Walsh type transforms for completely and incompletely specified multiple-valued input binary functions

Spectral representation of multiple-valued input binary functions is proposed for the first time. Such a representation is composed of a vector of Walsh transforms, each of which is defined for one pair of the input variables of the function. The new representation has the advantage of being real valued and having, therefore, an easy interpretation. Since two types of binary function value codings are used, two different spectra are introduced. The meaning of each spectral coefficient is discussed in classical logic terms. The mathematical relationships between the number of true, false, and don´t care minterms and spectral coefficients are stated. These relationships can be used to calculate the spectral coefficients directly from the graphical representations of binary functions. As do the spectral methods in classical logic design, the new spectral representation of binary functions find applications in many problems of analysis, synthesis, and testing of circuits described by such functions