Spectral transforms of mixed-radix MVL functions

Mixed-radix "Multiple Valued Logic" (MVL) functions are assumed to be finite and discrete-valued and depend on a finite-valued variable support set {x_i,...,x_j} such that x_i is q_i-valued and x_j is q_j-valued with q_i ≠ q_j. The spectra of such MVL functions is of interest to circuit designers and automated design tool researchers and developers. Spectral transforms are described that are applicable to such functions over the elementary additive (mod(p)) Abelian groups. Three formulation of such transforms are described here; a linear transformation matrix derived front a group character table, a Kronecker-based expansion allowing for a \´fast\´ transform algorithm, and a Cayley graph spectrum computation. It is shown that a particular spectral transformation of a discrete mixed-radix function over Z₆ is equivalent to that over Z₂ × Z₃ within a permutation. Also, it is shown that a Cayley graph may be formed over Z₆ with a generator corresponding to the discrete function of interest.