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Fuzzy Digital Filters with Triangular Norms

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Artificial Intelligence and Soft Computing (ICAISC 2010)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 6113))

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Abstract

The convolution operation is used to describe the relation between input and output in the linear filters theory. In this paper the product operation in discrete convolution is replaced by triangular norm operation. It is an extension of conventional idea of convolution. Such approach leads to nonlinear filtering. Some interesting properties as identical impulse, step, and frequency responses of digital filters with T-norms and conorms (S-norms) operations are shown. Moreover, filters with fuzzy parameters and crisp signals passing by such fuzzy nonlinear filters are investigated.

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Authors and Affiliations

  1. Warsaw University of Technology, Nowowiejska 15/19, 00-665, Warsaw, Poland

    Bohdan S. Butkiewicz

Authors
  1. Bohdan S. Butkiewicz
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Editors and Affiliations

  1. Department of Artificial Intelligence, Academy of Humanities and Economics, Poland

    Leszek Rutkowski

  2. Academy of Humanities and Economics in Łódź,, ul. Rewolucji 1905 nr 64, Łódź, Poland

    Rafał Scherer

  3. Institute of Automatics,, AGH University of Science and Technology, Al. Mickiewicza 30, PL-30-059, Kraków, Poland

    Ryszard Tadeusiewicz

  4. Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, Initiative in Soft Computing (BISC), 94720-1776, Berkeley, CA,  

    Lotfi A. Zadeh

  5. Computational Intelligence Laboratory Department of Electrical and Computer Engineering, University of Louisville, 40292, Louisville, KY

    Jacek M. Zurada

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© 2010 Springer-Verlag Berlin Heidelberg

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Butkiewicz, B.S. (2010). Fuzzy Digital Filters with Triangular Norms. In: Rutkowski, L., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds) Artificial Intelligence and Soft Computing. ICAISC 2010. Lecture Notes in Computer Science(), vol 6113. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13208-7_3

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  • DOI: https://doi.org/10.1007/978-3-642-13208-7_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-13207-0

  • Online ISBN: 978-3-642-13208-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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