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Discrete Wavelet Transforms in Walsh Analysis

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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 transforms considered with wavelet bases recently constructed and frames on the Cantor and Vilenkin groups are noted.

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  1. Russian Presidential Academy of National Economy and Public Administration, Moscow, Russia

    Yu. A. Farkov

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Correspondence to Yu. A. Farkov.

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Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 160, Proceedings of the International Conference on Mathematical Modelling in Applied Sciences ICMMAS’17, Saint Petersburg, July 24–28, 2017, 2019.

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Farkov, Y.A. Discrete Wavelet Transforms in Walsh Analysis. J Math Sci 257, 127–137 (2021). https://doi.org/10.1007/s10958-021-05476-2

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