基于模型降阶法的线性相位IIR滤波器设计

Design of Linear Phase IIR Filters via Method of Model Reduction

采用基于脉冲响应格拉姆阵的模型降阶法设计线性相位滤波器.为避免以往模型降阶算法在通过求解离散李亚谱诺夫方程得到脉冲响应格拉姆阵过程中的大量计算以及可能出现的病态计算,采用了直接构造格拉姆阵的方法;还根据汉克尔阵奇异值分布确定降阶模型的阶数.实验结果表明,所设计的 IIR 滤波器满足给定的幅频指标,相位在通带内呈线性,且保证了稳定性.

This paper designed linear phase IIR filters using method of model reduction based on impulse-response grammian Instead of being obtained from solving the discrete Lyapunov equation,which may result in large amount of computation and ill conditioning caculation,the grammian is constructed di- rectly using the Markov parameters.The order of the reduced model was deter- rmined according to the distribution of Hankel sigular values.The result showed that the obtained IIR filters satisfied the given magnitude specifications, and having linear phase in the passband.Their stabilities were guaranteed.