Spatial Matrix Filter with Dimension Reduction Design

LIANG Guo-long; ZHAO Wen-bin; FU Jin

doi:10.3969/j.issn.0372-2112.2017.02.021

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Spatial Matrix Filter with Dimension Reduction Design

更新时间：2025-07-16

- Spatial Matrix Filter with Dimension Reduction Design
- Acta Electronica Sinica Vol. 45, Issue 2, Pages: 417-423(2017)
- 作者机构：
  
  1. 哈尔滨工程大学水声技术重点实验室,黑龙江,哈尔滨,150001
  2. 哈尔滨工程大学水声工程学院,黑龙江,哈尔滨,150001
- 作者简介：
- 基金信息：
  
  Technology Basic Project (No.JSJL2016604B003)
- DOI：10.3969/j.issn.0372-2112.2017.02.021
  CLC： TN929.3
- Published Online：25 February 2017，
  
  Published：2017
- 稿件说明：
移动端阅览
LIANG Guo-long, ZHAO Wen-bin, FU Jin. Spatial Matrix Filter with Dimension Reduction Design[J]. Acta Electronica Sinica, 2017, 45(2): 417-423.
DOI：

LIANG Guo-long, ZHAO Wen-bin, FU Jin. Spatial Matrix Filter with Dimension Reduction Design[J]. Acta Electronica Sinica, 2017, 45(2): 417-423. DOI： 10.3969/j.issn.0372-2112.2017.02.021.

摘要

为解决降维滤波矩阵设计存在的维数与滤波性能之间的矛盾，提出了一种结合K-L变换（Karhunen-Loeve Transform）降维空域滤波矩阵的设计方法.该文首先推导出了滤波矩阵较大特征值的数量取决于滤波矩阵通带带宽的规律，并利用阻带衰减给出了区分大小特征值的门限，进而通过向大特征值对应的特征向量矩阵投影的方法，获得最终的降维空域滤波矩阵.仿真实验证明，由该方法获得的降维矩阵具有与降维前接近的空域滤波能力.

Abstract

The performance of spatial filter matrix degrades sharply in the presence of matrix dimension reduction.To solve the problem

a method using K-L (Karhunen-Loeve) Trans-form to reduce the matrix dimension is proposed.Theoretical derivation show the eigenvalues of the spatial-filter matrix and its conjugate transpose matrix product

has two characteristics.Firstly

there exists some eigenvalues that are much greater than the other eigenvalues.Secondly

the number of greater eigenvalues depends on the bandwidth of filter matrix pass-band.Based on those characteristics

K-L Trans-form was used to realize matrix dimension reduction through abandoning the eigenvectors corresponding to small eigenvalues.The proposed reduction dimension filter matrix has the advantage of orthogonality.Simulation results show the proposed reduction matrix and matrix with maximum dimension have similar filter capability.

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