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
이 논문은 부분적으로 검토 성격으로 작성되었으며 비정상 가우시안 프로세스의 선형 필터링 및 예측 문제에 대한 최근 이론적 결과를 제시합니다. 먼저 기본 개념인 신호와 잡음을 수학적으로 특성화하고 선형 확률미분방정식으로 정보원을 정의한다. 그런 다음, 비정상 시계열의 필터링 또는 예측이라는 기존 문제에 대한 해법은 원칙적으로 문제로 축소될 수 있으며, 그 해법은 다음과 같은 문제를 풀 수 있는 경우 Kalman-Bucy의 이론에 의해 제공됩니다. 고려 중인 시계열의 공분산 함수와 동일한 공분산 함수를 갖는 가우스 프로세스의 표준 표현입니다. 그러나 위에서 언급한 문제는 미해결 상태로 남아 있습니다. 또한, 시간-주파수 분석의 문제점을 논의하고 진화적, 즉 온라인 스펙트럼 분석기의 물리적 실현 가능성을 보여줍니다. 미분 연산자를 다루는 방법을 제시하고 그 기본 속성을 명확히 합니다. 마지막으로, 관련된 미해결 문제 중 일부가 제안되었습니다.
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부
Tosiro KOGA, "New Vistas to the Signal Processing of Nonstationary Time Series via an Operator Algebraic Way" in IEICE TRANSACTIONS on Fundamentals,
vol. E84-A, no. 1, pp. 14-30, January 2001, doi: .
Abstract: This paper is, in half part, written in review nature, and presents recent theoretical results on linear-filtering and -prediction problems of nonstationary Gaussian processes. First, the basic concepts, signal and noise, are mathematically characterized, and information sources are defined by linear stochastic differential equations. Then, it is shown that the solution to a conventional problem of filtering or prediction of a nonstationary time series is, in principle, reducible to a problem, of which solution is given by Kalman-Bucy's theory, if one can solve a problem of finding the canonical representation of a Gaussian process such that it has the same covariance functions as those of the time series under consideration. However, the problem mentioned above is left open. Further, the problem of time-frequency analysis is discussed, and physical realizability of the evolutionary, i.e., the online, spectral analyzer is shown. Methods for dealing with differential operators are presented and their basic properties are clarified. Finally, some of related open problems are proposed.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e84-a_1_14/_p
부
@ARTICLE{e84-a_1_14,
author={Tosiro KOGA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={New Vistas to the Signal Processing of Nonstationary Time Series via an Operator Algebraic Way},
year={2001},
volume={E84-A},
number={1},
pages={14-30},
abstract={This paper is, in half part, written in review nature, and presents recent theoretical results on linear-filtering and -prediction problems of nonstationary Gaussian processes. First, the basic concepts, signal and noise, are mathematically characterized, and information sources are defined by linear stochastic differential equations. Then, it is shown that the solution to a conventional problem of filtering or prediction of a nonstationary time series is, in principle, reducible to a problem, of which solution is given by Kalman-Bucy's theory, if one can solve a problem of finding the canonical representation of a Gaussian process such that it has the same covariance functions as those of the time series under consideration. However, the problem mentioned above is left open. Further, the problem of time-frequency analysis is discussed, and physical realizability of the evolutionary, i.e., the online, spectral analyzer is shown. Methods for dealing with differential operators are presented and their basic properties are clarified. Finally, some of related open problems are proposed.},
keywords={},
doi={},
ISSN={},
month={January},}
부
TY - JOUR
TI - New Vistas to the Signal Processing of Nonstationary Time Series via an Operator Algebraic Way
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 14
EP - 30
AU - Tosiro KOGA
PY - 2001
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E84-A
IS - 1
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - January 2001
AB - This paper is, in half part, written in review nature, and presents recent theoretical results on linear-filtering and -prediction problems of nonstationary Gaussian processes. First, the basic concepts, signal and noise, are mathematically characterized, and information sources are defined by linear stochastic differential equations. Then, it is shown that the solution to a conventional problem of filtering or prediction of a nonstationary time series is, in principle, reducible to a problem, of which solution is given by Kalman-Bucy's theory, if one can solve a problem of finding the canonical representation of a Gaussian process such that it has the same covariance functions as those of the time series under consideration. However, the problem mentioned above is left open. Further, the problem of time-frequency analysis is discussed, and physical realizability of the evolutionary, i.e., the online, spectral analyzer is shown. Methods for dealing with differential operators are presented and their basic properties are clarified. Finally, some of related open problems are proposed.
ER -