Digitization—reconstruction of binary Markovian process

Authors

  • V. A. Kazakov National Polytechnic Institute, Mexico
  • Yu. A. Goritskiy Moscow Power Engineering Institute, Russian Federation

DOI:

https://doi.org/10.3103/S0735272706110021

Abstract

The statistical description of digitization-reconstruction procedure of binary Markovian process by a conditional mean rule is performed. It is analytically shown, conditional distribution of the jump moment between two various samples represents the truncated exponential distribution which in specific case degenerates in uniform. Expressions for a conditional mean-value (as estimations for the jump moment) and for a conditional dispersion (as errors of this estimation) are produced. Statistical modelling results matching with theoretical relations are discussed.

References

REDMAN, S.J.; LAMPARD, D.G. "Stochastic sampling of a binary random process," IEEE Trans. Circuit Theory, v.10, n.1, р.3-24, Mar 1963. DOI: https://doi.org/10.1109/TCT.1963.1082096.

LACAZE, B. "Periodic bi-sampling of stationary processes," Signal Processing, v.68, n.3, р.283-293, 1998. DOI: https://doi.org/10.1016/S0165-1684(98)00078-4.

LACAZE, B. "Reconstruction of stationary processes sampled at random times," in: Nonuniform Sampling. Theory and Practice (ed. by F. Marvasti). N.Y.: Kluwer Academic/Plenum Publishers, 2001. Ch. 8. DOI: https://doi.org/10.1007/978-1-4615-1229-5_8.

KAZAKOV, V.A. "The interpolator of binary processes," RF Patent No. 756425, Bull. Inv., No. 30.

KAZAKOV, V.A. "Vosstanovlenie realizatcii sluchainykh protcessov posle nelineinykh bezynertcionnykh preobrazovanii," Radiotekhnika, v.31, n.9, p.40-42, 1988.

KAZAKOV, V.A.; BELYAEV, M.A. " Realizations reconstruction of non-stationary random processes by a set of discrete readings," Izv. VUZ. Radioelektronika, v.40, n.9, p.43-49, 1997.

KAZAKOV, V.A.; BELYAEV, M.A. "Sampling reconstruction procedure for non-stationary Gaussian processes based on conditional expectation rule," Sampling Theory in Signal and Image Processing, v.1, n.2, p.135-153, May 2002.

KAZAKOV, V. "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, n.1-2, p.98-115, 2005.

CRAMER, H. Mathematical Methods of Statistics. Princeton University Press, 1946.

Published

2006-11-02

Issue

Section

Research Articles