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Influence of a Discontinuity on the Spectral and Fractal Analysis of One-dimensional Data : Volume 11, Issue 5/6 (15/12/2004)

By Berton, R. P. H.

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Book Id: WPLBN0004019643
Format Type: PDF Article :
File Size: Pages 24
Reproduction Date: 2015

Title: Influence of a Discontinuity on the Spectral and Fractal Analysis of One-dimensional Data : Volume 11, Issue 5/6 (15/12/2004)  
Author: Berton, R. P. H.
Volume: Vol. 11, Issue 5/6
Language: English
Subject: Science, Nonlinear, Processes
Collections: Periodicals: Journal and Magazine Collection, Copernicus GmbH
Publication Date:
Publisher: Copernicus Gmbh, Göttingen, Germany
Member Page: Copernicus Publications


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H. Berto, R. P. (2004). Influence of a Discontinuity on the Spectral and Fractal Analysis of One-dimensional Data : Volume 11, Issue 5/6 (15/12/2004). Retrieved from

Description: ONERA, Chemin de la Hunière, F-91761 Palaiseau Cedex, France. 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.

Influence of a discontinuity on the spectral and fractal analysis of one-dimensional data


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