### Abstract

The probability density function (PDF) of the roughness, i.e., of the temporal variance, of 1/f^{α} 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/f^{α} processes.

Original language | English |
---|---|

Article number | 046140 |

Journal | Physical Review E - Statistical, Nonlinear, and Soft Matter Physics |

Volume | 65 |

Issue number | 4 |

DOIs | |

Publication status | Published - Apr 2002 |

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### ASJC Scopus subject areas

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

### Cite this

^{α}signals.

*Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*,

*65*(4), [046140]. https://doi.org/10.1103/PhysRevE.65.046140

**Roughness distributions for 1/f ^{α} signals.** / Antal, T.; Droz, M.; Györgyi, G.; Rácz, Z.

Research output: Contribution to journal › Article

^{α}signals',

*Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*, vol. 65, no. 4, 046140. https://doi.org/10.1103/PhysRevE.65.046140

^{α}signals. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics. 2002 Apr;65(4). 046140. https://doi.org/10.1103/PhysRevE.65.046140

}

TY - JOUR

T1 - Roughness distributions for 1/fα signals

AU - Antal, T.

AU - Droz, M.

AU - Györgyi, G.

AU - Rácz, Z.

PY - 2002/4

Y1 - 2002/4

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=41349100210&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=41349100210&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.65.046140

DO - 10.1103/PhysRevE.65.046140

M3 - Article

AN - SCOPUS:41349100210

VL - 65

JO - Physical review. E

JF - Physical review. E

SN - 2470-0045

IS - 4

M1 - 046140

ER -