A cost-effective and convenient approach for color imaging is to use a single sensor and mount a color filter array (CFA) in front of it, such that at each spatial position the scene information in only one color channel is captured. To estimate the missing colors at each pixel, a demosaicing algorithm is applied to the CFA samples. Besides the filter arrangement and the demosaicing method, the spectral sensitivity functions of the CFA filters considerably affect the quality of the demosaiced image. In this paper, we propose an algorithm to compute the optimum spectral sensitivities of filters in the single sensor imager. The proposed algorithm solves a constrained optimization problem to find optimum spectral sensitivities and the corresponding linear demosaicing method. An important constraint for this problem is the smoothness of spectral sensitivities, which is imposed by modeling these functions as a linear combination of several smooth kernels. Simulation results verify the effectiveness of the proposed algorithm in finding optimal spectral sensitivity functions, which outperform measured camera sensitivity functions.