Analytical representation of the statistical properties of random processes with arbitrary spectra
E.P. Orlov, I.M. Sizova

 

P.N. Lebedev Physical Institute, Russian Academy of Sciences, Moscow, Russia

Full text of article: Russian language.

Abstract:
A method of analytical representation of the statistical properties of narrow-band Gaussian random processes with arbitrary spectra is proposed. Although the method is not rigorously proven it is verified in a large number of computing experiments.

Keywords:
coherent and statistical optics, Gaussian random process, similarity, analytical representation.

Citation:
Orlov EP, Sizova IM. Analytical representation of the statistical properties of random processes with arbitrary spectra. Computer Optics 2016; 40(4): 560-571. DOI: 10.18287/2412-6179-2016-40-4-560-571.

References:

  1. Baskakov SI. Radio technical chains and signals [In Russian]. Moscow: “Visshaia Shkola” Publisher; 2000.
  2. Arecchi FT, Scully MO, Haken H, Weidlich W. Quantum fluctuations of laser radiation. In book: Glauber RJ, ed. Quantum Optics. New York: Academic Press; 1969: 4.
  3. Kutaev YuF, Mankevich SK, Nosach OYu, Orlov EP. Laser receiver with a quantum detection limit in the near-IR range. Quantum Electronics 2000; 30(9): 833-388. DOI: 10.1070/QE2000v030n09ABEH001819.
  4. Orlov EP, Sizova IM. On the similarity of the statistical characteristics of spontaneous radiation of a quantum amplifier at different gain factor. Journal of Russian Laser Research 2002; 23(4): 299-331. DOI: 10.1023/A:1016329509944.
  5. Orlov EP, Sizova IM. On the correlation time of an optical amplifier quantum noise from the position of its statistical characteristic similarity [In Russian]. Moscow: FIAN Preprint; 2002; 29.
  6. Orlov EP, Sizova IM. On the similarity and universal functions of random process statistical characteristics [In Russian]. Moscow: FIAN Preprint; 2008; 21.
  7. Orlov EP, Sizova IM. The similarity of statistical properties of narrow-band random processes with arbitrary spectra. Part I. Compact spectra [In Russian]. Moscow: FIAN Preprint; 2010; 14.
  8. Orlov EP, Sizova IM. The similarity of statistical properties of narrow-band random processes with arbitrary spectra. Part II. Noncompact diachromic spectra [In Russian]. Moscow: FIAN Preprint; 2011; 19
  9. Akhmanov SA, D’yakov YuE, Chirkin AS. Introduction to Statistical Optics and Radiophysics [In Russian]. Moscow: “Nauka” Publisher; 1981.
  10. Willis HF. A formula for expanding an integral as a series. Philosophical Magazine 1948; 39: 455-459. DOI: 10.1080/14786444808521694.
  11. Prudnikov AP, Brichkov YuA, Marichev OI. Integrals and series. Volume 1. Simple functions [In Russian]. Moscow: “Nauka” Publisher; 1981.
  12. Gradshtein IS, Rizik IM. Tables of integrals, sums, series and products [In Russian]. Moscow: “Fizmatlit” Publisher; 1971.

© 2009, IPSI RAS
Institution of Russian Academy of Sciences, Image Processing Systems Institute of RAS, Russia, 443001, Samara, Molodogvardeyskaya Street 151; e-mail: ko@smr.ru; Phones: +7 (846 2) 332-56-22, Fax: +7 (846 2) 332-56-20