Determining the characteristics of a random process by comparing them with values based on models of distribution laws

Safaryan O.A.
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The effectiveness of communication and data transmission systems (CSiPS), which are an integral part of modern systems in almost any field of science and technology, largely depends on the stability of the frequency of the generated signals. The signals generated in the CSiPD can be considered as processes, the frequency of which changes under the influence of a combination of external influences. Changing the frequency of the signals leads to a decrease in the signal-tonoise ratio (SNR) and, consequently, a deterioration in the characteristics of the signal-to-noise ratio, such as the probability of a bit error and bandwidth. It is most convenient to consider the description of such changes in the frequency of signals as random processes, the apparatus of which is widely used in the construction of mathematical models describing the functioning of systems and devices in various fields of science and technology. Moreover, in many cases, the characteristics of a random process, such as the distribution law, mathematical expectation, and variance, may be unknown or known with errors that do not allow us to obtain estimates of the signal parameters that are acceptable in accuracy. The article proposes an algorithm for solving the problem of determining the characteristics of a random process (signal frequency) based on a set of samples of its frequency, allowing to determine the sample mean, sample variance and the distribution law of frequency deviations in the general population. The basis of this algorithm is the comparison of the values of the observed random process measured over a certain time interval with a set of the same number of random values formed on the basis of model distribution laws. Distribution laws based on mathematical models of these systems and devices or corresponding to similar systems and devices can be considered as model distribution laws. When forming a set of random values for the accepted model distribution law, the sample mean value and variance obtained from the measurement results of the observed random process are used as mathematical expectation and variance. The feature of the algorithm is to compare the measured values of the observed random process ordered in ascending or descending order and the generated sets of values in accordance with the accepted models of distribution laws. The results of mathematical modeling illustrating the application of this algorithm are presented.

Keywords: random process, characteristics of a random process, sample mean, sample variance, correlation of ordered sets of samples of random values
Citation in English: Safaryan O.A. Determining the characteristics of a random process by comparing them with values based on models of distribution laws // Computer Research and Modeling, 2025, vol. 17, no. 6, pp. 1105-1118
Citation in English: Safaryan O.A. Determining the characteristics of a random process by comparing them with values based on models of distribution laws // Computer Research and Modeling, 2025, vol. 17, no. 6, pp. 1105-1118
DOI: 10.20537/2076-7633-2025-17-6-1105-1118
URL: http://crm-en.ics.org.ru/journal/article/3669/
Creative Commons License This work is licensed under a Creative Commons Attribution-NoDerivs 3.0 Unported License.

Copyright © 2025 Safaryan O.A.

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