In this paper, we investigate a method for designing FIR filters with CSD coefficients. Firstly, the H/W complexity of a CSD FIR filter is estimated in terms of number of gates. Using the estimated complexity, an optimal filter that can meet the required performance with minimal H/W complexity can be designed. Next, based on the MILP problem solver called BonsaiG, we present a filter design program. From the two design examples, it is demonstrated that an optimal filter can be obtained by comparing the complexity of the candidate filters in terms of the gate counts, whose differences are estimated to be about 400-600 gates.