The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. ex. Some numerals are expressed as "XNUMX".
Copyrights notice
The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. Copyrights notice
주어진 공분산 매개변수와 일치하는 선형 이산시간 시스템을 찾는 것은 신호 처리, 시스템 구현 및 시스템 식별에서 중요한 문제입니다. 이 문제는 주어진 공분산 매개변수를 보간하는 이산시간 양의 실수 함수를 찾는 문제로 공식화됩니다. 다양한 조사를 통해 문제에 대한 몇 가지 중요한 해결책이 도출되었지만 McMillan 학위와 관련된 중요한 미해결 문제가 남아 있습니다. 본 논문에서는 공분산 매개변수보다 더 일반적인 입출력 특성을 사용하고 이러한 특성을 보간하는 이산시간 양의 실수 행렬 함수를 찾는 것을 고려합니다. 입출력 특성은 개방형 단위 디스크의 일부 복소수 지점에서 Taylor 계열의 계수로 제공됩니다. 따라서 우리의 문제는 공분산 매개변수의 보간 문제를 일반화한 것입니다. 문제를 제약 조건이 있는 방향 보간 문제로 축소하고 상태 공간 기반의 새로운 접근 방식으로 솔루션을 개발합니다. 주요 결과는 주어진 특성을 보간하고 제한된 McMillan 차수를 갖는 이산시간 양의 실수 행렬 함수의 존재에 대한 필요 충분 조건과 이러한 모든 함수의 매개변수화로 구성됩니다. 이는 공개 문제에 대한 기여이자 이전 결과의 일반화입니다.
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부
Kazumi HORIGUCHI, "Discrete-Time Positive Real Matrix Functions Interpolating Input-Output Characteristics" in IEICE TRANSACTIONS on Fundamentals,
vol. E82-A, no. 8, pp. 1608-1618, August 1999, doi: .
Abstract: It is an important problem in signal processing, system realization and system identification to find linear discrete-time systems which are consistent with given covariance parameters. This problem is formulated as a problem of finding discrete-time positive real functions which interpolate given covariance parameters. Various investigations have yielded several significant solutions to the problem, while there remains an important open problem concerning the McMillan degree. In this paper, we use more general input-output characteristics than covariance parameters and consider finding discrete-time positive real matrix functions which interpolate such characteristics. The input-output characteristics are given by the coefficients of the Taylor series at some complex points in the open unit disk. Thus our problem is a generalization of the interpolation problem of covariance parameters. We reduce the problem to a directional interpolation problem with a constraint and develop the solution by a state-space based new approach. The main results consist of the necessary and sufficient condition for the existence of the discrete-time positive real matrix function which interpolates the given characteristics and has a limited McMillan degree, and a parameterization of all such functions. These are a contribution to the open problem and a generalization of the previous result.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e82-a_8_1608/_p
부
@ARTICLE{e82-a_8_1608,
author={Kazumi HORIGUCHI, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Discrete-Time Positive Real Matrix Functions Interpolating Input-Output Characteristics},
year={1999},
volume={E82-A},
number={8},
pages={1608-1618},
abstract={It is an important problem in signal processing, system realization and system identification to find linear discrete-time systems which are consistent with given covariance parameters. This problem is formulated as a problem of finding discrete-time positive real functions which interpolate given covariance parameters. Various investigations have yielded several significant solutions to the problem, while there remains an important open problem concerning the McMillan degree. In this paper, we use more general input-output characteristics than covariance parameters and consider finding discrete-time positive real matrix functions which interpolate such characteristics. The input-output characteristics are given by the coefficients of the Taylor series at some complex points in the open unit disk. Thus our problem is a generalization of the interpolation problem of covariance parameters. We reduce the problem to a directional interpolation problem with a constraint and develop the solution by a state-space based new approach. The main results consist of the necessary and sufficient condition for the existence of the discrete-time positive real matrix function which interpolates the given characteristics and has a limited McMillan degree, and a parameterization of all such functions. These are a contribution to the open problem and a generalization of the previous result.},
keywords={},
doi={},
ISSN={},
month={August},}
부
TY - JOUR
TI - Discrete-Time Positive Real Matrix Functions Interpolating Input-Output Characteristics
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1608
EP - 1618
AU - Kazumi HORIGUCHI
PY - 1999
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E82-A
IS - 8
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - August 1999
AB - It is an important problem in signal processing, system realization and system identification to find linear discrete-time systems which are consistent with given covariance parameters. This problem is formulated as a problem of finding discrete-time positive real functions which interpolate given covariance parameters. Various investigations have yielded several significant solutions to the problem, while there remains an important open problem concerning the McMillan degree. In this paper, we use more general input-output characteristics than covariance parameters and consider finding discrete-time positive real matrix functions which interpolate such characteristics. The input-output characteristics are given by the coefficients of the Taylor series at some complex points in the open unit disk. Thus our problem is a generalization of the interpolation problem of covariance parameters. We reduce the problem to a directional interpolation problem with a constraint and develop the solution by a state-space based new approach. The main results consist of the necessary and sufficient condition for the existence of the discrete-time positive real matrix function which interpolates the given characteristics and has a limited McMillan degree, and a parameterization of all such functions. These are a contribution to the open problem and a generalization of the previous result.
ER -