SUBBAND ANALYSIS AND SYNTHESIS OF SIGNALS
Currently, a wide class of modern wireless telecommunications systems is based on the use of broadband signals. The problems of synthesis for their formation and processing algorithm are extremely important for such systems, especially under the conditions of various types of disturbances, which is impossible without scientifically based analysis of signal properties.
Â The article presents the results of signal property and synthesis sub-band analysis obtained by the division of the Fourier cosine transformation (transformants) definition domain for signal record into sub-bands (frequency representations). It is shown that the basis of the mathematical apparatus proposed for sub-band analysis and signal synthesis is a new class of matrices, called sub-band ones. The use of this mathematical apparatus allows to solve the tasks of sub-band analysis and signal synthesis without the transfer to the cosine transformation definition domain (without its calculation, but in the signal definition domain directly).Some properties of the eigenvalues for these matrices are established; the problem of additive signal component optimal selection is formulated and solved.
. W. Zhou et al., "Power Frequency Interference and Suppression in Measurement of Power Transmission Tower Grounding Resistance," in IEEE Transactions on Power Delivery, vol. 30, no. 2, pp. 1016-1023, April 2015. doi: 10.1109/TPWRD.2014.2370037.
. Malle S. Wavelets in signal processing. M.: Mir, 2005. Accessed from https://scholar.google.com/scholar?q=%22S.%20Malla,%20Wavelets%20in%20signal%20processing,%20Mir,%20Moskow,%202005.%22
. Lanczosh K. Practical methods of applied analysis. M.: Nauka, 1961.
. Gantmakher F.R. Theory of matrices. Moscow, Nauka, 1967. Accessed from https://books.google.co.ke/books?hl=en&lr=&id=ePFtMw9v92sC&oi=fnd&pg=PR3&ots=slbgpF9RG8&sig=auOpoh0XrqVZqdAmAnspbg5SsIY&redir_esc=y#v=onepage&q&f=false
. Balashov V.A., Vorobienko P.P., Lyakhovetsky L.M. Transmission systems with orthogonal harmonic signals. M.: Ecotrends, 2012. â€“ 228 p.
. Chobanu M. Multidimensional Multi-Speed Systems of Processing of a Signal(Mnogomernye mnogoskorostnye sistemy obrabotki signalov), Moscow, 2009, 480 Ñ€. (in Russian.)
. Evgeny G. Zhilyakov, Sergey P. Belov, Denis V. Ursol About signals allowing to provide sustainability to impacts of short-term and or focused on spectrum interference. International Journal of Engineering & Technology, 7 (2.2) (2018). pp.16-20.
. Victor Golikov, Marco Rodriguez-Blanco, Olga Lebedeva Robust multipixel matched subspace detection with signal-dependent background power// Journal of Applied Remote Sensing, Janâ€“Mar 2016 â€¢ Vol. 10(1). pp. 1975-1983.
. Abramovits M., Stigan I.A (edited.). Hand book of Mathematical Functions with formulas, graphs and mathematical tables, National Bureau of Standards, Applied Mathematics, Washington, D.C., 1979. â€“ 832 p.
. Zhilyakov, E.G. Optimal sub-band methods for analysis and synthesis of finite-duration signals ,2015, Automation and Remote Control 76(4). pp. 589-602.
. Zhilyakov, E.G. Constructing trends of time series segments, 2017, Automation and Remote Control, 78(3). pp. 450-462.
. Mallat, S., A. Wavelet Tour of Signal Processing, New York: Academic Press, 1999. Translated under the title, 368 p.
. Guryanov I.O. Cognitive radio: new approaches to RF resource provisioning for advanced radio technologies (Kognitivnoye radio: novyye podkhody k obespecheniyu radiochastotnymi resursami peredovykh radiotekhnologiy) / Elektrosvyaz, No. 8, 2012, pp.5-8. [in Russian]
. Stevenson CR, Cordeiro C, Sofer E, Chouinard G. Functional Requirements for the 802.22 WRAN Standard. IEEE 802.22-05/0007r46. New York, NY, USA: IEEE, 2005
. 15. Theory and methods of statistical solutions in radio engineering and communications: Textbook / Zhilyakov EG, Firsova AA. Belgorod: Publishing house of the National Research University "BelGU", 2014. 51-67 p.
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