We have defined the number of degrees of freedom of order n (the n-th order NDF) kn(T) of a piece of an ergodic stationary random process X(t) of length T by using the variance of an estimate Zn(T) of the n-th moment of X(t). Zn(T) is here calculated by averaging Xn(t) over a time interval T. The NDF denotes a quantitative measure of the effective number of independent or uncorrelated random variables Xn(ti) included in the time interval T. Correlation times and equivalent bandwidths, which are important in random processes and some fields in physics, are deduced from the NDF's. In this paper, we study the NDF's from the viewpoint of information theory. First, a simple information measure Jn(T) based on the uncertainty (Shannon's entropy) of Zn(T) is defined. It is natural that we introduce such Jn(T) because kn(T) has been defined based on the variance of Zn(T). We show that the relation J1(T)
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Sho KIKKAWA, Tatsuo YANO, "Information-Theoretic Considerations in Number of Degrees of Freedom of a Random Process" in IEICE TRANSACTIONS on transactions,
vol. E71-E, no. 6, pp. 574-580, June 1988, doi: .
Abstract: We have defined the number of degrees of freedom of order n (the n-th order NDF) kn(T) of a piece of an ergodic stationary random process X(t) of length T by using the variance of an estimate Zn(T) of the n-th moment of X(t). Zn(T) is here calculated by averaging Xn(t) over a time interval T. The NDF denotes a quantitative measure of the effective number of independent or uncorrelated random variables Xn(ti) included in the time interval T. Correlation times and equivalent bandwidths, which are important in random processes and some fields in physics, are deduced from the NDF's. In this paper, we study the NDF's from the viewpoint of information theory. First, a simple information measure Jn(T) based on the uncertainty (Shannon's entropy) of Zn(T) is defined. It is natural that we introduce such Jn(T) because kn(T) has been defined based on the variance of Zn(T). We show that the relation J1(T)
URL: https://global.ieice.org/en_transactions/transactions/10.1587/e71-e_6_574/_p
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@ARTICLE{e71-e_6_574,
author={Sho KIKKAWA, Tatsuo YANO, },
journal={IEICE TRANSACTIONS on transactions},
title={Information-Theoretic Considerations in Number of Degrees of Freedom of a Random Process},
year={1988},
volume={E71-E},
number={6},
pages={574-580},
abstract={We have defined the number of degrees of freedom of order n (the n-th order NDF) kn(T) of a piece of an ergodic stationary random process X(t) of length T by using the variance of an estimate Zn(T) of the n-th moment of X(t). Zn(T) is here calculated by averaging Xn(t) over a time interval T. The NDF denotes a quantitative measure of the effective number of independent or uncorrelated random variables Xn(ti) included in the time interval T. Correlation times and equivalent bandwidths, which are important in random processes and some fields in physics, are deduced from the NDF's. In this paper, we study the NDF's from the viewpoint of information theory. First, a simple information measure Jn(T) based on the uncertainty (Shannon's entropy) of Zn(T) is defined. It is natural that we introduce such Jn(T) because kn(T) has been defined based on the variance of Zn(T). We show that the relation J1(T)
keywords={},
doi={},
ISSN={},
month={June},}
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TY - JOUR
TI - Information-Theoretic Considerations in Number of Degrees of Freedom of a Random Process
T2 - IEICE TRANSACTIONS on transactions
SP - 574
EP - 580
AU - Sho KIKKAWA
AU - Tatsuo YANO
PY - 1988
DO -
JO - IEICE TRANSACTIONS on transactions
SN -
VL - E71-E
IS - 6
JA - IEICE TRANSACTIONS on transactions
Y1 - June 1988
AB - We have defined the number of degrees of freedom of order n (the n-th order NDF) kn(T) of a piece of an ergodic stationary random process X(t) of length T by using the variance of an estimate Zn(T) of the n-th moment of X(t). Zn(T) is here calculated by averaging Xn(t) over a time interval T. The NDF denotes a quantitative measure of the effective number of independent or uncorrelated random variables Xn(ti) included in the time interval T. Correlation times and equivalent bandwidths, which are important in random processes and some fields in physics, are deduced from the NDF's. In this paper, we study the NDF's from the viewpoint of information theory. First, a simple information measure Jn(T) based on the uncertainty (Shannon's entropy) of Zn(T) is defined. It is natural that we introduce such Jn(T) because kn(T) has been defined based on the variance of Zn(T). We show that the relation J1(T)
ER -