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Discrete orthogonal transforms on lattices of integer elements of quadratic fields
V.M. Chernov 1,2

1 IPSI RAS – Branch of the FSRC "Crystallography and Photonics" RAS,
443001, Samara, Russia, Molodogvardeyskaya 151,
2 Samara National Research University, 443086, Samara, Russia, Moskovskoye Shosse 34

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DOI: 10.18287/2412-6179-CO-809

Pages: 142-148.

Full text of article: Russian language.

Abstract:
In this paper, we introduce a new class of discrete orthogonal transforms (DОT) defined on lattices of integer elements of quadratic fields. The method of synthesis of such transforms essentially uses the specifics of the representation of integer quadratic elements in the so-called quasi-canonical number systems. This article, which presents the results of the first part of the author's research, deals exclusively with problems related to binary number systems in quadratic fields. We also consider the issues of synthesis of fast algorithms of the introduced and the possibility of their application to the analysis of fractal (or self-similar) objects. We also consider the issues of synthesis of fast algorithms of the introduced methods and the possibility of their application for the analysis of fractal (or self-similar) objects.

Keywords:
discrete orthogonal transformations, number systems, quadratic fields, machine arithmetic.

Citation:
Chernov VM. Discrete orthogonal transformations on lattices of integer elements of quadratic fields. Computer Optics 2021; 45(1): 142-148. DOI: 10.18287/2412-6179-CO-809.

Acknowledgements:
The work was partly funded by the Russian Federation Ministry of Science and Higher Education within a state contract with the "Crystallography and Photonics" Research Center of the RAS under agreement 007-ГЗ/Ч3363/26 in part of «number systems» and by Russian Foundation for Basic Research (Grants 19-07-00357 А and 18-29-03135_ мк) in part of "machine arithmetic".

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