Ternary polynomial expansions based on generalized fastest linearly independent arithmetic transforms

Spectral expansions are alternative representations of logic functions/signals in which the information are redistributed and presented differently in terms of spectral coefficients. The use of spectral representations often allows certain operations or analysis to be performed more efficiently on the data. In this paper, spectral expansions for ternary functions based on new fastest linearly independent arithmetic transforms are presented and discussed. The new transforms are generalizations of some existing ternary transforms through permutation and reordering operations. They have regular structures and can be computed using fast transforms. Formulae for their fast forward and inverse transformations as well as their corresponding fast flow graphs are shown here. Computational costs and some properties of the transforms and their spectra are also given. Finally, experimental results of the transforms are presented which show that the new transforms can represent some functions more compactly than the existing transforms.