SUMMARYIn this work, the well-known system of orthogonal piecewise-constant Harmut basis functions is investigated. As a result of research, their shortcomings are revealed such as weak convergence, discontinuity and others. To eliminate these problems, a new basis of piecewise-quadratic Harmut functions is proposed and a fast spectral transformation algorithm is developed in this basis. For examples of analytically set and experimentally verified dependencies, the advantages of the algorithm for spectral transformations in a basis of piecewise-quadratic Harmut functions are demonstrated. The proposed system and algorithm could find wide application in such areas as computer graphics, image processing and restoration, machine vision and multimedia, animation and programming of computer games.
In this article, the Grebennikov cubic spline, the Ryabenky cubic spline, and we offer the local interpolation cubic spline models are selected. The construction details of the models were given and the processes of approximating the functions were performed using selected local cubic splines. We can also say that the local interpolation cubic spline models considered in this study provide high accuracy in digital processing of signals, which helps experts to make the right decision as a result of digital processing of signals. For instance, the initial values of the gastroentrological signal were calculated after that they digitally processed, and the error results were taken. Approximation of the considered models and digital processing of the gastroenterological signal by getting error results were specific analyzed comparatively based on numerical and graphical comparisons.
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