Authors: Stanković, Radomir 
Astola, Jaakko
Moraga, Claudio
Title: Multiple-valued logic networks with regular structure obtained from fast Fourier transforms on finite groups
Journal: Proceedings - 41st IEEE International Symposium on Multiple-Valued Logic, ISMVL 2011
First page: 54
Last page: 61
Conference: 41st IEEE International Symposium on Multiple-Valued Logic, ISMVL 2011; Tuusula; Finland; 23 May 2011 through 25 May 2011
Issue Date: 18-Aug-2011
ISBN: 978-0-769-54405-2
DOI: 10.1109/ISMVL.2011.27
In this paper, we discuss the Fast Fourier transform (FFT) on finite groups as a useful method in synthesis for regularity. FFT is the algorithm for efficient calculation of the Discrete Fourier transform (DFT) and has been extended to computation of various Fourier-like transforms. The algorithm has a very regular structure that can be easily mapped to technology by replacing nodes in the corresponding flow-graphs by circuit modules performing the operations in the flow-graphs. In this way, networks with highly regular structure for implementing functions from their spectra are derived. Fourier transforms on non-Abelian groups offer additional advantages for reducing the required hardware due to matrix-valued spectral coefficients and the way how such coefficients are used in reconstructing the functions. Methods for optimization of spectral representations of functions on finite groups may be applied to improve networks with regular structure.
Keywords: Fast Fourier transform | Logic networks | Multiple-valued logic | non-Abelian groups
Publisher: IEEE

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