The Impact of Linear Filter Preprocessing in the Interpretation of Permutation Entropy
Permutation Entropy (PE) is a powerful tool for measuring the amount of information contained within a time series. However, this technique is rarely applied directly on raw signals. Instead, a preprocessing step, such as linear filtering, is applied in order to remove noise or to isolate specific f...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-06-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/23/7/787 |
| _version_ | 1797529234362597376 |
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| author | Antonio Dávalos Meryem Jabloun Philippe Ravier Olivier Buttelli |
| author_facet | Antonio Dávalos Meryem Jabloun Philippe Ravier Olivier Buttelli |
| author_sort | Antonio Dávalos |
| collection | DOAJ |
| description | Permutation Entropy (PE) is a powerful tool for measuring the amount of information contained within a time series. However, this technique is rarely applied directly on raw signals. Instead, a preprocessing step, such as linear filtering, is applied in order to remove noise or to isolate specific frequency bands. In the current work, we aimed at outlining the effect of linear filter preprocessing in the final PE values. By means of the Wiener–Khinchin theorem, we theoretically characterize the linear filter’s intrinsic PE and separated its contribution from the signal’s ordinal information. We tested these results by means of simulated signals, subject to a variety of linear filters such as the moving average, Butterworth, and Chebyshev type I. The PE results from simulations closely resembled our predicted results for all tested filters, which validated our theoretical propositions. More importantly, when we applied linear filters to signals with inner correlations, we were able to theoretically decouple the signal-specific contribution from that induced by the linear filter. Therefore, by providing a proper framework of PE linear filter characterization, we improved the PE interpretation by identifying possible artifact information introduced by the preprocessing steps. |
| first_indexed | 2024-03-10T10:10:52Z |
| format | Article |
| id | doaj.art-9cfcc6afa4234ffea378e12c3b8b327f |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-10T10:10:52Z |
| publishDate | 2021-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-9cfcc6afa4234ffea378e12c3b8b327f2023-11-22T01:11:32ZengMDPI AGEntropy1099-43002021-06-0123778710.3390/e23070787The Impact of Linear Filter Preprocessing in the Interpretation of Permutation EntropyAntonio Dávalos0Meryem Jabloun1Philippe Ravier2Olivier Buttelli3Laboratoire Pluridisciplinaire de Recherche en Ingénierie des Systèmes, Mécanique, Énergétique (PRISME), University of Orléans, 45100 Orléans, FranceLaboratoire Pluridisciplinaire de Recherche en Ingénierie des Systèmes, Mécanique, Énergétique (PRISME), University of Orléans, 45100 Orléans, FranceLaboratoire Pluridisciplinaire de Recherche en Ingénierie des Systèmes, Mécanique, Énergétique (PRISME), University of Orléans, 45100 Orléans, FranceLaboratoire Pluridisciplinaire de Recherche en Ingénierie des Systèmes, Mécanique, Énergétique (PRISME), University of Orléans, 45100 Orléans, FrancePermutation Entropy (PE) is a powerful tool for measuring the amount of information contained within a time series. However, this technique is rarely applied directly on raw signals. Instead, a preprocessing step, such as linear filtering, is applied in order to remove noise or to isolate specific frequency bands. In the current work, we aimed at outlining the effect of linear filter preprocessing in the final PE values. By means of the Wiener–Khinchin theorem, we theoretically characterize the linear filter’s intrinsic PE and separated its contribution from the signal’s ordinal information. We tested these results by means of simulated signals, subject to a variety of linear filters such as the moving average, Butterworth, and Chebyshev type I. The PE results from simulations closely resembled our predicted results for all tested filters, which validated our theoretical propositions. More importantly, when we applied linear filters to signals with inner correlations, we were able to theoretically decouple the signal-specific contribution from that induced by the linear filter. Therefore, by providing a proper framework of PE linear filter characterization, we improved the PE interpretation by identifying possible artifact information introduced by the preprocessing steps.https://www.mdpi.com/1099-4300/23/7/787permutation entropytime serieslinear filterspreprocessing |
| spellingShingle | Antonio Dávalos Meryem Jabloun Philippe Ravier Olivier Buttelli The Impact of Linear Filter Preprocessing in the Interpretation of Permutation Entropy Entropy permutation entropy time series linear filters preprocessing |
| title | The Impact of Linear Filter Preprocessing in the Interpretation of Permutation Entropy |
| title_full | The Impact of Linear Filter Preprocessing in the Interpretation of Permutation Entropy |
| title_fullStr | The Impact of Linear Filter Preprocessing in the Interpretation of Permutation Entropy |
| title_full_unstemmed | The Impact of Linear Filter Preprocessing in the Interpretation of Permutation Entropy |
| title_short | The Impact of Linear Filter Preprocessing in the Interpretation of Permutation Entropy |
| title_sort | impact of linear filter preprocessing in the interpretation of permutation entropy |
| topic | permutation entropy time series linear filters preprocessing |
| url | https://www.mdpi.com/1099-4300/23/7/787 |
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