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| Titel |
Influence of a discontinuity on the spectral and fractal analysis of one-dimensional data |
| VerfasserIn |
R. P. H. Berton |
| Medientyp |
Artikel
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| Sprache |
Englisch
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| ISSN |
1023-5809
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| Digitales Dokument |
URL |
| Erschienen |
In: Nonlinear Processes in Geophysics ; 11, no. 5/6 ; Nr. 11, no. 5/6 (2004-12-15), S.659-682 |
| Datensatznummer |
250008995
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| Publikation (Nr.) |
 copernicus.org/npg-11-659-2004.pdf |
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| Zusammenfassung |
| The analysis of a data area or segment containing steep transitions between
regions with different textures (for example a cloud and its background)
leads to addressing the problem of discontinuities and their impact on
texture analysis. In that purpose, an original one-dimensional analytical
model of spectrum and roughness function has been worked out, with a
discontinuity between two fractal regions, each one specified by its average
µ, standard deviation σ, spectral index β and Hurst
exponent H. This has the advantage of not needing the generation of a
fractal structure with a particular algorithm or random functions and
clearly puts into evidence the role played by the average in generating
spectral poles and side lobes. After validation of the model calibration, a parametric study is carried out
in order to understand the influence of this discontinuity on the estimation
of the spectral index β and the Hurst parameter H. It shows that for
a pure µ-gap, H is well estimated everywhere, though overestimated, and
β is overestimated in the anti-correlation range and saturates in the
correlation range. For a pure σ-gap the retrieval of H is excellent
everywhere and the behaviour of β is better than for a µ-gap,
leading to less overestimation in the anti-correlation range. For a pure
β-gap, saturation degrades measurements in the case of raw data and
the medium with smaller spectral index is predominant in the case of
trend-corrected data. For a pure H-gap, there is also dominance of the
medium with smaller fractal exponent. |
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