DESIGN METHODS OF FIR FILTERS WITH SIGNED POWER OF TWO COEFFICIENTS USING A NEW LINEAR PROGRAMMING RELAXATION WITH TRIANGLE INEQUALITIES
Rika Ito, Tetsuya Fujie, Kenji Suyama, Ryuichi Hirabayashi · 2006
Recently, a semi-definite programming relaxation method (SDP relaxation) for the design problem of FIR filters with SP2 coefficients is proposed. In this paper, we propose a new linear programming relaxation method (LP relaxation) with triangle inequalities based on the SDP relaxation method. Here, the polynomiality of the method is guaranteed by exploiting the interior point methods to solve the LP relaxation prob- lem. We will compare the LP relaxation methods proposed here and the SDP relaxation methods through numerical experiments and show that the quality of the solution for the LP relaxation method is better than that of SDP relaxation method. keyword: Digital filter, Optimization, Semi-definite programming, Linear program- ming, Linear programming relaxation, Signed power of two, Approximation