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We propose a new design method of FIR filters with discrete coefficients. In the proposed method, the design problem of FIR filters is formulated as Mixed Integer Linear Programming (MILP), which then can be solved by a branch and bound technique. It is possible to obtain the optimal discrete coefficients with desired word-length and flatness constraints, and the optimality of the obtained solution can be guaranteed. Several numerical examples are provided to demonstrate the superior performance of our design in comparison with other existing methods.