Title :
Walsh-Hadamard spectral minimization of fixed polarity Reed-Muller expansions
Author :
Falkowski, Bogdan J. ; Yan, Shixing
Author_Institution :
Sch. of Electr. & Electron. Eng., Nanyang Technol. Univ., Singapore
Abstract :
By investigating links between Reed-Muller expansions and Walsh-Hadamard spectra an exact and non-exhaustive algorithm for the generation of optimal Reed-Muller expansions directly from just few Walsh-Hadamard spectral coefficients has been developed. The algorithm makes use of the properties of Walsh-Hadamard spectra and by investigating only few Walsh-Hadamard coefficients the optimal Reed-Muller expansion is obtained for all Boolean functions through the provided equations in the new algorithm.
Keywords :
Boolean functions; Hadamard transforms; Walsh functions; minimisation; spectral analysis; Boolean functions; Walsh-Hadamard spectral coefficients; Walsh-Hadamard spectral minimization; fixed polarity Reed-Muller expansions; nonexhaustive algorithm; Boolean functions; Character generation; Design optimization; Equations; Logic design; Logic functions; Logic testing; Matrix decomposition; Multiplexing; Transforms;
Conference_Titel :
Circuits and Systems, 2004. MWSCAS '04. The 2004 47th Midwest Symposium on
Print_ISBN :
0-7803-8346-X
DOI :
10.1109/MWSCAS.2004.1354039
