Skip to main content
Log in

Discretization-restoration of Gaussian processes under random appearance of samples

  • Published:
Radioelectronics and Communications Systems Aims and scope Submit manuscript

Abstract

A general algorithm of statistical description of the discretization-restoration procedure of Gaussian random processes when the moments of appearance of several or even all samples are described using probability densities is obtained. As a result a kind of averaged base function and the functions of average restoration error are determined. Examples of discretization-restoration of Markovian process for two types of probability densities of the samples time of appearance are given in which the restoration errors and the kinds of base functions are analyzed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. A. Balakrishnan, “On the Problem of Time Jitter in Sampling,” IRE Trans. on Information Theory IT-8, 226 (1962).

    Article  Google Scholar 

  2. T. M. Souders, D. R. Flach, C. Hagwood, and G. L. Yang, “The Effect of Timing Jitter in Sampling Systems,” IEEE Trans. Instrum., Meas. 39, No. 1, 80 (1990).

    Article  Google Scholar 

  3. V. Kazakov and D. Rodriguez, “Sampling-Reconstruction Procedure of Gaussian processes with a Finite Number of Simples with Jitter,” in Proceedings of the Fourth International Symposium “Communication Systems, Networks and Digital Signal Processing” CSNDSP-04, Newcastle, 20–22 July (UK, 2004), pp. 557–560.

  4. G. V. Gorelov, Non-Regular Discretization of Signals (Radio i Svyaz’, Moscow, 1982) [in Russian].

    Google Scholar 

  5. F. J. Beutler and O. A. Z. Leneman, “Random Sampling of Random Processes: Stationary Point Processes,” Information and Control 9, 325 (1966).

    Article  MATH  MathSciNet  Google Scholar 

  6. O. A. Z. Leneman, “Random Sampling of Random Processes: Impulse Processes,” Information and Control 9, 347 (1966).

    Article  MATH  MathSciNet  Google Scholar 

  7. O. A. Z. Leneman and J. B. Lewis, “Random Sampling of Random Processes: Mean-Square Comparison of Various Interpolators,” IEEE Trans. Automatic Control 11, 396 (1966).

    Article  Google Scholar 

  8. O. A. Z. Leneman, “Random Sampling of Random Process: Optimal Linear Interpolation,” Journal Franclin Institute 281, No. 4, 302 (1966).

    Article  MATH  Google Scholar 

  9. E. Masry, “Poisson Sampling and Spectral Estimation of Continuous-Time Processes,” IEEE Trans. Inf. Theory IT-24,No. 2, 173 (1978).

    Article  MathSciNet  Google Scholar 

  10. G. T. Artamonov and V. D. Tyurin, Analysis of Information Managing Systems with Random Signal’s Quantization Interval in Time (Energiya, Moscow, 1977) [in Russian].

    Google Scholar 

  11. L. A. Baranov, “Error Estimates of the Restoration of a Continuous Random Signal when the Sampling is Irregular,” Telecommunication and Radioengineering 37–38,No. 8, 37 (1983).

    Google Scholar 

  12. V. A. Kazakov, “The Sampling-Reconstruction Procedure with a Limited Number of Samples of Stochastic Processes and Fields on the Basis of the Conditional Mean Rule,” Electromagnetic Waves and Electronic Systems 10, No. 1–2, 98 (2005).

    Google Scholar 

  13. V. Kazakov and D. Rodriguez, “Reconstruction of Gaussian Processes with an Arbitrary Number of Samples and Discrete Jitter,” IETE Journal of Research 51, No. 5, 361 (2005).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Original Russian Text © V.A. Kazakov, D. Rodriguez, 2008, published in Izv. Vyssh. Uchebn. Zaved., Radioelektron., 2008, Vol. 51, No. 3, pp. 11–20.

About this article

Cite this article

Kazakov, V.A., Rodriguez, D. Discretization-restoration of Gaussian processes under random appearance of samples. Radioelectron.Commun.Syst. 51, 122–128 (2008). https://doi.org/10.3103/S0735272708030023

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S0735272708030023

Keywords

Navigation