The general linear model (GLM) was popularly used in both functional magnetic resonance imaging (fMRI) and functional near-infrared spectroscopy (fNIRS). fNIRS is non-invasive technique, good temporal resolution, and applicable in real-time (Naseer et al. 2013, Kamran and Hong 2013). The design matrix in GLM was constructed from the predicted hemodynamic response (HR) and its temporal derivatives (Calhoun et al. 2004, Lindquist et al. 2009). The first coefficient of GLM indicated the brain activity strength (Hu et al. 2010). However, the predicted HR generated by convolving the canonical HR function and a stimulus series (Friston et al., 1998; Lindquist et al., 2009) was not easy to develop GLM for detecting brain activity in real-time.

To cope with the difficulty, we modeled the HR to an impulse stimulus of the motor cortex as a state-space model (SSM). The coefficient matrices in this model were identified by recursive instrument variable (RIV) method (Soderstrom and Stoica 1989). The output of SSM could be considered as the predicted HR without convolving the HR function and a stimulus series. The SSM based predicted HR was comparable with the predicted HR from the difference of two-gamma function. Therefore, our proposed model could be used as the HR function of the design matrix in GLM.