Symmetry in Signals: A New Insight
Symmetry is a fundamental property of many natural systems, which is observable through signals. In most out-of-equilibrium complex dynamic systems, the observed signals are asymmetric. However, for certain operating modes, some systems have demonstrated a resurgence of symmetry in their signals. Re...
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MDPI AG
2024-11-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/26/11/941 |
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| author | Jean-Marc Girault |
| author_facet | Jean-Marc Girault |
| author_sort | Jean-Marc Girault |
| collection | DOAJ |
| description | Symmetry is a fundamental property of many natural systems, which is observable through signals. In most out-of-equilibrium complex dynamic systems, the observed signals are asymmetric. However, for certain operating modes, some systems have demonstrated a resurgence of symmetry in their signals. Research has naturally focused on examining time invariance to quantify this symmetry. Measures based on the statistical and harmonic properties of signals have been proposed, but most of them focused on harmonic distortion without explicitly measuring symmetry. This paper introduces a new mathematical framework based on group theory for analyzing signal symmetry beyond time invariance. It presents new indicators to evaluate different types of symmetry in non-stochastic symmetric signals. Both periodic and non-periodic symmetric signals are analyzed to formalize the problem. The study raises critical questions about the completeness of symmetry in signals and proposes a new classification for periodic and non-periodic signals that goes beyond the traditional classification based on Fourier coefficients. Furthermore, new measures such as “symmetrometry” and “distorsymmetry” are introduced to quantify symmetry. These measures outperform traditional indicators like Total Harmonic Distortion (THD) and provide a more accurate measurement of symmetry in complex signals from applications where duty cycle plays a major role. |
| format | Article |
| id | doaj-art-b95a2d380a1b4613b2d4430bf7874e16 |
| institution | Kabale University |
| issn | 1099-4300 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj-art-b95a2d380a1b4613b2d4430bf7874e162024-11-26T18:03:09ZengMDPI AGEntropy1099-43002024-11-01261194110.3390/e26110941Symmetry in Signals: A New InsightJean-Marc Girault0Groupe ESEO, 49000 Angers, FranceSymmetry is a fundamental property of many natural systems, which is observable through signals. In most out-of-equilibrium complex dynamic systems, the observed signals are asymmetric. However, for certain operating modes, some systems have demonstrated a resurgence of symmetry in their signals. Research has naturally focused on examining time invariance to quantify this symmetry. Measures based on the statistical and harmonic properties of signals have been proposed, but most of them focused on harmonic distortion without explicitly measuring symmetry. This paper introduces a new mathematical framework based on group theory for analyzing signal symmetry beyond time invariance. It presents new indicators to evaluate different types of symmetry in non-stochastic symmetric signals. Both periodic and non-periodic symmetric signals are analyzed to formalize the problem. The study raises critical questions about the completeness of symmetry in signals and proposes a new classification for periodic and non-periodic signals that goes beyond the traditional classification based on Fourier coefficients. Furthermore, new measures such as “symmetrometry” and “distorsymmetry” are introduced to quantify symmetry. These measures outperform traditional indicators like Total Harmonic Distortion (THD) and provide a more accurate measurement of symmetry in complex signals from applications where duty cycle plays a major role.https://www.mdpi.com/1099-4300/26/11/941symmetrydistortionsymmetry groupirreversibilitysignalsymmetrometry |
| spellingShingle | Jean-Marc Girault Symmetry in Signals: A New Insight Entropy symmetry distortion symmetry group irreversibility signal symmetrometry |
| title | Symmetry in Signals: A New Insight |
| title_full | Symmetry in Signals: A New Insight |
| title_fullStr | Symmetry in Signals: A New Insight |
| title_full_unstemmed | Symmetry in Signals: A New Insight |
| title_short | Symmetry in Signals: A New Insight |
| title_sort | symmetry in signals a new insight |
| topic | symmetry distortion symmetry group irreversibility signal symmetrometry |
| url | https://www.mdpi.com/1099-4300/26/11/941 |
| work_keys_str_mv | AT jeanmarcgirault symmetryinsignalsanewinsight |