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The Reed-Muller-Fourier Transform—Computing Methods and Factorizations

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Book cover Claudio Moraga: A Passion for Multi-Valued Logic and Soft Computing

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 349))

Abstract

Reed–Muller (RM) expressions are an important class of functional expressions for binary valued (Boolean) functions which have a double interpretation, as analogues to both Taylor series or Fourier series in classical mathematical analysis. In matrix notation, the set of basic functions in terms of which they are defined can be represented by a binary triangular matrix. Reed-Muller-Fourier (RMF) expressions are a generalisation of RM expressions to multiple valued functions preserving properties of RM expressions including the triangular structure of the transform matrix. In this paper, we discuss different methods for computing RMF coefficients over different data structure efficiently in terms of space and time. In particular, we consider algorithms. corresponding to Cooley-Tukey and constant geometry algorithms for Fast Fourier transform. We also consider algorithms based on various decompositions borrowed from the decomposition of the Pascal matrix and related computing algorithms.

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Authors and Affiliations

  1. Faculty of Electronics, Department of Computer Science, University of Nis, Niš, Serbia

    Radomir S. Stanković

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  1. Radomir S. Stanković
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Correspondence to Radomir S. Stanković .

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  1. Escuela de IngenieríaInformática, Pontificia Universidad Católica de Valparaíso, Valparaíso, Chile

    Rudolf Seising

  2. Geschichte der Nat, "Ernst-Haeckel-Haus", Deutsches Museum, Munich, Germany

    Héctor Allende-Cid

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Stanković, R.S. (2017). The Reed-Muller-Fourier Transform—Computing Methods and Factorizations. In: Seising, R., Allende-Cid, H. (eds) Claudio Moraga: A Passion for Multi-Valued Logic and Soft Computing. Studies in Fuzziness and Soft Computing, vol 349. Springer, Cham. https://doi.org/10.1007/978-3-319-48317-7_9

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  • DOI: https://doi.org/10.1007/978-3-319-48317-7_9

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