A Sparse Algorithm of Digital Filter State Space Realization Based on <italic style="font-style: italic">L</italic><sub>2 </sub>-Sensitivity Minimization

ZHUANG Ling; ZHANG Wen-jing; WANG Guang-yu

doi:10.12263/DZXB.20220019

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A Sparse Algorithm of Digital Filter State Space Realization Based on L₂-Sensitivity Minimization

PAPERS | 更新时间：2025-12-11

- A Sparse Algorithm of Digital Filter State Space Realization Based on L₂-Sensitivity Minimization
- ACTA ELECTRONICA SINICA Vol. 52, Issue 2, Pages: 518-527(2024)
- 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：
- 基金信息：
  
  the 29th Research Institute of CETC
- DOI：10.12263/DZXB.20220019
  CLC： TN911.72;TN713.7
- Received：03 January 2022，
  
  Revised：2022-08-26，
  
  Published：25 February 2024
- 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

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

灵敏度表达式，并进行稀疏化校准，将

灵敏度最小化问题转换为凸函数求最值问题，求导得到

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

-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

-sensitivity expression based on a similar transformation matrix is obtained according to a controllable and observable Gram matrix

sparse calibration is carry out

-sensitivity minimization problem is converted into a convex function optimization problem

and derivation is carried out to obtain an

-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.

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references

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Related Institution

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⁰

A Sparse Algorithm of Digital Filter State Space Realization Based on L2 -Sensitivity Minimization

DOI：10.12263/DZXB.20220019

摘要

Abstract

关键词

Keywords

references

A Sparse Algorithm of Digital Filter State Space Realization Based on L₂-Sensitivity Minimization