On the Spectral Representation and Related Properties of Periodically Correlated Stochastic Process
Summary :
Some properties of periodically correlated stochastic processes such as the mean ergodicity and asymptotic befavior of the periodgram of the processes are studied in this paper. A periodically correlated process (PC-process) is also called periodic nonstationary process, cyclo stationary process and even periodic stationary process although the process may not be stationary, and these are mainly studied as models of signals especially as pulse trains in the communication theory. Although many of interesting results obtained so far are important from the theoretical point of view, they are rather intuitively derived. Therefore we reformulate the process in a rigorous manner, introduce the spectral representation of it when the process is harmonizable in Loève's sense and study mainly about the mean ergodic properties and the limiting behavior of the mean periodgram of the process. Furthermore we study some pulse train processes as particular examples and we show simple examples of nonharmonizable PC-processes which had been thought of as unusual. We point out that by such a theoretical treatment, the position of PC-processes in the theory of nonstatonary processes will be better recognizable and the results obtained here will be useful as the foundation of practical time series and signal analysis in the communication and information theories.
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- IEICE TRANSACTIONS on transactions Vol.E65-E No.12 pp.723-729
- Publication Date
- 1982/12/25
- Publicized
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- Type of Manuscript
- PAPER
- Category
- Mathematics
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Ikuji HONDA, "On the Spectral Representation and Related Properties of Periodically Correlated Stochastic Process" in IEICE TRANSACTIONS on transactions,
vol. E65-E, no. 12, pp. 723-729, December 1982, doi: .
Abstract: Some properties of periodically correlated stochastic processes such as the mean ergodicity and asymptotic befavior of the periodgram of the processes are studied in this paper. A periodically correlated process (PC-process) is also called periodic nonstationary process, cyclo stationary process and even periodic stationary process although the process may not be stationary, and these are mainly studied as models of signals especially as pulse trains in the communication theory. Although many of interesting results obtained so far are important from the theoretical point of view, they are rather intuitively derived. Therefore we reformulate the process in a rigorous manner, introduce the spectral representation of it when the process is harmonizable in Loève's sense and study mainly about the mean ergodic properties and the limiting behavior of the mean periodgram of the process. Furthermore we study some pulse train processes as particular examples and we show simple examples of nonharmonizable PC-processes which had been thought of as unusual. We point out that by such a theoretical treatment, the position of PC-processes in the theory of nonstatonary processes will be better recognizable and the results obtained here will be useful as the foundation of practical time series and signal analysis in the communication and information theories.
URL: https://global.ieice.org/en_transactions/transactions/10.1587/e65-e_12_723/_p
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@ARTICLE{e65-e_12_723,
author={Ikuji HONDA, },
journal={IEICE TRANSACTIONS on transactions},
title={On the Spectral Representation and Related Properties of Periodically Correlated Stochastic Process},
year={1982},
volume={E65-E},
number={12},
pages={723-729},
abstract={Some properties of periodically correlated stochastic processes such as the mean ergodicity and asymptotic befavior of the periodgram of the processes are studied in this paper. A periodically correlated process (PC-process) is also called periodic nonstationary process, cyclo stationary process and even periodic stationary process although the process may not be stationary, and these are mainly studied as models of signals especially as pulse trains in the communication theory. Although many of interesting results obtained so far are important from the theoretical point of view, they are rather intuitively derived. Therefore we reformulate the process in a rigorous manner, introduce the spectral representation of it when the process is harmonizable in Loève's sense and study mainly about the mean ergodic properties and the limiting behavior of the mean periodgram of the process. Furthermore we study some pulse train processes as particular examples and we show simple examples of nonharmonizable PC-processes which had been thought of as unusual. We point out that by such a theoretical treatment, the position of PC-processes in the theory of nonstatonary processes will be better recognizable and the results obtained here will be useful as the foundation of practical time series and signal analysis in the communication and information theories.},
keywords={},
doi={},
ISSN={},
month={December},}
Copy
TY - JOUR
TI - On the Spectral Representation and Related Properties of Periodically Correlated Stochastic Process
T2 - IEICE TRANSACTIONS on transactions
SP - 723
EP - 729
AU - Ikuji HONDA
PY - 1982
DO -
JO - IEICE TRANSACTIONS on transactions
SN -
VL - E65-E
IS - 12
JA - IEICE TRANSACTIONS on transactions
Y1 - December 1982
AB - Some properties of periodically correlated stochastic processes such as the mean ergodicity and asymptotic befavior of the periodgram of the processes are studied in this paper. A periodically correlated process (PC-process) is also called periodic nonstationary process, cyclo stationary process and even periodic stationary process although the process may not be stationary, and these are mainly studied as models of signals especially as pulse trains in the communication theory. Although many of interesting results obtained so far are important from the theoretical point of view, they are rather intuitively derived. Therefore we reformulate the process in a rigorous manner, introduce the spectral representation of it when the process is harmonizable in Loève's sense and study mainly about the mean ergodic properties and the limiting behavior of the mean periodgram of the process. Furthermore we study some pulse train processes as particular examples and we show simple examples of nonharmonizable PC-processes which had been thought of as unusual. We point out that by such a theoretical treatment, the position of PC-processes in the theory of nonstatonary processes will be better recognizable and the results obtained here will be useful as the foundation of practical time series and signal analysis in the communication and information theories.
ER -
English
