Design of Multidimensional Digital Filters via System Balancing Concept and its CAS System

基于系统平衡概念的多维数字滤波器及其CAS系统设计

• 批准号: 01550318
• 负责人: KAWAMATA Masayuki
• 金额: $ 1.09万
• 依托单位: Tohoku University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for General Scientific Research (C)
• 财政年份: 1989
• 资助国家: 日本
• 起止时间: 1989 至 1990
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-01550318/
• 关键词: system balancing; multidimensional digital filters; optimal design; CAD; sensitivity; state-space approach; 設計; 多次元ディジタル信号処理

The controllability and observability gramians are defined for multi-dimensional state-space digital filters. Using the controllability and observability gramians, balanced realizations of multi-dimensional state-space digital filters are synthesized.Sensitivity of one- and multi-dimensional state-space filters is analyzed by using the state-space description. This analysis shows that sensitivity of linear multidimensional state-space digital filters is described by their controllability gramian and the observability gramians. Sensitivity can be minimized by using equivalent transformations, and as a result minimum sensitivity of multi-dimensional state-space digital filters can be achieved when their controllability gramian and observability gramian are identical.Several design methods of multi-dimensional state-space digital filters are proposed. These methods design multi-dimensional state-space digital filters via system balancing concept, and can approximate given frequency or spatial domain specifications with very small error. The computational time for the design can be reduced to half of conventional design method by utilizing symmetries of specifications.Computer programs for multi-dimensional state-space digital filtering, system balancing, and several design methods are implemented in FORTRAN and C.

定义了多维状态空间数字滤波器的能控性和能观性。利用可控性和能观性，综合了多维状态空间数字滤波器的平衡实现，并利用状态空间描述分析了一维和多维状态空间数字滤波器的灵敏度。这种分析表明，线性多维状态空间数字滤波器的灵敏度由其可控性文法和可观测性文法来描述。提出了几种多维状态空间数字滤波器的设计方法，利用等价变换使灵敏度最小，从而使多维状态空间数字滤波器的可控性文法与可观测性文法相同时，其灵敏度达到最小。这些方法利用系统平衡的概念设计多维状态空间数字滤波器，能够以很小的误差逼近给定的频域或空域指标。用FORTRAN和C语言实现了多维状态空间数字滤波、系统平衡和几种设计方法的计算机程序。

项目成果

〓,川又: "周波数仕様の低次元分解に基づく分母子分離形2次元ディジタルフィルタの設計" 電子情報通信学会論文誌(A). J72ーA. 1392-1399 (1989)

〓，Kawamata：“基于频率规范的低维分解的分母分离二维数字滤波器”，电子、信息和通信工程师学会汇刊（A）1392-1399（1989）。

M.Ohki,M.Kawamata: "Design of threeーdimensional digital filters based on the outer product expansion" IEEE Trans.on Circuits and Systems. 37. 1164-1167 (1990)

M.Ohki、M.Kawamata：“基于外积展开的三维数字滤波器的设计”IEEE Trans.on 电路与系统 37. 1164-1167 (1990)。

M. Ohki, M. Kawamata and T. Higuchi: ""Design of parallel separable three-dimensional digital filters for frequency domain specifications, "" Trans. of IEICE, J72-A. No. 8. 1247-1252 (1989)

M. Ohki、M. Kawamata 和 T. Higuchi：“用于频域规范的并行可分离三维数字滤波器的设计”，Trans。

M. Iwatsuki, M. Kawamata, and T. Higuchi: ""Statistical sensitivity and minimum sensitivity structures with fewer coefficients in discrete time linear system, "" IEEE Trans. on Circuits and Systems. Vol. 37, No. 1,. 72-80 (1990)

M. Iwatsuki、M. Kawamata 和 T. Higuchi：“离散时间线性系统中系数较少的统计灵敏度和最小灵敏度结构”，IEEE Trans。

T.Deng,川又政征: "周波数領域仕様の低次元分解に基づく分母分離形2次元ディジタルフィルタの設計" 電子情報通信学会論文誌(A). J72-A,9. 1392-1399 (1989)

T. Deng、Masaaki Kawamata：“基于频域规范低维分解的分母分离二维数字滤波器的设计”，电子、信息和通信工程师学会汇刊 (A)，9。 1392-1399 (1989)