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Russian Microelectronics

, Volume 30, Issue 2, pp 118–124 | Cite as

Digital Simulation of Fractal Measurements

  • P. A. Arutyunov
Article
  • 22 Downloads

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.

Keywords

Signal Processing Convolution Reference Point Fractal Dimension Sampling Rate 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© MAIK “Nauka/Interperiodica” 2001

Authors and Affiliations

  • P. A. Arutyunov
    • 1
  1. 1.Moscow State Institute of Electronics and MathematicsMoscowRussia

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