Multirate systems are abundant in industry. In this paper, the problem studied is designing a residual generator for fault detection based on multirate sampled data. The key new feature of such a residual generator is that it operates at a fast rate for prompt fault detection. The design is based on optimizing a performance index to obtain an optimal parity space based residual generator. The lifting technique is used to convert the time-varying multirate design problem into a time-invariant one with a causality constraint for implementability. A procedure for computing an explicit optimal, causal solution is proposed. The advantages of this design are shown through an example. (C) 2004 Elsevier Ltd. All rights reserved.