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| Titel |
Characterizing the structure of nonlinear systems using gradual wavelet reconstruction |
| VerfasserIn |
C. J. Keylock |
| 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 ; 17, no. 6 ; Nr. 17, no. 6 (2010-11-16), S.615-632 |
| Datensatznummer |
250013753
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| Publikation (Nr.) |
 copernicus.org/npg-17-615-2010.pdf |
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| Zusammenfassung |
| In this paper, classical surrogate data methods for testing hypotheses
concerning nonlinearity in time-series data are extended using a
wavelet-based scheme. This gives a method for systematically exploring the
properties of a signal relative to some metric or set of metrics. A signal
continuum is defined from a linear variant of the original signal (same
histogram and approximately the same Fourier spectrum) to the exact
replication of the original signal. Surrogate data are generated along this
continuum with the wavelet transform fixing in place an increasing proportion
of the properties of the original signal. Eventually, chaotic or nonlinear
behaviour will be preserved in the surrogates. The technique permits various
research questions to be answered and examples covered in the paper include
identifying a threshold level at which signals or models for those signals
may be considered similar on some metric, analysing the complexity of the
Lorenz attractor, characterising the differential sensitivity of metrics to
the presence of multifractality for a turbulence time-series, and determining
the amplitude of variability of the Hölder exponents in a multifractional
Brownian motion that is detectable by a calculation method. Thus, a wide
class of analyses of relevance to geophysics can be undertaken within this
framework. |
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