FIR数字滤波器幅频响应约束最大加权相位误差最小化设计

多数信号滤波应用，对滤波器幅频响应的要求高于相频响应.本文研究了满足幅频响应约束的有限脉冲响应（Infinite Impulse Response，FIR）数字滤波器设计，提出了最大加权相位误差最小化方法.用凸的椭圆误差约束代替非凸的幅值误差约束，将设计问题转化为凸问题；通过与二分技术结合，提出了给定权函数的幅值误差约束最大加权相位误差最小化设计的求解算法.以此算法为核心，构建了迭代重加权最大加权相位误差最小化算法，其中的权函数不再固定，而是基于修改的群延迟误差包络线在迭代中不断更新.权函数收敛后，所得滤波器具有近似等纹波的群延迟误差，最大群延迟误差得到了有效减小.仿真实验表明，与现有相位误差约束最大幅值误差最小化方法相比，得到的FIR滤波器具有更小的最大相位误差和最大群延迟误差.

Design of FIR Digital Filters by a Magnitude-Response Constrained Minimax Weighted Phase Error Method

In many signal filtering applications,the requirement on the magnitude response of the filter is higher than that on the phase response.The design of magnitude-response constrained finite impulse response (FIR) filters was considered and a minimax weighted phase error design method was proposed.Replacing the nonconvex magnitude error constraint with an elliptic error constraint makes the design problem a convex one.Incorporating with a bisection technique,a design algorithm was firstly obtained for the case with a preset phase-error weight.Using this algorithm as the iteration core,an iterative reweighted minimax phase error design algorithm was constructed,where the phase-error weight is not fixed but updated using a modified envelop of the group-delay error function.After the iterative algorithm converges,the resultant filter has a near equiripple group-delay error and a reduced maximum group-delay error.Experiments demonstrate that the proposed method has obtained smaller passband phase error and group-delay error than the existing phase-error constrained minimax magnitude error method.