The determination of spectral responsivities plays a significant role in analyzing and predicting the performance of digital imaging systems for remote sensing. For example, given the spectral response functions, we can readily obtain the colorimetric data from a camera corresponding to the remote illuminated objects. In this paper, we develop a filter-based optical system to estimate these functions. The design objective of this system is to effectively select a limited amount of spectral (or broadband) filters to characterize the spectral features of color imaging processes, which are contaminated with noise, so that the spectral response functions can be estimated with satisfactory accuracy. In our approach, a theoretical study is first presented to pave the way for this work, and then we propose a filter selection method based on the technique of orthogonal-triangular (QR) decomposition with column pivoting, called QRCP method. This method involves QR computations and a column permutation process, which determines a permutation matrix to conduct the subset (or filter) selection. Experimental results reveal that the proposed technique is truly consistent with the theoretical study on filter selections. As expected, the optical system with the filters selected from the QRCP method is much less sensitive to noise than those with other spectral filters from different selections. It turns out that our approach is an effective way to implement the optical system for estimating spectral responsivities of digital imaging systems.