Linearly independent ternary arithmetic helix transforms, their properties and relations

New classes of linearly independent ternary arithmetic transforms in standard algebra called ternary arithmetic helix transforms are introduced. Four types of helix transform matrices with detailed recursive equations are shown. Various properties, mutual relationships among transform matrices and spectra as well as results of helix transforms for some special cases of ternary logic functions are discussed. Computational costs for the calculation of new transforms are also presented.