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In this paper, we propose new design methods for linear phase FIR (finite impulse response) filters with signed power-of-two (SP2) coefficients based on a semi-definite programming (SDP) relaxation method. The proposed methods include a linear programming (LP) relaxation and a relaxation by adding triangle inequalities. Although such design problems are known as NP-hard problems, these methods can solve the design problems with low computational cost in comparison to traditional SDP relaxation methods. It is shown by several numerical experiments that these method are superior to the simple SDP relaxation method.