This paper deals with the problem of observer-based fault detection for linear discrete time-varying (LDTV) systems. A problem formulation is first proposed to address the optimization of the fault detection filter (FDF) design, which is expressed in terms of maximizing a finite horizon H-infinity/H-infinity or H-/H-infinity performance index. This formulation can be applied to FDF design of LDTV systems subject to l(2)-norm bounded unknown inputs or stochastic noise sequences. It is shown that a unified optimal solution to the FDF can be obtained by solving the discrete time Riccati equation and the optimal FDF is not unique. A numerical example is given to illustrate the proposed method. (C) 2010 Elsevier Ltd. All rights reserved.