Consecutive differences as a method of signal fractal analysis
Abstract
We propose a new method for calculating fractal dimension (DF) of a signal y(t), based on coefficients m(y)((n)), mean absolute values of its nth order derivatives (consecutive finite differences for sampled signals). We found that logarithms of m(y)((n)), = 2, 3,..., n(max), exhibited linear dependence on n: log (m(y)((n))) = (slope)n + Y(int) with stable slopes and Y-intercepts proportional to signal DF values. Using a family of Weierstrass functions, we established a link between Y-intercepts and signal fractal dimension: DF = A(n(max))Y(int) + B(n(max)), and calculated parameters A(n(max)) and B(n(max)) for n(max) = 3,..., 7. Compared to Higuchi's algorithm, advantages of this method include greater speed and eliminating the need to choose value for k(max), since the smallest error was obtained with n(max) = 3.
Keywords:
Weierstrass functions / Higuchi's algorithm / fractal dimension / consecutive differences methodSource:
Fractals-Complex Geometry Patterns and Scaling in Nature and Society, 2005, 13, 4, 283-292Publisher:
- World Scientific Publ Co Pte Ltd, Singapore
DOI: 10.1142/S0218348X05002933
ISSN: 0218-348X
WoS: 000234165400003
Scopus: 2-s2.0-27744590465
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Institution/Community
Institut za multidisciplinarna istraživanjaTY - JOUR AU - Kalauzi, Aleksandar AU - Spasić, Slađana AU - Culic, M AU - Grbic, G AU - Martać, Ljiljana PY - 2005 UR - http://rimsi.imsi.bg.ac.rs/handle/123456789/123 AB - We propose a new method for calculating fractal dimension (DF) of a signal y(t), based on coefficients m(y)((n)), mean absolute values of its nth order derivatives (consecutive finite differences for sampled signals). We found that logarithms of m(y)((n)), = 2, 3,..., n(max), exhibited linear dependence on n: log (m(y)((n))) = (slope)n + Y(int) with stable slopes and Y-intercepts proportional to signal DF values. Using a family of Weierstrass functions, we established a link between Y-intercepts and signal fractal dimension: DF = A(n(max))Y(int) + B(n(max)), and calculated parameters A(n(max)) and B(n(max)) for n(max) = 3,..., 7. Compared to Higuchi's algorithm, advantages of this method include greater speed and eliminating the need to choose value for k(max), since the smallest error was obtained with n(max) = 3. PB - World Scientific Publ Co Pte Ltd, Singapore T2 - Fractals-Complex Geometry Patterns and Scaling in Nature and Society T1 - Consecutive differences as a method of signal fractal analysis EP - 292 IS - 4 SP - 283 VL - 13 DO - 10.1142/S0218348X05002933 ER -
@article{ author = "Kalauzi, Aleksandar and Spasić, Slađana and Culic, M and Grbic, G and Martać, Ljiljana", year = "2005", abstract = "We propose a new method for calculating fractal dimension (DF) of a signal y(t), based on coefficients m(y)((n)), mean absolute values of its nth order derivatives (consecutive finite differences for sampled signals). We found that logarithms of m(y)((n)), = 2, 3,..., n(max), exhibited linear dependence on n: log (m(y)((n))) = (slope)n + Y(int) with stable slopes and Y-intercepts proportional to signal DF values. Using a family of Weierstrass functions, we established a link between Y-intercepts and signal fractal dimension: DF = A(n(max))Y(int) + B(n(max)), and calculated parameters A(n(max)) and B(n(max)) for n(max) = 3,..., 7. Compared to Higuchi's algorithm, advantages of this method include greater speed and eliminating the need to choose value for k(max), since the smallest error was obtained with n(max) = 3.", publisher = "World Scientific Publ Co Pte Ltd, Singapore", journal = "Fractals-Complex Geometry Patterns and Scaling in Nature and Society", title = "Consecutive differences as a method of signal fractal analysis", pages = "292-283", number = "4", volume = "13", doi = "10.1142/S0218348X05002933" }
Kalauzi, A., Spasić, S., Culic, M., Grbic, G.,& Martać, L.. (2005). Consecutive differences as a method of signal fractal analysis. in Fractals-Complex Geometry Patterns and Scaling in Nature and Society World Scientific Publ Co Pte Ltd, Singapore., 13(4), 283-292. https://doi.org/10.1142/S0218348X05002933
Kalauzi A, Spasić S, Culic M, Grbic G, Martać L. Consecutive differences as a method of signal fractal analysis. in Fractals-Complex Geometry Patterns and Scaling in Nature and Society. 2005;13(4):283-292. doi:10.1142/S0218348X05002933 .
Kalauzi, Aleksandar, Spasić, Slađana, Culic, M, Grbic, G, Martać, Ljiljana, "Consecutive differences as a method of signal fractal analysis" in Fractals-Complex Geometry Patterns and Scaling in Nature and Society, 13, no. 4 (2005):283-292, https://doi.org/10.1142/S0218348X05002933 . .