Abstract: In this paper，a quadratic programming method based on semidefinite programming is given to solve the design of FIR filters with discrete coefficients in the light of literature 6，which can give a better bound than a semidefinite programming relaxation method.Based on the model，the Branch-and-Bound algorithm is　used　to solve this problem.Compared with the conventional randomized method，this one can obtain a better sub-optimal performance.This method is very effective for the design of high-precision FIR digital filters.The simulations have proved it.

摘要： 基于离散系数滤波器设计问题已有的半定规划松弛模型，利用文献[6]的方法给出了该问题的二次规划松弛模型，该模型能给出比半定规划模型更好的界，然后运用分支定界方法求解该模型。与随机扰动方法相比，该方法能得到一个性能更好的次优解，对于精度要求较高的滤波器设计问题，这种方法非常有效，并通过了仿真实验的证实。