Properties and experimental results of fastest linearly independent ternary arithmetic transforms

Two categories of fastest linearly independent ternary arithmetic transforms, which possesses forward and inverse butterfly diagrams with the lowest computational complexity have been identified and their various properties have been presented in this paper. This family is recursively defined and has consistent formulas relating forward and inverse transform matrices. Computational costs of the calculation for new transforms are also discussed. Some experimental results for standard ternary benchmark functions and comparison with multi-polarity ternary arithmetic transform are also presented.