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Article title MATHEMATICAL MODEL OF TRIGONOMETRIC-LOGARITHMIC BASIS FUNCTIONS OF MELLIN TRANSFORM AND THEIR DIGITAL IMPLEMENTATION
Authors A. M. Makarov, S. S. Postovalov
Section SECTION I. METHODS AND ALGORITHMS OF INFORMATION PROCESSING
Month, Year 03, 2018 @en
Index UDC 519.7, 004.9
DOI
Abstract Possibilities of application of the Mellin transform for different tasks are discussed. Marked is the lack of research of transformations for building universal transformation digital models and the task to perform boundary options and build a generalized model conversion for digital processing is set. Selected is the basis function of the Mellin transform that satisfies the equality Parseval, or the law of conservation of energy. The main difficulties in the generation of basic function are the uneven distribution of the function control points and their displacement, the problem of selection of the sampling step. These difficulties are partially resolved in the process of work. Demonstrated are the regularities of the basis functions, direct and recursive formulas for finding the reference points, zeros and extremes of the basis Mellin function, the comparative efficiency of the two methods of calculation within the framework of the digital model is demonstrated. The most convenient reference points are also indicated, the beginning of the reference for the simple determination of the remaining reference points and the zeros of the function as not subjected to displacement due to the agreement with the Parseval equality. Partially resolved is the problem of choosing the sampling rate due to irregular lengths of basis function periods via a constant adjustment of the sampling rate or the choice of a step coming from the properties of the function.

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Keywords Mellin transform; Mellin basis function; mathematics; IT.
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