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In this paper, a new efficient algorithm is proposed for the synthesis of low-complexity finite-impulse response (FIR) filters with resource sharing. The original problem statement based on the minimization of signed-power-of-two (SPT) terms has been reformulated to account for the sharable adders. The minimization of common SPT (CSPT) terms that were considered in our proposed algorithm addresses the optimization of the reusability of adders for two major types of common subexpressions, together with the minimization of adders that are needed for the spare SPT terms. The coefficient set is synthesized in two stages. In the first stage, CSPT terms in the vicinity of the scaled and rounded canonical signed digit (CSD) coefficients are allocated to obtain a CSD coefficient set, with the total number of CSPT terms not exceeding the initial coefficient set. The balanced normalized peak ripple magnitude due to the quantization error is fulfilled in the second stage by a local search method. The algorithm uses a common-subexpression-based hamming weight pyramid to seek for low-cost candidate coefficients with preferential consideration of shared common subexpressions. Experimental results demonstrate that our algorithm is capable of synthesizing FIR filters with the least CSPT terms compared with existing filter synthesis algorithms.