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We propose a common-subexpression-elimination (CSE) method for the synthesis of fixed-point finite-impulse response (FIR) filters. The proposed CSE algorithm considers both the redundancy among the canonic-signed-digit (CSD) filter coefficients and the length of the critical path in the multiplier block of a transposed-form FIR filter. Therefore, the proposed CSE method can perform tradeoff designs between complexity and the throughput rate. The number of adders synthesized by our method is commensurate with that by the graph-dependence algorithms. On the other hand, our method can synthesize a high-order complicated FIR filter in a few seconds.