Discrete Function KL Spectrum Computation over Symmetry Groups of Arbitrary Size

The Karhunen-Loève spectrum of a discrete function can vary depending on how symmetry group objects are mapped to function minterms. For completely specified functions with a range space smaller than the cardinality of a symmetry group, we propose a technique to assign the symmetry group don’t cares to maximize the number of zero-valued KL spectral coefficients of the function. To evaluate these approaches, we compare the average number of zero-valued KL spectral coefficients with those occurring in the Chrestenson spectrum.