近似线性相位全通数字滤波器的迭代重加权Minimax设计

An Iterative Reweighted Minimax Design of All-pass Filters for Nearly Linear Phases

近似线性相位是许多滤波系统希望具有的重要特性,全通滤波器则是实现这个特性的重要技术手段.提出全通数字滤波器的一种迭代重加权minimax设计方法,最小化最大加权线性相位偏差,并利用群延迟偏差信息对权函数进行迭代更新,使群延迟偏差函数近似等纹波.为展现该方法的优越性,将该方法应用于线性相位希尔伯特变换器及相位均衡器的设计.设计例子展示了算法良好的收敛性,以及在实现滤波系统近似线性相位和近似常数群延迟方面的优良性能.

Linear phases are often a requisite in many signal filtering applications.All-pass digital filters are the main device to realize the linear phases.An iterative reweighted minimax method is proposed for the design of all-pass digital filters.The method minimizes the maximum weighted phase deviation from some linear phase,and reduces the maximum group-delay deviation from some constant group delay through updating the phase-error weight function iteratively by virtue of the group-delay deviation.To demonstrate its advantages,the proposed method is applied in the designs of phase equilizers and linear-phase Hilbert transformers.Simulation results show that the proposed algorithm has good convergence properties,and is very effective in realizing the nearly linear phase and nearly constant group delay of the filtering system.