Stability of the multifractal spectra by transformations of discrete series
In this work we use α-bi-Lipschitz transformation of signals both from empirical and theoretical sources to obtain new tests for the accomplishment of the multifractal formalisms associated with many methods (Wavelet Leaders, Wavelet Transform Modulus Maxima, Multifractal Detrended Fluctuation Analy...
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_0277786X_v6701_n_p_Corvalan |
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todo:paper_0277786X_v6701_n_p_Corvalan2023-10-03T15:16:37Z Stability of the multifractal spectra by transformations of discrete series Corvalán, A. Serrano, E. bi-Lipschitz transformations Multifractal spectrum Non-linear forecasting Signal processing Wavelet leaders Bi-Lipschitz transformations Multifractal spectrum Non-linear forecasting Algorithms Fractals Numerical methods Signal processing Spectrum analysis Wavelet transforms In this work we use α-bi-Lipschitz transformation of signals both from empirical and theoretical sources to obtain new tests for the accomplishment of the multifractal formalisms associated with many methods (Wavelet Leaders, Wavelet Transform Modulus Maxima, Multifractal Detrended Fluctuation Analysis, Box Counting, and other) and we give improvements of the present algorithms that result numerically more trustworthy. Moreover the multifractal spectrum does not change in the theory, but as the numeric implementation of the computations may differ for discrete series so we can analyze its variation to study the stability of the proposed algorithms to compute it. In addition some single coefficients that have been proposed to quantify the whole irregularity of the signal are preserved by enough high a-bi-Lipschitz transformations. We exhibit the performance of the tests and the improvements of this methods not only in signals generated from deterministic (or sometimes random) numerical processes performed with the computer but also against series from empirical sources in which the multifractal spectrum and the irregularity coefficient were proven of utility both from the analysis and the segmentation of the signal in significant parts as series of Longwave outgoing radiation of tropical regions (and the consequent forecasting applications of precipitations) and certain series of EEG (from patients with crisis of brain absences for instance) and the ability to distinguish (and perhaps to predict) the beginning of the consecutive stages. CONF info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_0277786X_v6701_n_p_Corvalan |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| topic |
bi-Lipschitz transformations Multifractal spectrum Non-linear forecasting Signal processing Wavelet leaders Bi-Lipschitz transformations Multifractal spectrum Non-linear forecasting Algorithms Fractals Numerical methods Signal processing Spectrum analysis Wavelet transforms |
| spellingShingle |
bi-Lipschitz transformations Multifractal spectrum Non-linear forecasting Signal processing Wavelet leaders Bi-Lipschitz transformations Multifractal spectrum Non-linear forecasting Algorithms Fractals Numerical methods Signal processing Spectrum analysis Wavelet transforms Corvalán, A. Serrano, E. Stability of the multifractal spectra by transformations of discrete series |
| topic_facet |
bi-Lipschitz transformations Multifractal spectrum Non-linear forecasting Signal processing Wavelet leaders Bi-Lipschitz transformations Multifractal spectrum Non-linear forecasting Algorithms Fractals Numerical methods Signal processing Spectrum analysis Wavelet transforms |
| description |
In this work we use α-bi-Lipschitz transformation of signals both from empirical and theoretical sources to obtain new tests for the accomplishment of the multifractal formalisms associated with many methods (Wavelet Leaders, Wavelet Transform Modulus Maxima, Multifractal Detrended Fluctuation Analysis, Box Counting, and other) and we give improvements of the present algorithms that result numerically more trustworthy. Moreover the multifractal spectrum does not change in the theory, but as the numeric implementation of the computations may differ for discrete series so we can analyze its variation to study the stability of the proposed algorithms to compute it. In addition some single coefficients that have been proposed to quantify the whole irregularity of the signal are preserved by enough high a-bi-Lipschitz transformations. We exhibit the performance of the tests and the improvements of this methods not only in signals generated from deterministic (or sometimes random) numerical processes performed with the computer but also against series from empirical sources in which the multifractal spectrum and the irregularity coefficient were proven of utility both from the analysis and the segmentation of the signal in significant parts as series of Longwave outgoing radiation of tropical regions (and the consequent forecasting applications of precipitations) and certain series of EEG (from patients with crisis of brain absences for instance) and the ability to distinguish (and perhaps to predict) the beginning of the consecutive stages. |
| format |
CONF |
| author |
Corvalán, A. Serrano, E. |
| author_facet |
Corvalán, A. Serrano, E. |
| author_sort |
Corvalán, A. |
| title |
Stability of the multifractal spectra by transformations of discrete series |
| title_short |
Stability of the multifractal spectra by transformations of discrete series |
| title_full |
Stability of the multifractal spectra by transformations of discrete series |
| title_fullStr |
Stability of the multifractal spectra by transformations of discrete series |
| title_full_unstemmed |
Stability of the multifractal spectra by transformations of discrete series |
| title_sort |
stability of the multifractal spectra by transformations of discrete series |
| url |
http://hdl.handle.net/20.500.12110/paper_0277786X_v6701_n_p_Corvalan |
| work_keys_str_mv |
AT corvalana stabilityofthemultifractalspectrabytransformationsofdiscreteseries AT serranoe stabilityofthemultifractalspectrabytransformationsofdiscreteseries |
| _version_ |
1807316488250458112 |