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This paper presents a method for designing sharp linear phase FIR filters with power-of-two coefficients based on the frequency-response masking technique. The power-of-two coefficients and continuous scaling parameters of the subfilters are taken to be decision variables. Minimizing peak weighted ripple (PWR) of the system is taken to be a design objective. To find the optimum power-of-two coefficients, the alternating variable method is used. In this method, the coefficients of the subfilters are improved iteratively. Optimization of a subfilter over a subregion is done via a branch and bound based method. This method is guaranteed to find a global minimum in each subregion and requires very little search time. The effectiveness of the method is demonstrated through a lowpass linear phase sharp FIR digital filter example.