Conferencia
Abstract:
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.
Registro:
| Documento: | Conferencia |
| Título: | Stability of the multifractal spectra by transformations of discrete series |
| Autor: | Corvalán, A.; Serrano, E. |
| Ciudad: | San Diego, CA |
| Filiación: | Departamento de Matemática, Facultad de Ciencias Exactas, UBA Instituto del Desarrollo Humano, UNGS Escuela de Ciencia y Tecnología, UNSAM |
| Palabras clave: | 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 |
| Año: | 2007 |
| Volumen: | 6701 |
| DOI: | http://dx.doi.org/10.1117/12.733317 |
| Título revista: | Wavelets XII |
| Título revista abreviado: | Proc SPIE Int Soc Opt Eng |
| ISSN: | 0277786X |
| CODEN: | PSISD |
| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0277786X_v6701_n_p_Corvalan |
Referencias:
- Cardo, R., Corvalán, A., Figliola, A., Serrano, E., Analysis of the irregularity of time series of EEG by means of the multifractal spectrum (2007) Exposed as communication at the Latinoamerican Statistical Physics and Interdisciplinary Applications Conference, , February 14
- Corvalán. Álvaro, and Serrano. Eduardo. Multifractal Spectrum computation, ergodicity and forecasting applications. Exposed as contributed communication in the Mecánica Estadística y Física No Lineal. International Conference. Medyfinol 06 (December 2006); Jacquet, G., Harba, R., (2004) Wavelet based estimator for fractional Brownian Motion: An experimental point of view, , Eusipco
- Falconer, K., (1997) Techniques in Fractal Geometry, , John Wiley & Sons. Ed
- Jaffard. Stéphane. Some Mathematical Results about the Multifractal Formalism for Functions. Wavelets: Theory, Algorithms, and Applications. C. Chui, L. Montefusco and L. Puccio (Eds); Jaffard. Stéphane.Wavelet Techniques in Multifractal Analysis. Proceedings of Symposia in Pure Mathematics. AMS, 72. Part 1 (2004); Jaffard. Stéphane, Lashermes. Bruno, and Abry. Patrice. Wavelets Leaders in Multifractal analysis Preprint, 2005; Kantelhardt, J., Multifractal detrended fluctuation Analysis of nonstationary time series (2002) Physica A, 316
- Owen Dafydd. J. and Yuan Shen A non-parametric test for self-similarity and stationarity in network traffic. Chapter in: Fractals in Engineering New Trends in Theory and Applications Lévy-Véhel. J. and Lutton. E. (Eds) (2005); Sadegh Movahed. M.et al. Multifractal Detrended Fluctuation Analysis of Sunspot Time Series arXiv:physics/0508149 v2 13 Feb 2006; Soltani, S., Simard, P., Boichu, D., Estimation of the self-similarity parameter using the wavelet transform (2004) Source Signal Processing archive, 84 (1). , JanuaryA4 - The International Society for Optical Engineering (SPIE)
Citas:
---------- APA ----------
Corvalán, A. & Serrano, E. (2007) . Stability of the multifractal spectra by transformations of discrete series. Wavelets XII, 6701.http://dx.doi.org/10.1117/12.733317
---------- CHICAGO ----------
Corvalán, A., Serrano, E. "Stability of the multifractal spectra by transformations of discrete series" . Wavelets XII 6701 (2007).http://dx.doi.org/10.1117/12.733317
---------- MLA ----------
Corvalán, A., Serrano, E. "Stability of the multifractal spectra by transformations of discrete series" . Wavelets XII, vol. 6701, 2007.http://dx.doi.org/10.1117/12.733317
---------- VANCOUVER ----------
Corvalán, A., Serrano, E. Stability of the multifractal spectra by transformations of discrete series. Proc SPIE Int Soc Opt Eng. 2007;6701.http://dx.doi.org/10.1117/12.733317
