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This paper presents a new method for the design of sharp linear phase FIR filters using the frequency-response masking (FRM) technique. The method is based on a weighted least square (WLS) approach, and the design problem is solved iteratively. The original least square (LS) problem is decomposed into two LS problems, each of which can be solved analytically. The effectiveness of the method is demonstrated through the design of a lowpass linear phase sharp FIR digital filter.