Efficient computation of fixed polarity arithmetic expansions for ternary functions

An efficient algorithm for generating fixed polarity arithmetic expansions for ternary functions is presented. It calculates the required spectral coefficients in a recursive manner based on a developed definition of the polarity matrix. The application of the algorithm for generating both complete polarity matrix and selected fixed polarity arithmetic expansion is given. Computational cost of the algorithm in terms of required number of additions and multiplications is also derived and it is shown to be more efficient than the calculation by matrix multiplication. Fast flow diagrams for implementation of the algorithm on hardware are also shown