Authors: Stanković, Radomir 
Title: The reed-muller-fourier transform—computing methods and factorizations
Journal: Claudio Moraga: A Passion for Multi-Valued Logic and Soft Computing
Series/Report no.: Studies in Fuzziness and Soft Computing
Volume: 349
First page: 121
Last page: 151
Issue Date: 1-Oct-2017
ISBN: 978-3-319-48316-0
ISSN: 1434-9922
DOI: 10.1007/978-3-319-48317-7_9
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.
Publisher: Springer Link

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