On the orthogonal transforms in multiple-valued logic spectral approach

Mixed-radix logic functions of which the Boolean and multiple-valued logic functions are special cases are defined. In order to accomplish transform processing of digital logic signals, the logic functions are represented in the function space R^N formed by all the mappings from a finite Abelain group to a commutative ring, R, with unity. The sufficient and necessary conditions for generalized discrete transforms (GDFTs) to exist in R^N are given. It is shown that there are many GDFTs to be chosen in spectral techniques. The fast algorithms of GDFT and spectral operations of logic functions are discussed