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A novel algorithm for designing low-power and hardware-efficient linear-phase finite-impulse response (FIR) filters is presented. The algorithm finds filter coefficients with reduced number of signed-power-of-two (SPT) terms given the filter frequency response characteristics. The algorithm is a branch-and-bound-based algorithm that fixes a coefficient to a certain value. The value is determined by finding the boundary values of the coefficient using linear programming. Although the worst case run time of the algorithm is exponential, its capability to find appreciably good solutions in a reasonable amount of time makes it a desirable CAD tool for designing low-power and hardware-efficient filters. The superiority of the algorithm on existing methods in terms of SPT term count, design time, hardware complexity, and power performance is shown with several design examples. Up to 30% reduction in the number of SPT terms is achieved over unoptimized Remez coefficients, which is 20% better than compared optimization methods. The average power saving is 20% over unoptimized coefficients, which is up to 14% better than optimized coefficients obtained with existing methods.