Digital Simulation of Fractal Measurements

Digital Simulation of Fractal Measurements 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 G 1/G 2or the ratio of residues G R 1/G R 2of two equations of measurement (instrument-response equations) is represented in the form of an equivalent digital model of the ratio F 1/F 2of 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Russian Microelectronics Springer Journals

Digital Simulation of Fractal Measurements

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Publisher
Kluwer Academic Publishers-Plenum Publishers
Copyright
Copyright © 2001 by MAIK “Nauka/Interperiodica”
Subject
Engineering; Electrical Engineering
ISSN
1063-7397
eISSN
1608-3415
D.O.I.
10.1023/A:1009438028681
Publisher site
See Article on Publisher Site

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 G 1/G 2or the ratio of residues G R 1/G R 2of two equations of measurement (instrument-response equations) is represented in the form of an equivalent digital model of the ratio F 1/F 2of 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.

Journal

Russian MicroelectronicsSpringer Journals

Published: Oct 10, 2004

References

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