Properties of Logic Functions in Spectral Domain of Sign Hadamard-Haar Transform

A non-linear transform, called ‘Sign Hadamard-Haar transform’ is introduced. The transform is unique and converts ternary vectors into ternary spectral domain. Recursive definition and fast transform have been developed. Formulae to represent Sign Hadamard-Haar spectra for basic logic functions and their variables for two different codings are shown. New transform is extremely effective in terms of computational costs when compared with known ternary transforms. Advantage of new transform over known Sign Walsh transform in ternary communication system is also discussed.