THEOREM ON STOCHASTIC DISCRETIZATION of IMAGES IN RADar AND COMMUNICATIONS

 

Yu. N.  Gorbunov ^1,2

1 Fryazino Branch of Kotelnikov Institute of Radioengineering and Electronics of Russian Academy of Sciences, Vvedensky Sq.1, Fryazino Moscow region 141190, Russia,

2 Russian Technological University (MIREA), Vernadskogo avenue, 78, Moscow 119454, Russia

 

The paper is received on April 20, 2018

 

Abstract. A theorem on stochastic discretization of images in radiolocation and communication is formulated. A stochastic approach is proposed, which assumes the use of random time discretization scales and level quantization. The proposed approach is conceptual for creating a base of signal processing algorithms using the concepts of ordinary and spatial frequencies and randomization. The necessity of randomizing the parameters of rectangular windows is recommended, since along with the choice of weighting functions (window functions), the implementation of stochastic (randomized) averaging of discretized data is important.

The boundaries of the application of the sampling theorem to the case of quantization of images using stochastic signal discretization scales for time and quantization by level have been extended. The proposed methods provide the ability to operate analog electronic circuits in effective key modes “with cut-off”, which is important for building high-potential radar and communication systems. Analog-to-digital converters are becoming low-bit - in the limit of one-bit ([± 1]). In digital processing, it is possible to account for the hardware and computational resources of the digital signal processor.

Dark, television and computer images in radar systems and communications in their digital representation are a set of values ​​of the intensities of the luminous flux, distributed on a final area, which usually has a rectangular shape. The intensity of the emitted light energy from a surface unit at a point with coordinates (x, y) of the image will be represented by a certain number in (x, y) characterizing the brightness of a pixel with coordinates (x, y). When digitally processing, the values ​​in (x, y) must be represented by a finite number of discrete samples in time t and a finite number of binary digits (bits) in amplitude. The use of rectangular spatial and temporal windows leads to side lobes in the rejection zones and to pulsations in the transparency zones of the DH devices. The organization of repeatability by splitting into stages with rectangular windows does not remove the Gibbs phenomenon, the maximum petals remain at the level of ~ 13 dB. With an analog implementation, an image is required to be filtered prior to discretization; prefiltration is often used — weighting using the Gauss function. Digital implementation requires multi-digit multipliers for the implementation of precision weighing using windows Hamming, Hann, Kaiser, Kravchenko and others.

Keywords: stochastic discretization by time, stochastic discretization by space, stochastic discretization by level.

References

1.     V.P.Dvorkovich. Tsifrovye videoinformatsionnye sistemy teoriya I praktika) [Digital video information systems (theory and practice)]. Moscow, Technosphera Publ., 2012, 1008 p. (In Russian)

2.     S. M. Kej, S. L. Marpl. Spectrum analysis – a modern perspectives. Proceedings of the IEEE, 1981, Vol. 69, No. 11, pp. 1380-1419.  DOI 10.1109/PROC.1981.12184

3.     Spectral estimation. Thematic Issue. Proceeding of the IEEE, Vol. 70, Issue 9, September 1982.

4.     Yu.N.Gorbunov, B.S.Lobanov., G.V.Kulikov. Vvedenie v stokhasticheskuyu radiolokatsiyu [Introduction to stochastic radiolocation. Textbook for universities].  Moscow, Goryachaya liniya-Telekom Publ., 2015. 376 p. (In Russian)

5.     Yu.N.Gorbunov. Stochastic temporal and spatial quantization in a flat aperture phased array.  Proceedings of the X International scientific and technical conference "Radar, radio navigation and communication".  Voronezh, NPF "Sequoia" Publ., 2005, Vol. III. pp. 1790-1798. (In Rusian)

6.     Steve Smith. Scientific and technical guidance on Digital Signal Processing.  California, California technical publishing house San Diego, 1999, Available at http:www.autex.spb.ru.

7.     Yu..N. Gorbunov. Randomized signal processing in radar and communications. ISBN 978-3-659-37797-6. LAPLAMBERT Academic Publishing, 66121, Saarbrücken, Germany, 2015, 150 p.

8.     Yu.N.Gorbunov. On the possibility of reducing the number of quantization levels in digital filters of SDC by applying randomized algorithms. Radiotekhnika – Radio Engineering.  1983, No. 6. pp. 45-47. (In Russian)

 

For citation:

Yu. N. Gorbunov. Theorem on stochastic discretization of images in radar and communication. Zhurnal Radioelektroniki - Journal of Radio Electronics. 2018. No. 10. Available at http://jre.cplire.ru/jre/oct18/8/text.pdf

DOI  10.30898/1684-1719.2018.10.8