Roughness distributions for 1/fα signals

T. Antal, M. Droz, G. Györgyi, Z. Rácz

Research output: Contribution to journalArticle

80 Citations (Scopus)

Abstract

The probability density function (PDF) of the roughness, i.e., of the temporal variance, of 1/fα noise signals is studied. Our starting point is the generalization of the model of Gaussian, time periodic, 1/f noise, discussed in our recent Letter [Phys. Rev. Lett. 87, 240601 (2001)], to arbitrary power law. We investigate three main scaling regions (α≤1/2, 1/2 1/2 they differ from the Gaussian and from each other. Both deviations increase with growing a. That conclusion, based on numerics, is reinforced by analytic results for α=2 and α→∞, in the latter limit the scaling function of the PDF being finite for periodic signals, but developing a singularity for the aperiodic ones. Finally, an overview is given for the scaling of cumulants of the roughness and the various scaling regions in arbitrary dimensions. We suggest that our theoretical and numerical results open a different perspective on the data analysis of 1/fα processes.

Original languageEnglish
Article number046140
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume65
Issue number4
DOIs
Publication statusPublished - Apr 2002

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Roughness
1/f Noise
roughness
Scaling
scaling
Probability density function
probability density functions
Cumulants
Scaling Function
Arbitrary
Numerics
Data analysis
Power Law
Deviation
Singularity
Numerical Results
deviation
Model
Generalization

ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Condensed Matter Physics
  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

Roughness distributions for 1/fα signals. / Antal, T.; Droz, M.; Györgyi, G.; Rácz, Z.

In: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, Vol. 65, No. 4, 046140, 04.2002.

Research output: Contribution to journalArticle

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