Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Roughness distributions for 1/f^alpha signals   The probability density function (PDF) of the roughness, i.e., of the
temporal variance, of 1/f^alpha 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 [T. Antal et al., PRL, vol. 87, 240601 (2001)],
to arbitrary power law. We investigate three main scaling regions,
distinguished by the scaling of the cumulants in terms of the microscopic scale
and the total length of the period. Various analytical representations of the
PDF allow for a precise numerical evaluation of the scaling function of the PDF
for any alpha. A simulation of the periodic process makes it possible to study
also non-periodic signals on short intervals embedded in the full period. We
find that for alpha=<1/2 the scaled PDF-s in both the periodic and the
non-periodic cases are Gaussian, but for alpha>1/2 they differ from the
Gaussian and from each other. Both deviations increase with growing alpha. That
conclusion, based on numerics, is reinforced by analytic results for alpha=2
and alpha->infinity. We suggest that our theoretical and numerical results open
a new perspective on the data analysis of 1/f^alpha processes.

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The categories of this paper are: ao-sci
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The categories of this paper are: patt-sol
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The categories of this paper are: acc-phys
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-alg
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The categories of this paper are: chem-ph
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The categories of this paper are: solv-int
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The categories of this paper are: atom-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: math-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: nlin
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The categories of this paper are: econ
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The categories of this paper are: eess
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-ph