Filtering-based Analysis Comparing the DFA with the CDFA for Wide Sense Stationary Processes
| Autor: | Jean-Marc André, Eric Grivel, Pierrick Legrand, Patrick Mazoyer, Thierry Ferreira, Bastien Berthelot |
|---|---|
| Přispěvatelé: | Laboratoire de l'intégration, du matériau au système (IMS), Centre National de la Recherche Scientifique (CNRS)-Institut Polytechnique de Bordeaux-Université Sciences et Technologies - Bordeaux 1, Quality control and dynamic reliability (CQFD), Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), COGNITIQUE, Centre National de la Recherche Scientifique (CNRS)-Institut Polytechnique de Bordeaux-Université Sciences et Technologies - Bordeaux 1-Centre National de la Recherche Scientifique (CNRS)-Institut Polytechnique de Bordeaux-Université Sciences et Technologies - Bordeaux 1, Ecole Nationale Supérieure de Cognitique (ENSC), Institut Polytechnique de Bordeaux, THALES, Université Sciences et Technologies - Bordeaux 1-Institut Polytechnique de Bordeaux-Centre National de la Recherche Scientifique (CNRS), Université Sciences et Technologies - Bordeaux 1-Institut Polytechnique de Bordeaux-Centre National de la Recherche Scientifique (CNRS)-Université Sciences et Technologies - Bordeaux 1-Institut Polytechnique de Bordeaux-Centre National de la Recherche Scientifique (CNRS), Université Sciences et Technologies - Bordeaux 1 (UB)-Institut Polytechnique de Bordeaux-Centre National de la Recherche Scientifique (CNRS), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS)-Inria Bordeaux - Sud-Ouest, Université Sciences et Technologies - Bordeaux 1 (UB)-Institut Polytechnique de Bordeaux-Centre National de la Recherche Scientifique (CNRS)-Université Sciences et Technologies - Bordeaux 1 (UB)-Institut Polytechnique de Bordeaux-Centre National de la Recherche Scientifique (CNRS), THALES [France] |
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Hurst exponent
Stationary process Covariance function 020206 networking & telecommunications 02 engineering and technology Filter (signal processing) Function (mathematics) Correlation function (astronomy) Wavelet [INFO.INFO-TS]Computer Science [cs]/Signal and Image Processing 0202 electrical engineering electronic engineering information engineering Detrended fluctuation analysis 020201 artificial intelligence & image processing Algorithm Computer Science::Databases ComputingMilieux_MISCELLANEOUS Mathematics |
| Zdroj: | EUSIPCO 2019-27th European Signal Processing Conference EUSIPCO 2019-27th European Signal Processing Conference, Sep 2019, A Coruna, Spain EUSIPCO |
| Popis: | The detrended fluctuation analysis (DFA) is widely used to estimate the Hurst exponent. Although it can be outperformed by wavelet based approaches, it remains popular because it does not require a strong expertise in signal processing. Recently, some studies were dedicated to its theoretical analysis and its limits. More particularly, some authors focused on the so-called fluctuation function by searching a relation with an estimation of the normalized covariance function under some assumptions. This paper is complementary to these works. We first show that the square of the fluctuation function can be expressed in a similar matrix form for the DFA and the variant we propose, called Continuous-DFA (CDFA), where the global trend is constrained to be continuous. Then, using the above representation for wide-sense-stationary processes, the statistical mean of the square of the fluctuation function can be expressed from the correlation function of the signal and consequently from its power spectral density, without any approximation. The differences between both methods can be highlighted. It also confirms that they can be seen as ad hocwavelet based techniques. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|