A common way to design a digital control system is to design an analog controller first and discretize it for digital implemention. In this paper, optimal digital controller design is studied within the framework of sampled -data control theory. In particular, multirate discretization of analog controller is considered using an Η$_2$optimality criterion. Solutions are obtained via multirate H2 optimization with a causality constraint due to the multirate structure. In design example, the comparison of the proposed methods is made with the conventional discretization methods, and demonstrate the superiority of the multirate design method.