- PII
- 10.31857/S0555292324010029-1
- DOI
- 10.31857/S0555292324010029
- Publication type
- Article
- Status
- Published
- Authors
- Volume/ Edition
- Volume 60 / Issue number 1
- Pages
- 4-16
- Abstract
- Для определенных нестационарных источников вещественных гауссовских векторных процессов авторегрессии со скользящим средним (ARMA-процессов) вычисляются скорость создания дифференциальной энтропии и скорость как функция искажения.
- Keywords
- Date of publication
- 18.09.2025
- Year of publication
- 2025
- Number of purchasers
- 0
- Views
- 16
References
- 1. Shannon C.E. A Mathematical Theory of Communication // Bell Syst. Tech. J. 1948. V. 27. № 3. P. 379–423. https://doi.org/10.1002/j.1538-7305.1948.tb01338.x
- 2. Wyner A. Fundamental Limits in Information Theory // Proc. IEEE. 1981. V. 69. № 2. P. 239–251. https://doi.org/10.1109/PROC.1981.11956
- 3. Cover T.M., Thomas J.A. Elements of Information Theory. Hoboken, NJ: Wiley, 2006.
- 4. Toms W., Berger T. Information Rates of Stochastically Driven Dynamic Systems // IEEE Trans. Inform. Theory. 1971. V. 17. № 1. P. 113–114. https://doi.org/10.1109/TIT.1971.1054569
- 5. Guti´errez-Guti´errez and Multivariate ARMA Processes // IEEE Trans. Inform. Theory. 2011. V. 57. № 8. P. 5444–5454. https://doi.org/10.1109/TIT.2011.2159042
- 6. Gray R.M. Toeplitz and Circulant Matrices: A Review // Found. Trends Commun. Inform. Theory. 2006. V. 2. № 3. P. 155–239. https://doi.org/10.1561/0100000006
- 7. Guti´errez-Guti´errez J., Crespo P.M. Block Toeplitz Matrices: Asymptotic Results and Applications // Found. Trends Commun. Inform. Theory. 2011. V. 8. № 3. P. 179–257. https://doi.org/10.1561/0100000066
- 8. Ephraim Y., Lev-Ari H., Gray R.M. Asymptotic Minimum Discrimination Information Measure for Asymptotically Weakly Stationary Processes // IEEE Trans. Inform. Theory. 1988. V. 34. № 5. P. 1033–1040. https://doi.org/10.1109/18.21226
- 9. Gersho A., Gray R.M. Vector Quantization and Signal Compression. New York: Springer, 2012.
- 10. Guti´errez-Guti´errez J., Barasoain-Echepare ´I., Z´arraga-Rodr´ıguez M., Insausti X. Necessary and Sufficient Conditions for AR Vector Processes to Be Stationary: Applications in Information Theory and in Statistical Signal Processing // Appl. Math. Comput. 2023. V. 445, Article 127824 (14 pp.). https://doi.org/10.1016/j.amc.2022.127824
- 11. Guti´errez-Guti´errez J., Z´arraga-Rodr´ıguez M., Insausti X. On the Asymptotic Optimality of a Low-Complexity Coding Strategy for WSS, MA, and AR Vector Sources // Entropy. 2020. V. 22. № 12, Article 1378 (20 pp.). https://doi.org/10.3390/e22121378
- 12. Kolmogorov A. On the Shannon Theory of Information Transmission in the Case of Continuous Signals // IRE Trans. Inform. Theory. 1956. V. 2. № 4. P. 102–108. https://doi.org/10.1109/TIT.1956.1056823
- 13. Guti´errez-Guti´errez J. A Modified Version of the Pisarenko Method to Estimate the Power Spectral Density of Any Asymptotically Wide Sense Stationary Vector Process // Appl. Math. Comput. 2019. V. 362, Article 124526 (11 pp.). https://doi.org/10.1016/j.amc.2019.06.040
- 14. Guti´errez-Guti´errez J., Z´arraga-Rodr´ıguez M., Crespo P.M., Insausti X. Rate Distortion Function of Gaussian Asymptotically WSS Vector Processes // Entropy. 2018. V. 20. № 9, Article 719 (12 pp.). https://doi.org/10.3390/e20090719
- 15. Bhatia R. Matrix Analysis. New York: Springer, 1997.