To a question of formation of complex white Gaussian noise

I.M. Lerner; M.I. Khayrullin; V.I. Il-in

To a question of formation of complex white Gaussian noise

I.M. Lerner¹, M.I. Khayrullin², V.I. Il-in³

research article Pages: 28-31

¹ Ph.D. (Phys.-Math.), Senior Researcher, Doctoral Student, Kazan National Research Technical University named after A.N. Tupolev
² Post-graduate Student, Engineer, Kazan National Research Technical University named after A.N. Tupolev
³ Dr.Sc. (Eng.), Professor, Head of Department of Power and Electrical Engineering, Branch of Kazan Federal University, Nabereznye Chelny

Keywords: complex Gaussian white noise poliharmonic interference

Abstract

The work is dedicated to developing a mathematical model of the complex white Gaussian noise by applying the central limit theorem to the sum of harmonic oscillations defined in the complex form, thereby providing a solution of the problem - amplitude, phase, frequency?. The number of components of the generating noise needed to achieve a given accuracy of approximation of its distribution function with respect to the standard normal distribution was evaluated on the basis of the converted inequality Berry - Essen for the random component having the same random distribution. The results of numerical experiments confirm the correctness of the proposed mathematical model. It is shown that the optimal cost of machine time is the accuracy of the approximation that does not exceed , when the number of components in a sum is 24. In addition, the work presented a graph that allows to determine the number of components depending on the desired accuracy of approximation.

How to cite

Лернер И.М., Хайруллин М.И., Ильин В.И. Формирование белого шума в комплексном виде // Нелинейный мир. 2017. № 1. С. 28–31.

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[1] Zolotarev I.D., Miller JA.EH. Perekhodnye processy v kolebatelnykh sistemakh i cepjakh. M.: Radiotekhnika. 2010. 304 s.

[2] Lerner I.M., KHajjrullin M.I., Ilin G.I. Model idealnogo fazovogo detektora // Fizika volnovykh processov i radiotekhnicheskie sistemy. 2015. T. 18. № 4. S. 45-50.

[3] Borisov JU.P., Cvetnov V.V. Matematicheskoe modelirovanie radiotekhnicheskikh sistem i ustrojjstv. M.: Radio i svjaz. 1985. 176 s.

[4] Evtjanov S.I. Izbrannye trudy. M.: Izdatelskijj dom MEHI. 2013. 304 s.

[5] Korolev V.Yu., Shevtsova I.G. On the upper bound for the absolute constant in the Berry-Esseen inequality // Theory of Probability and its Applications. V. 54. № 4. P. 638-658.

[6] Gonorovskijj I.S. Radiosignaly i perekhodnye javlenija v radiocepjakh. M.: Svjazizdat. 1954. 325 s.

[7] Shevtsova I. On the absolute constants in the Berry Esseen type inequalities for identically distributed summands // arXiv.org:1111.6554 [math.PR] URL: https://arxiv.org/pdf/1111.6554v1.pdf(data obrashhenija 25.09.2016).