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.;
