Processes with significant dead times are difficult to control using standard feedback controllers. When the process has a significant dead time, the performance of the closed-loop system can be improved by using a predictor structure. Both the Modified Smith Predictor (MSP) and the state predictor using a Finite Spectrum Array (FSA) approach are considered here. Precisely, the paper focuses on the distributed delay and the problem of its implementation. It proposes a rational approximation whose nice property are highlighted and compared with those of approximation previously considered in the literature. Moreover, it makes the link to the traditional approach consisting to get a rational approximation of the delay before the design, and highlights the underlying structure.