FIR数字滤波器零极点灵敏度分析及优化实现

Analysis and optimal realization of pole-zero sensitivity for FIR digital filters

针对有限字长效应导致滤波器零极点的位置偏移问题,基于状态空间实现结构研究FIR数字滤波器零极点对系数误差的灵敏性。不同于IIR滤波器,FIR滤波器状态空间模型中的系统矩阵具有亏损性。引入亏损矩阵广义特征向量分析极点的灵敏性,导出灵敏度表达式,并依据相似变换理论找寻最佳变换矩阵,提出FIR滤波器零极点灵敏度的优化实现。理论推导及仿真实验表明,FIR滤波器极点对系数误差敏感度较高,且所提优化实现方案能够降低灵敏度。

Aiming at the deviation of pole and zero in filters which caused by the finite word length(FWL)effects,the sensitivity of pole and zero for FIR digital filters to coefficient errors was studied based on the state-space model.Unlike the IIR filter,the system matrix in state-space model of the FIR filter was defective.A set of generalized eigenvectors of defective matrix was introduced to analyze the pole sensitivity and derive the measure expression,and optimal realizations with respect to pole-zero sensitivity for FIR filters were proposed by finding optimal transformation matrices according to the similarity transformation theory.Theoretical analysis and simulation experiments show that the poles of a FIR filter are more sensitive to coefficient errors,and the proposed optimal realizations can reduce the sensitivity.