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vol 67 / February, 2024
Article

DOI 10.17586/0021-3454-2016-59-3-211-218

UDC 519.61; 004.02; 004.67

ON REDUCTION OF SPACE DIMENSION AT DIGITAL SIGNALS CORRELATION AND CONVOLUTION

A. Y. Grishentsev
ITMO University, Saint Petersburg, 197101, Russian Federation; Associate professor


A. G. Korobeynikov
Saint Petersburg Branch Organization of the Russian Academy of Sciences “Institute of Earth Magnetism, Ionosphere and Radio waves named after N.V. Pushkov RAS”;ITMO University, Saint Petersburg, 197101, Russian Federation ; Deputy Director for Science


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Abstract. Theorems on reduction of space dimension at correlation and convolution of n-dimensional digital signals are formulated and proved, specifically for fast convolution on the base of the fast Fourier transformation. Several examples are presented as illustrations. The theorems are reported to have possible applications in the problems of digital processing of n-dimensional signal, broadband radio communication, optoelectronics, in solitary waves (solitons) research, and in other fields of fundamental and applied natural sciences.
Keywords: correlation, convolution, fast convolution, multi-dimensional signals, optimization of computing, digital signal processing, broadband signals

References:

 

  1. Gantmacher F.R. The Theory of Matrices,  AMS Chelsea Publishing: Reprinted by American Mathematical Society, 2000, 660 р.
  2. Zharinov O.O., Zharinov I.O. Izv. vuzov. Priborostroenie, 2014, no. 1(57), pp. 29–38. (in Russ.)
  3. Novikov S.P., Taymanov I.A. Sovremennye geometricheskie struktury i polya (Modern Geometrical Structures and Fields), Moscow, 2005. 584 p. (in Russ.)
  4. Oppenheim A.V. and Schafer R.W. Digital Signal Processing, Englewood Cliffs, NJ, Prentice-Hall, Inc., 1975.
  5. Korobeynikov A.G., Gatchin Yu.A., Dukel'skiy K.V., Ter-Nersesyants E.V. Scientific and Technical Journal of Information Technologies, Mechanics and Optics, 2014, no. 1(89), pp. 31–38. (in Russ.)
  6. Ipatov V.P. Spread Spectrum and CDMA. Principles and Applications, Wiley, 2005, 400 р.
  7. Brey B.B. The Intel microprocessors 8086/8088, 80186/80188, 80286, 80386, 80486. The: Architecture, Programming, and Interfacing, Prentice Hall, 2008, 944 р.
  8. Red'kin P.P. Mikrokontrollery Atmel, arkhitektura AVR32 semeystva AT32UC3. Rukovodstvo pol'zovatelya (Atmel Microcontrollers, Architecture of AVR32 of AT32UC3 Family. User's Guide), Moscow, 2010, 784 p. (in Russ.)
  9. Gerasimov I.V., Saf'yannikov N.M., Yakimovskiy D.O. Slozhno-funktsional'nye bloki smeshannykh sistem na kristalle: avtomatizatsiya funktsional'nogo proektirovaniya (Complex-Function Blocks of the Mixed Systems on a Chip: Automation of Functional Design), St. Petersburg, 2012, 237 p. (in Russ.)
  10. Anisimov V.I. Topologicheskiy raschet elektronnykh skhem (Topological Calculation of Electronic Schemes), Leningrad, 1977, 240 p. (in Russ.)
  11. Chobanu M. Mnogomernye mnogoskorostnye sistemy obrabotki signalov (Multidimensional Multi-Speed Systems of Processing of a Signal), Moscow, 2009, 480 р. (in Russ.)
  12. Dubois E. Proc. IEEE, 1985, no. 4(73), pp. 502–522.
  13. Vaidyanathan P.P. Multirate Systems and Filtеr Banks, Englewood Cliffs, Prentice Hall, 1993, 944 p.
  14. Smith S.W. The Scientist & Engineer's Guide to Digital Signal Processing, 1999, 650 р.
  15. Grishentsev A.Yu., Korobeynikov A.G. Scientific and Technical Journal of Information Technologies, Mechanics and Optics, 2012, no. 4(80), pp. 75–79. (in Russ.)
  16. Grishentsev A.Yu., Korobeynikov A.G. Metody i modeli tsifrovoy obrabotki izobrazheniy (Models and Methods of Digital Image Processing), St. Petersburg, 2014, 190 p. (in Russ.)
  17. Documentation the mathworks Matlab 2-d convolution, http://www.mathworks.com/ help/matlab/ref/conv2.html.