We propose a novel approach for designing a low power datapath in wireless communication systems. Especially, we focus on the digital FIR filter. Our proposed approach can reduce the power consumption and the circuit area of the digital FIR filter by optimizing the bitwidth of the each filter coefficient with keeping the filter calculation accuracy. At first, we formulate the constraints about keeping accuracy of the filter calculations. We define the problem to find the optimized bitwidth of each filter coefficient. Our defined problem can be solved by using the commercial optimization tool. We evaluate the effects of consuming power reduction by comparing the digital FIR filters designed in the same bitwidth of all coefficients. We confirm that our approach is effective for a low power digital FIR filter.