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Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2021, Volume 21, Issue 4, Pages 520–531
DOI: https://doi.org/10.18500/1816-9791-2021-21-4-520-531
(Mi isu914)
 

Scientific Part
Computer Sciences

Wavelet $p$-analogs of the discrete Haar transform

M. S. Bespalov

Vladimir State University, 87 Gorky St., Vladimir 600000, Russia
References:
Abstract: Two $p$-analogs (for $p>2$) of the discrete version of the Haar system in vector symbolism are proposed and fast algorithms are constructed based on them. The main wavelet principles for constructing these Haar-like systems are proposed, such as the presence of several parent functions, $p$-ary dilations and shifts. One of the systems retains an orthogonality property. The calculation procedure has been simplified for another almost orthogonal system. The developed algorithms are presented with decimation in time, methods of their representation with decimation in frequency are indicated.
Key words: discrete harmonic analysis, discrete Haar transform, wavelet, shifts and dilations, fast algorithm.
Received: 17.11.2020
Accepted: 24.04.2021
Bibliographic databases:
Document Type: Article
UDC: 519.688
Language: Russian
Citation: M. S. Bespalov, “Wavelet $p$-analogs of the discrete Haar transform”, Izv. Saratov Univ. Math. Mech. Inform., 21:4 (2021), 520–531
Citation in format AMSBIB
\Bibitem{Bes21}
\by M.~S.~Bespalov
\paper Wavelet $p$-analogs of the discrete Haar transform
\jour Izv. Saratov Univ. Math. Mech. Inform.
\yr 2021
\vol 21
\issue 4
\pages 520--531
\mathnet{http://mi.mathnet.ru/isu914}
\crossref{https://doi.org/10.18500/1816-9791-2021-21-4-520-531}
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    Известия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика
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