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RESEARCH PRODUCT

The Wavelet Scalogram in the Study of Time Series

Rafael BenítezVicente J. Bolós

subject

Discrete wavelet transformsymbols.namesakeWaveletSeries (mathematics)Computer sciencesymbolsLyapunov exponentDynamical systemAlgorithmMeasure (mathematics)Continuous wavelet transformComplement (set theory)

description

Wavelet theory has been proved to be a useful tool in the study of time series. Specifically, the scalogram allows the detection of the most representative scales (or frequencies) of a signal. In this work, we present the scalogram as a tool for studying some aspects of a given signal. Firstly, we introduce a parameter called scale index, interpreted as a measure of the degree of the signal’s non-periodicity. In this way, it can complement the maximal Lyapunov exponent method for determining chaos transitions of a given dynamical system. Secondly, we introduce a method for comparing different scalograms. This can be applied for determining if two time series follow similar patterns.

yearjournalcountryeditionlanguage
2014-01-01
https://doi.org/10.1007/978-3-319-06953-1_15