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Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 2019, Volume 160, Pages 126–136 (Mi into431)  

Discrete wavelet transforms in Walsh analysis

Yu. A. Farkov

Russian Academy of National Economy and Public Administration under the President of the Russian Federation, Moscow

Abstract: A review of discrete wavelet transforms defined through Walsh functions and used for image processing, compression of fractal signals, analysis of financial time series, and analysis of geophysical data is presented. Relationships of the discrete transformations considered with wavelet bases recently constructed and frames on the Cantor and Vilenkin groups are noted.

Keywords: Walsh functions, Haar system, Weierstrass function, wavelet, frame, zero-dimensional group, discrete transformation, image processing, signal coding, analysis of geophysical data

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Document Type: Article
UDC: 517.518, 621.391
MSC: 42C40, 65T60

Citation: Yu. A. Farkov, “Discrete wavelet transforms in Walsh analysis”, Proceedings of the International Conference onáMathematicaláModellingáináAppliedáSciences ICMMAS-17, St. Petersburg Polytechnic University, July 24-28, 2017, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 160, VINITI, Moscow, 2019, 126–136

Citation in format AMSBIB
\Bibitem{Far19}
\by Yu.~A.~Farkov
\paper Discrete wavelet transforms in Walsh analysis
\inbook Proceedings of the International Conference onáMathematicaláModellingáináAppliedáSciences ICMMAS-17,
St. Petersburg Polytechnic University, July 24-28, 2017
\serial Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz.
\yr 2019
\vol 160
\pages 126--136
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into431}


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