Near-ideal predictors and causal filters for discrete-time signals

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Abstract

The paper presents linear predictors and causal lters for discrete-time signals featuring some di erent kinds of spectrum degeneracy. These predictors and lters are based on approximation of ideal noncausal transfer functions by causal transfer functions represented by polynomials of the Z-transform of the unit step signal.

About the authors

N. G Dokuchaev

Zhejiang University

Email: dokuchaev@intl.zju.edu.cn
Haining, Zhejiang Province, China

References

  1. Butzer P.L., Stens R.L. Linear Prediction by Samples from the Past // Advanced Topics in Shannon Sampling and Interpolation Theory. New York: Springer, 1993. P. 157-183. https://doi.org/10.1007/978-1-4613-9757-1_5
  2. Higgins J.R. Sampling Theory in Fourier and Signal Analysis: Foundations. Oxford: Clarendon; New York: Oxford Univ. Press, 1996.
  3. Li Z., Han J., Song Y. On the Forecasting of High-Frequency Financial Time Series Based on ARIMA Model Improved by Deep Learning // J. Forecast. 2020. V. 39. № 7. P. 1081-1097. https://doi.org/10.1002/for.2677
  4. Luo S., Tian C. Financial High-Frequency Time Series Forecasting Based on Sub-step Grid Search Long Short-Term Memory Network // IEEE Access. 2020. V. 8. P. 203183-203189. https://doi.org/10.1109/ACCESS.2020.3037102
  5. Knab J.J. Interpolation of Band-Limited Functions Using the Approximate Prolate Series // IEEE Trans. Inform. Theory. 1979. V. 25. № 6. P. 717-720. https://doi.org/10.1109/TIT.1979.1056115
  6. Lyman R.J., Edmonson W.W., McCullough S., Rao M. The Predictability of Continuous-Time, Bandlimited Processes // IEEE Trans. Signal Process. 2000. V. 48. № 2. P. 311-316. https://doi.org/10.1109/78.823959
  7. Lyman R.J., Edmonson W.W. Linear Prediction of Bandlimited Processes with Flat Spectral Densities // IEEE Trans. Signal Process. 2001. V. 49. № 7. P. 1564-1569. https://doi.org/10.1109/78.928709
  8. Papoulis A. A Note on the Predictability of Band-limited Processes // Proc. IEEE. 1985. V. 73. № 8. P. 1332-1333. https://doi.org/10.1109/PROC.1985.13284
  9. Vaidyanathan P.P. On Predicting a Band-limited Signal Based on Past Sample Values // Proc. IEEE. 1987. V. 75. № 8. P. 1125-1127. https://doi.org/10.1109/PROC.1987.13856
  10. Dokuchaev N. Predictors for Discrete Time Processes with Energy Decay on Higher Frequencies // IEEE Trans. Signal Process. 2012. V. 60. № 11. P. 6027-6030. https://doi.org/10.1109/TSP.2012.2212436
  11. Dokuchaev N. On Predictors for Band-limited and High-Frequency Time Series // Signal Process. 2012. V. 92. № 10. P. 2571-2575. https://doi.org/10.1016/j.sigpro.2012.04.006
  12. Dokuchaev N. Near-ideal Causal Smoothing Filters for the Real Sequences // Signal Process. 016. V. 118. № 1. P. 285-293. https://doi.org/10.1016/j.sigpro.2015.07.002
  13. Dokuchaev N. Limited Memory Predictors Based on Polynomial Approximation of Periodic Exponentials // J. Forecast. 2022. V. 41. № 5. P. 1037-1045. https://doi.org/10.1002/for.2843
  14. Докучаев Н.Г. Предикторы для высокочастотных сигналов на основе аппроксимации периодических экспонент рациональными многочленами // Пробл. передачи информ. 2022. Т. 58. № 4. С. 84-94. https://doi.org/10.31857/S0555292322040076
  15. Stone M.H. The Generalized Weierstrass Approximation Theorem // Math. Mag. 1948. V. 21. № 4. P. 167-184; № 5. P. 237-254 (continued). https://doi.org/10.2307/3029750; https://doi.org/10.2307/3029337

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