Decision diagram based computation of linearly independent ternary arithmetic transform spectra

Classes of fastest linearly independent ternary arithmetic (FLITA) expansions have been proposed recently. They operate in arithmetic domain and have been shown to be useful for optimization of ternary functions representation. All FLITA transforms possess fast forward and inverse transforms and therefore can be calculated by fast transform method. However, it has been shown that for manipulation of large functions it is more advantageous to start from decision diagrams rather than truth vector. Hence in this paper new algorithm to obtain FLITA spectrum from ternary decision diagram is presented. It is developed based on the new notations for spectrum of an FLITA transform introduced here. The algorithm derives each spectral coefficient independently from each other, allowing the coefficients to be calculated in parallel manner. By starting from decision diagram, the algorithm enables the FLITA expansion to be computed for large functions for which the fast transform based algorithm may fail.