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An efficient filter synthesis algorithm is proposed to minimize the number of adders required in the design of finite-impulse response filters. Given a specification, a filter can be synthesized by conducting two main steps: coefficient generation and multiplier-block synthesis. While most of previous works have focused on only one of the steps, the proposed algorithm integrates the two steps in an interleaved manner so as to take into account the effect of multiplier-block synthesis in generating coefficients. In addition, the concept of sensitivity is developed to reduce the complexity of computing the variable ranges of coefficients. Experimental results show that the proposed algorithm outperforms previous algorithms in terms of adder cost and takes a relatively short computation time.