Properties and relations of new fastest linearly independent arithmetic transforms for ternary functions

A novel representation of four new classes of ternary fastest linearly independent arithmetic transforms are introduced in this paper. The new transforms have consistent formulas related to their forward and inverse matrices. They also have fast forward and inverse butterfly diagrams which can be easily generated for any ternary switching functions. The introduced transforms are generalized by applying to them the concept of permutation matrices. Properties on the structures, relations, and computational costs of the new transforms are presented. Their experimental results are also given and compared with the known transforms.