基于二阶锥优化的复系数FIR滤波器设计

A design of complex coefficient FIR filter beased on SOCP

针对设计具有任意幅相响应的复系数FIR滤波器的工程问题,采用二阶锥优化算法计算出合适的复系数FIR滤波器系数。常规FIR滤波器具有良好的线性相位特性,但在某些场合中FIR滤波器的相位有特殊要求,因此复系数FIR滤波器具有广大应用场景。构建合适的最小l1范数优化准则,将设计任意幅相响应的复系数FIR滤波器问题转化为二阶锥优化形式,最后利用CVX工具箱计算复FIR滤波器系数。该方法简单实用,设计出的FIR滤波器与期望响应非常接近,大量实例设计实验证明该算法有效而可靠。

Focused on the engineering problem on the complex coefficient FIR filter with arbitrary amplitude-phase response, the SOCP algorithm is adopted to calculate the suitable complex coefficient for the FIR filter. Normal FIR fiher often has subtle linear phase property, however, under some conditions, the phase of FIR filter needs to be specifically required. Thus, complex coefficient FIR filter has great potential for practical application. The minimum norm optimization principle is constructed, the complex coefficient FIR filter with arbitrary amplitude-phase response problem are transferred into the SOCP . Then, the FIR filter coefficient will be calculated by CVX tool box. This method is quite easily understandable and practical, which can design the suitable FIR filter approximated to the expected response, which was verified through a large amount of engineering experiments.