Abstract
The principles of digital signal processing are extended for the existing methods of fractal measurements in terms of Hausdorff–Bezikovich and Mandelbrojt dimensions. Fractal dimension as a rational number G1/G2or the ratio of residues GR1/GR2of two equations of measurement (instrument-response equations) is represented in the form of an equivalent digital model of the ratio F1/F2of two sampling rates in some linear digital system. It is shown that such a system is described by generalized convolution, which, in turn, is represented as a cascade connection of interpolators and decimators with integer-valued conversion coefficients. For error-free processing of fractal dimension, it is necessary to convert a rational number to an integer and use Farey fractions in terms of unimodular and multimodular arithmetic. The Farey fractions can then be used as references points in metrological scales.
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