF to be known. This assumption may not be appropriate when the HRF varies from subject to subject or from region to region. In this paper, a deconvolution algorithm to estimate the HRF is presented. The advantage of this method is no prior hypothesis about the shape of the HRF is required. In addition, in order to increase the sensitivity of NIRS to functional brain activity, an adaptive filter is designed to remove physiological noises from the noisy NIRS data. In order to verify the effectiveness of the proposed methods, numerical simulations were performed, the results of which are provided herein.