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In this paper, we consider the design of FIR prototype filter of DFT filter banks, where the coefficients are expressed as sums of signed powers-of-two terms. The infinite precision solution can be obtained for given amplitude distortion or aliasing power. However, the finite precision solution may not be satisfied. This problem is formulated as a constrained optimization problem and can be transformed into an unconstrained integer programming problem. An efficient algorithm based on a discrete filled function is developed for solving the finite precision solution.