基于
L 2灵敏度最小化的数字滤波器状态空间实现稀疏化方法A Sparse Algorithm of Digital Filter State Space Realization Based on
L 2 -Sensitivity Minimization- 电子学报 2024年52卷第2期 页码：518-527
- 作者机构：
1.重庆邮电大学通信与信息工程学院,重庆 400065
2.移动通信教育部工程研究中心,重庆 400065
3.移动通信技术重庆市重点实验室,重庆400065
- 作者简介：
[ "庄陵 女，1978年生，重庆人.副教授.多载波通信及信号处理. E-mail: zhuangling@cqupt.edu.cn" ]
[ "张文静 女，1995年生，安徽蚌埠人.硕士生.主要研究方向为数字信号处理、滤波器结构设计. E-mail: zhang_wenjing0818@163.com" ]
[ "王光宇 男，1964年生，贵州兴义人.博士教授.主要研究方向为高速信号处理、多速率滤波器组理论. E-mail: wangguangy@cqupt.edu.cn" ]
- 基金信息：中国电子科技集团公司第二十九研究所资助课题
DOI：10.12263/DZXB.20220019
中图分类号： TN911.72;TN713.7收稿：2022-01-03，
修回：2022-08-26，
纸质出版：2024-02-25
- 稿件说明：
移动端阅览
庄陵,张文静,王光宇.基于L2灵敏度最小化的数字滤波器状态空间实现稀疏化方法[J].电子学报,2024,52(02):518-527.
ZHUANG Ling, ZHANG Wen-jing, WANG Guang-yu.A Sparse Algorithm of Digital Filter State Space Realization Based on L2 -Sensitivity Minimization[J].Acta Electronica Sinica, 2024, 52(02): 518-527.
庄陵,张文静,王光宇.基于L2灵敏度最小化的数字滤波器状态空间实现稀疏化方法[J].电子学报,2024,52(02):518-527. DOI：10.12263/DZXB.20220019
ZHUANG Ling, ZHANG Wen-jing, WANG Guang-yu.A Sparse Algorithm of Digital Filter State Space Realization Based on L2 -Sensitivity Minimization[J].Acta Electronica Sinica, 2024, 52(02): 518-527. DOI：10.12263/DZXB.20220019
摘要
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
L
2
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
L
2
灵敏度表达式，并进行稀疏化校准，将
L
2
灵敏度最小化问题转换为凸函数求最值问题，求导得到
L
2
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.
Abstract
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
L
2
-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
L
2
-sensitivity expression based on a similar transformation matrix is obtained according to a controllable and observable Gram matrix
sparse calibration is carry out
an
L
2
-sensitivity minimization problem is converted into a convex function optimization problem
and derivation is carried out to obtain an
L
2
-sensitivity minimization expression. The sparse state space realization of the forward difference operator digital filter is obtained by substitution.The simulation results show that the digital filter designed by the proposed method has better resistance to the FWL effect.
关键词
Keywords
references
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