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Near-Ideal Predictors and Causal Filters for Discrete-Time Signals

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Abstract

The paper presents linear predictors and causal filters for discrete-time signals featuring some different kinds of spectrum degeneracy. These predictors and filters 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.

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References

  1. Butzer, P.L. and Stens, R.L., Linear Prediction by Samples from the Past, Advanced Topics in Shannon Sampling and Interpolation Theory, Marks, R.J., Ed., New York: Springer, 1993, pp. 157–183. https://doi.org/10.1007/978-1-4613-9757-1_5

    Chapter  Google Scholar 

  2. Higgins, J.R., Sampling Theory in Fourier and Signal Analysis: Foundations, Oxford: Clarendon; New York: Oxford Univ. Press, 1996.

    Book  Google Scholar 

  3. Li, Z., Han, J., and Song, Y., On the Forecasting of High-Frequency Financial Time Series Based on ARIMA Model Improved by Deep Learning, J. Forecast., 2020, vol. 39, no. 7, pp. 1081–1097. https://doi.org/10.1002/for.2677

    Article  MathSciNet  Google Scholar 

  4. Luo, S. and Tian, C., Financial High-Frequency Time Series Forecasting Based on Sub-step Grid Search Long Short-Term Memory Network, IEEE Access, 2020, vol. 8, pp. 203183–203189. https://doi.org/10.1109/ACCESS.2020.3037102

    Article  Google Scholar 

  5. Knab, J.J., Interpolation of Band-Limited Functions Using the Approximate Prolate Series, IEEE Trans. Inform. Theory, 1979, vol. 25, no. 6, pp. 717–720. https://doi.org/10.1109/TIT.1979.1056115

    Article  MathSciNet  Google Scholar 

  6. Lyman, R.J., Edmonson, W.W., McCullough, S., and Rao, M., The Predictability of Continuous-Time, Bandlimited Processes, IEEE Trans. Signal Process., 2000, vol. 48, no. 2, pp. 311–316. https://doi.org/10.1109/78.823959

    Article  Google Scholar 

  7. Lyman, R.J. and Edmonson, W.W., Linear Prediction of Bandlimited Processes with Flat Spectral Densities, IEEE Trans. Signal Process., 2001, vol. 49, no. 7, pp. 1564–1569. https://doi.org/10.1109/78.928709

    Article  MathSciNet  Google Scholar 

  8. Papoulis, A., A Note on the Predictability of Band-limited Processes, Proc. IEEE, 1985, vol. 73, no. 8, pp. 1332–1333. https://doi.org/10.1109/PROC.1985.13284

    Article  Google Scholar 

  9. Vaidyanathan, P.P., On Predicting a Band-limited Signal Based on Past Sample Values, Proc. IEEE, 1987, vol. 75, no. 8, pp. 1125–1127. https://doi.org/10.1109/PROC.1987.13856

    Article  Google Scholar 

  10. Dokuchaev, N., Predictors for Discrete Time Processes with Energy Decay on Higher Frequencies, IEEE Trans. Signal Process., 2012, vol. 60, no. 11, pp. 6027–6030. https://doi.org/10.1109/TSP.2012.2212436

    Article  MathSciNet  Google Scholar 

  11. Dokuchaev, N., On Predictors for Band-limited and High-Frequency Time Series, Signal Process., 2012, vol. 92, no. 10, pp. 2571–2575. https://doi.org/10.1016/j.sigpro.2012.04.006

    Article  Google Scholar 

  12. Dokuchaev, N., Near-ideal Causal Smoothing Filters for the Real Sequences, Signal Process., 2016, vol. 118, no. 1, pp. 285–293. https://doi.org/10.1016/j.sigpro.2015.07.002

    Article  MathSciNet  Google Scholar 

  13. Dokuchaev, N., Limited Memory Predictors Based on Polynomial Approximation of Periodic Exponentials, J. Forecast., 2022, vol. 41, no. 5, pp. 1037–1045. https://doi.org/10.1002/for.2843

    Article  MathSciNet  Google Scholar 

  14. Dokuchaev, N.G., Predictors for High Frequency Signals Based on Rational Polynomial Approximation of Periodic Exponentials, Probl. Peredachi Inf., 2022, vol. 58, no. 4, pp. 84–94 [Probl. Inf. Transm. (Engl. Transl.), 2022, vol. 58, no. 4, pp. 372–381]. https://doi.org/10.1134/S003294602204007X

    MathSciNet  Google Scholar 

  15. Stone, M.H., The Generalized Weierstrass Approximation Theorem, Math. Mag., 1948, vol. 21, no. 4, pp. 167–184; no. 5, pp. 237–254 (continued). https://doi.org/10.2307/3029750; https://doi.org/10.2307/3029337

    Article  MathSciNet  Google Scholar 

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Funding

This work was supported by ongoing institutional funding. No additional grants to carry out or direct this particular research were obtained.

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Correspondence to N. G. Dokuchaev.

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Translated from Problemy Peredachi Informatsii, 2023, Vol. 59, No. 2, pp. 32–48. https://doi.org/10.31857/S0555292323020031

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Dokuchaev, N.G. Near-Ideal Predictors and Causal Filters for Discrete-Time Signals. Probl Inf Transm 59, 99–114 (2023). https://doi.org/10.1134/S0032946023020035

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  • DOI: https://doi.org/10.1134/S0032946023020035

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