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This paper presents a new method for designing sharp linear phase FIR filters with power-of-two coefficients. The method is based on a frequency-response masking technique. In this method, the power-of-two coefficients and continuous scaling parameters of the subfilters are taken to be decision variables, and peak weighted ripple (PWR) is taken to be the design objective. The resulting nonlinear mixed integer optimization problem for each subfilter is first reduced to an equivalent discrete optimization problem whose search region is then cropped for efficiency of computation, similar to the approach in (J. Yli-Kaakinen and T. Saramaki, Proc. IEEE Int. Symp. on Circuits Syst., ISCAS 2001, vol. 2, pp. 185-188, 2001), although different subregions are used here. The effectiveness of the method is demonstrated through a low pass linear phase sharp FIR digital filter example.