With the fast development of digital computers, more industrial processes are controlled by digital processors and there is an increasing demand for improving the system reliabilities. The robustness in model-based fault detection has received a lot of attention during the last two decades, and RFDO (Robust Fault Detection Observer) forms an important branch of fault detection. However, most of current research focuses on continuous-time domain and needs relative more computation. Further studies on DRFDO (Discrete-time Robust Fault Detection Observer) are required. In this paper, a frequency weighted robustness index is proposed and a left-eigenvector assignment based DRFDO design method is presented. A genetic algorithm is applied to optimize such an observer. As illustrated in the simulation, a better disturbance attenuation and faster fault detection are achieved. The main contribution of this paper is that the disturbance is attenuated further by combining frequency dependent performance indices and genetic algorithms.