IEICE TRANSACTIONS on Fundamentals
New Vistas to the Signal Processing of Nonstationary Time Series via an Operator Algebraic Way
Summary :
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.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E84-A No.1 pp.14-30
- Publication Date
- 2001/01/01
- Publicized
- Online ISSN
- DOI
- Type of Manuscript
- Special Section INVITED PAPER (Special Section on the 10th Anniversary of the IEICE Transactions of Fundamentals: "Last Decade and 21st Century")
- Category
Authors
Keyword
Latest Issue
Copyrights notice of machine-translated contents
The copyright of the original papers published on this site belongs to IEICE. Unauthorized use of the original or translated papers is prohibited. See IEICE Provisions on Copyright for details.
Cite this
Copy
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
Copy
@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},}
Copy
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 -
English
