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Mat. Zametki, 2011, Volume 89, Issue 6, Pages 914–928 (Mi mz8704)  

This article is cited in 6 scientific papers (total in 6 papers)

Discrete Wavelets and the Vilenkin–Chrestenson Transform

Yu. A. Farkov

Russian State Geological Prospecting University

Abstract: In the spaces of complex periodic sequences, we use the Vilenkin–Chrestenson transforms to construct new orthogonal wavelet bases defined by finite collections of parameters. Earlier similar bases were defined for the Cantor and Vilenkin groups by means of generalized Walsh functions. It is noted that similar constructions can be realized for biorthogonal wavelets as well as for the space $\ell^2(\mathbb{Z}_+)$.

Keywords: Walsh functions, Haar basis, Cantor group, Vilenkin–Chrestenson transform, Hausholder transform, discrete wavelets, biorthogonal wavelets, multiresolution analysis, complex periodic sequences

DOI: https://doi.org/10.4213/mzm8704

Full text: PDF file (497 kB)
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English version:
Mathematical Notes, 2011, 89:6, 871–884

Bibliographic databases:

UDC: 517.518.34
Received: 20.01.2010

Citation: Yu. A. Farkov, “Discrete Wavelets and the Vilenkin–Chrestenson Transform”, Mat. Zametki, 89:6 (2011), 914–928; Math. Notes, 89:6 (2011), 871–884

Citation in format AMSBIB
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\paper Discrete Wavelets and the Vilenkin--Chrestenson Transform
\jour Mat. Zametki
\yr 2011
\vol 89
\issue 6
\pages 914--928
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\crossref{https://doi.org/10.4213/mzm8704}
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\vol 89
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\pages 871--884
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Yu. A. Farkov, M. E. Borisov, “Periodic dyadic wavelets and coding of fractal functions”, Russian Math. (Iz. VUZ), 56:9 (2012), 46–56  mathnet  crossref  mathscinet
    2. Farkov Yu.A., Rodionov E.A., “On Biorthogonal Discrete Wavelet Bases”, Int. J. Wavelets Multiresolut. Inf. Process., 13:1 (2015), 1550002  crossref  mathscinet  zmath  isi  scopus
    3. E. A. Rodionov, “O primenenii veivletov k tsifrovoi obrabotke signalov”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 16:2 (2016), 217–225  mathnet  crossref  mathscinet  elib
    4. Yu. A. Farkov, “Diskretnye veivlet-preobrazovaniya v analize Uolsha”, Materialy mezhdunarodnoi konferentsii «International Conference on Mathematical Modelling in Applied Sciences, ICMMAS-17», Sankt-Peterburgskii politekhnicheskii universitet, 24–28 iyulya 2017 g., Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 160, VINITI RAN, M., 2019, 126–136  mathnet  mathscinet
    5. Yu. A. Farkov, M. G. Robakidze, “Parseval Frames and the Discrete Walsh Transform”, Math. Notes, 106:3 (2019), 446–456  mathnet  crossref  crossref  isi  elib
    6. Yu. A. Farkov, “Konechnye freimy Parsevalya v analize Uolsha”, Materialy Voronezhskoi zimnei matematicheskoi shkoly «Sovremennye metody teorii funktsii i smezhnye problemy». 28 yanvarya–2 fevralya 2019 g.  Chast 1, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 170, VINITI RAN, M., 2019, 118–128  mathnet  crossref
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