Discrete wavelet transforms in Walsh analysis

Yu. A. Farkov

Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference on Mathematical Modelling in Applied Sciences ICMMAS-17, St. Petersburg Polytechnic University, July 24-28, 2017, Tome 160 (2019), pp. 126-136.

Résumé

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.

Détail

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

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