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.
Discrete orthogonal transforms on lattices of integer elements of quadratic fields
