DocumentCode
1101973
Title
A Transform for Logic Networks
Author
Menger, Karl S., Jr.
Issue
3
fYear
1969
fDate
3/1/1969 12:00:00 AM
Firstpage
241
Lastpage
250
Abstract
The transform presented in this paper applies to functions which describe logic network behavior. Given a function G defined over a finite domain, it is shown that G(u) = Et F(t)ut for each element u in the domain, where finite-field arithmetic is assumed. Here, function F is the transform of G, and it is shown that F(t) = Eu G(u)(-u)-t for each integer t in a finite set. Both form and development of this transform pair resembles the Fourier transform in harmonic analysis.
Keywords
Coding, Fourier transform, Galois fields, integrated circuit modules, logic network, network synthesis, polynomial expansion, sequential network, switching functions.; Arithmetic; Boolean functions; Digital systems; Fourier transforms; Galois fields; Integrated circuit synthesis; Logic; Network synthesis; Polynomials; Signal synthesis; Coding, Fourier transform, Galois fields, integrated circuit modules, logic network, network synthesis, polynomial expansion, sequential network, switching functions.;
fLanguage
English
Journal_Title
Computers, IEEE Transactions on
Publisher
ieee
ISSN
0018-9340
Type
jour
DOI
10.1109/T-C.1969.222637
Filename
1671230
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