为解决传统数字滤波器在有限精度实现时因有限字长(Finite Word Length,FWL)效应导致滤波器性能下降的问题,提出一种L2灵敏度最小化的数字滤波器状态空间实现稀疏化方法.推导前向差分算子数字滤波器结构传输函数及其等效状态空间实现,根据可控及可观格莱姆矩阵得到基于相似变换矩阵的L2灵敏度表达式,并进行稀疏化校准,将L2灵敏度最小化问题转换为凸函数求最值问题,求导得到L2灵敏度最小化表达式,代回即得前向差分算子数字滤波器的稀疏化状态空间实现.仿真结果表明,所提方法设计的数字滤波器具有更好的抗FWL效应.
A Sparse Algorithm of Digital Filter State Space Realization Based on L2-Sensitivity Minimization
In order to solve the problem of filter performance degradation caused by finite word length(FWL)effect when traditional digital filter is implemented in finite precision,a sparse algorithm of digital filter state space realization based on L2-sensitivity minimization is proposed.A transmission function of a forward difference operator digital filter structure and an equivalent state space realization of that forward difference operator digital filter structure are deduce,an L2-sensitivity expression based on a similar transformation matrix is obtained according to a controllable and observable Gram matrix,sparse calibration is carry out,an L2-sensitivity minimization problem is converted into a convex function optimiza-tion problem,and derivation is carried out to obtain an L2-sensitivity minimization expression.The sparse state space real-ization of the forward difference operator digital filter is obtained by substitution.The simulation results show that the digi-tal filter designed by the proposed method has better resistance to the FWL effect.
digital filterfinite word lengthforward difference discretizationsparse matrixL2-sensitivity
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