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".
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The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. Copyrights notice
É um problema importante no processamento de sinais, realização de sistemas e identificação de sistemas encontrar sistemas lineares de tempo discreto que sejam consistentes com determinados parâmetros de covariância. Este problema é formulado como um problema de encontrar funções reais positivas de tempo discreto que interpolam determinados parâmetros de covariância. Várias investigações produziram várias soluções significativas para o problema, embora permaneça um importante problema em aberto relativo ao grau de McMillan. Neste artigo, usamos características de entrada-saída mais gerais do que parâmetros de covariância e consideramos encontrar funções de matriz real positiva em tempo discreto que interpolam tais características. As características de entrada-saída são dadas pelos coeficientes da série de Taylor em alguns pontos complexos do disco unitário aberto. Assim, nosso problema é uma generalização do problema de interpolação de parâmetros de covariância. Reduzimos o problema a um problema de interpolação direcional com uma restrição e desenvolvemos a solução por meio de uma nova abordagem baseada no espaço de estados. Os principais resultados consistem na condição necessária e suficiente para a existência da função matricial real positiva de tempo discreto que interpola as características dadas e tem um grau de McMillan limitado, e uma parametrização de todas essas funções. Estas são uma contribuição para o problema aberto e uma generalização do resultado anterior.
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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
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@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},}
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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 -