This paper solves the problem of a delay-dependent general robust $H_{infty}$ singular filter design method for uncertain discrete descriptor systems with interval time-varying delay by linear matrix inequality (LMI) technique. Being different from previous approaches, the discrete singular filtering problem with a new Lyapunov function is considered without any changes of variables, Schur complements, and transformations of conditions for robust $H_{infty}$ filtering. The purpose is to design a delaydependent general $H_{infty}$ filter such that the delayed filtering error descriptor system is regular, causal, and stable with $H_{infty}$ norm bound. Moreover, it is shown that the presented design method by the selection of rank in the singular filter provides reduced-order filters including static filter indirectly. Also, the filter design method can be easily extended to uncertain descriptor systems. Finally, numerical examples are presented to illustrate the feasibility and applicability of the proposed method.