Some Remarks about Entropy of Digital Filtered Signals
The finite numerical resolution of digital number representation has an impact on the properties of filters. Much effort has been done to develop efficient digital filters investigating the effects in the frequency response. However, it seems that there is less attention to the influence in the entr...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-03-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/22/3/365 |
| _version_ | 1818015701305131008 |
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| author | Vinícius S. Borges Erivelton G. Nepomuceno Carlos A. Duque Denis N. Butusov |
| author_facet | Vinícius S. Borges Erivelton G. Nepomuceno Carlos A. Duque Denis N. Butusov |
| author_sort | Vinícius S. Borges |
| collection | DOAJ |
| description | The finite numerical resolution of digital number representation has an impact on the properties of filters. Much effort has been done to develop efficient digital filters investigating the effects in the frequency response. However, it seems that there is less attention to the influence in the entropy by digital filtered signals due to the finite precision. To contribute in such a direction, this manuscript presents some remarks about the entropy of filtered signals. Three types of filters are investigated: Butterworth, Chebyshev, and elliptic. Using a boundary technique, the parameters of the filters are evaluated according to the word length of 16 or 32 bits. It has been shown that filtered signals have their entropy increased even if the filters are linear. A significant positive correlation (<i>p</i> < 0.05) was observed between order and Shannon entropy of the filtered signal using the elliptic filter. Comparing to signal-to-noise ratio, entropy seems more efficient at detecting the increasing of noise in a filtered signal. Such knowledge can be used as an additional condition for designing digital filters. |
| first_indexed | 2024-04-14T07:01:25Z |
| format | Article |
| id | doaj.art-6e6ee440d4b64e4bb5cfd06a476aad73 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-04-14T07:01:25Z |
| publishDate | 2020-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-6e6ee440d4b64e4bb5cfd06a476aad732022-12-22T02:06:45ZengMDPI AGEntropy1099-43002020-03-0122336510.3390/e22030365e22030365Some Remarks about Entropy of Digital Filtered SignalsVinícius S. Borges0Erivelton G. Nepomuceno1Carlos A. Duque2Denis N. Butusov3Control and Modelling Group (GCOM), Department of Electrical Engineering, Federal University of São João del-Rei, São João del-Rei 36307-352, BrazilControl and Modelling Group (GCOM), Department of Electrical Engineering, Federal University of São João del-Rei, São João del-Rei 36307-352, BrazilDepartment of Electrical Engineering, Federal University of Juiz de Fora, Juiz de Fora 36036-900, BrazilYouth Research Institute, Saint-Petersburg Electrotechnical University “LETI”, Saint Petersburg 197376, RussiaThe finite numerical resolution of digital number representation has an impact on the properties of filters. Much effort has been done to develop efficient digital filters investigating the effects in the frequency response. However, it seems that there is less attention to the influence in the entropy by digital filtered signals due to the finite precision. To contribute in such a direction, this manuscript presents some remarks about the entropy of filtered signals. Three types of filters are investigated: Butterworth, Chebyshev, and elliptic. Using a boundary technique, the parameters of the filters are evaluated according to the word length of 16 or 32 bits. It has been shown that filtered signals have their entropy increased even if the filters are linear. A significant positive correlation (<i>p</i> < 0.05) was observed between order and Shannon entropy of the filtered signal using the elliptic filter. Comparing to signal-to-noise ratio, entropy seems more efficient at detecting the increasing of noise in a filtered signal. Such knowledge can be used as an additional condition for designing digital filters.https://www.mdpi.com/1099-4300/22/3/365theory of informationcomputer arithmeticdigital filtershannon entropy |
| spellingShingle | Vinícius S. Borges Erivelton G. Nepomuceno Carlos A. Duque Denis N. Butusov Some Remarks about Entropy of Digital Filtered Signals Entropy theory of information computer arithmetic digital filter shannon entropy |
| title | Some Remarks about Entropy of Digital Filtered Signals |
| title_full | Some Remarks about Entropy of Digital Filtered Signals |
| title_fullStr | Some Remarks about Entropy of Digital Filtered Signals |
| title_full_unstemmed | Some Remarks about Entropy of Digital Filtered Signals |
| title_short | Some Remarks about Entropy of Digital Filtered Signals |
| title_sort | some remarks about entropy of digital filtered signals |
| topic | theory of information computer arithmetic digital filter shannon entropy |
| url | https://www.mdpi.com/1099-4300/22/3/365 |
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