Operations on Boolean functions and variables in spectral domain of arithmetic transform

The unique relationships between Arithmetic spectra of switching functions and the spectra of Boolean AND, OR and XOR of such functions are presented. Essential operations used in classification and optimization of logical network have been also analyzed in Arithmetic spectral domain. Some of such operations involve input and output negations and permutations of input variables. By using presented methods, the computation of the total spectrum of any Arithmetic expression for an equivalent switching network is straight forward, and many of the equivalent operations in Arithmetic domain are simpler than their Boolean counterparts which should increase practical interest in usage of Arithmetic transform for design automation tools