Study on Coded Permutation Entropy of Finite Length Gaussian White Noise Time Series

SUN Huihui; ZHANG Xiaofeng

doi:10.23919/cje.2022.00.209

Volume 33 Issue 1

Jan. 2024

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Article Navigation > Chinese Journal of Electronics > 2024 > 33(1): 185-194

Huihui SUN and Xiaofeng ZHANG, “Study on Coded Permutation Entropy of Finite Length Gaussian White Noise Time Series,” Chinese Journal of Electronics, vol. 33, no. 1, pp. 185–194, 2024 doi: 10.23919/cje.2022.00.209

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Huihui SUN and Xiaofeng ZHANG, “Study on Coded Permutation Entropy of Finite Length Gaussian White Noise Time Series,” Chinese Journal of Electronics, vol. 33, no. 1, pp. 185–194, 2024 doi: 10.23919/cje.2022.00.209

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Study on Coded Permutation Entropy of Finite Length Gaussian White Noise Time Series

doi: 10.23919/cje.2022.00.209

SUN Huihui,
ZHANG Xiaofeng^,

1.
School of Physics and Information Technology, Shaanxi Normal University, Xi’an 710119, China

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Author Bio:
Huihui SUN was born in 1997. She received the M.S. degree at Shaanxi Normal University, Xi’an, China. Her research interests include intelligent information processing and detection technology. (Email: huihuisun@snnu.edu.cn)

Xiaofeng ZHANG was born in 1971. She received the Ph.D. degree in underwater acoustic engineering from Northwestern Polytechnical University, Xi’an, China, in 2003. Currently, she is a Professor at Shaanxi Normal University. Her research interests include sound controlling, intelligent information processing and detection technology. Prof. ZHANG is a Member of the Acoustical Society of Japan and a Fellow of the Acoustical Society of Xi’an City. (Email: xiaofengzhang71@snnu.edu.cn)
Corresponding author: Email: xiaofengzhang71@snnu.edu.cn
Received Date: 2022-07-09
Accepted Date: 2022-09-01

Available Online: 2022-09-07

Publish Date: 2024-01-05

Abstract

Abstract

As an extension of permutation entropy (PE), coded permutation entropy (CPE) improves the performance of PE by making a secondary division for ordinal patterns defined in PE. In this study, we provide an exploration of the statistical properties of CPE using a finite length Gaussian white noise time series theoretically. By means of the Taylor series expansion, the approximate expressions of the expected value and variance of CPE are deduced and the Cramér-Rao low bound (CRLB) is obtained to evaluate the performance of the CPE estimator. The results indicate that CPE is a biased estimator, but the bias only depends on relevant parameters of CPE and it can be easily corrected for an arbitrary time series. The variance of CPE is related to the encoding patterns distribution, and the value converges to the CRLB of the CPE estimator when the time series length is large enough. For a finite-length Gaussian white noise time series model, the predicted values can match well with the actual values, which further validates the statistic theory of CPE. Using the theoretical expressions of CPE, it is possible to better understand the behavior of CPE for most of the time series.
- Coded permutation entropy,
- Gaussian white noise,
- Finite-length time series,
- Cramér-Rao low bound

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References(29)

References

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