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Open AccessArticle

Some Remarks about Entropy of Digital Filtered Signals

1
Control and Modelling Group (GCOM), Department of Electrical Engineering, Federal University of São João del-Rei, São João del-Rei 36307-352, Brazil
2
Department of Electrical Engineering, Federal University of Juiz de Fora, Juiz de Fora 36036-900, Brazil
3
Youth Research Institute, Saint-Petersburg Electrotechnical University “LETI”, Saint Petersburg 197376, Russia
*
Author to whom correspondence should be addressed.
Entropy 2020, 22(3), 365; https://doi.org/10.3390/e22030365
Received: 10 February 2020 / Revised: 5 March 2020 / Accepted: 17 March 2020 / Published: 23 March 2020
(This article belongs to the Section Information Theory, Probability and Statistics)
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 (p < 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. View Full-Text
Keywords: theory of information; computer arithmetic; digital filter; shannon entropy theory of information; computer arithmetic; digital filter; shannon entropy
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Borges, V.S.; Nepomuceno, E.G.; Duque, C.A.; Butusov, D.N. Some Remarks about Entropy of Digital Filtered Signals. Entropy 2020, 22, 365.

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