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research-article

Rhythm-adaptive statistical estimation methods of probabilistic characteristics of cyclic random processes

Published: 18 July 2024 Publication History

Abstract

The paper is devoted to the rhythm-adaptive statistical estimation methods of cyclic random processes probabilistic characteristics. The main goal of the article is development and research of rhythm-adaptive methods of cyclic random processes statistical processing. Based on the fundamental fact of invariance of probabilistic characteristics of a cyclic random process to time shifts determined by its rhythm function, rhythm-adaptive statistical estimations of initial, central and mixed moment functions of cyclic random processes of discrete parameter were obtained. The article analytically proves the unbiasedness and consistency of rhythm-adaptive statistical estimates of the mathematical expectation and the initial moment functions of the higher order of cyclic random process. By conducting a series of computer simulation experiments, it has been demonstrated, that the absolute errors of rhythm-adaptive methods of statistical estimation are significantly smaller than the corresponding errors for classical non-rhythm adaptive methods of statistical estimation of cyclic stochastic signals probabilistic characteristics. The effectiveness of using rhythm-adaptive methods of statistical estimation of probabilistic characteristics of ECG signals has been demonstrated. The results obtained in the work clearly demonstrate the essential advantages of rhythm-adaptive methods of statistical processing of cyclic stochastic signals with a variable (irregular) rhythm in comparison with non-rhythm-adaptive analogues.

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Published In

cover image Digital Signal Processing
Digital Signal Processing  Volume 151, Issue C
Aug 2024
491 pages

Publisher

Academic Press, Inc.

United States

Publication History

Published: 18 July 2024

Author Tags

  1. Сyclic random process
  2. Cyclic stochastic signals computer simulation
  3. Cyclic stochastic signals digital processing
  4. ECG statistical processing
  5. Moment functions estimates

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