A new algorithm is given that converts a reduced representation of Boolean functions in the form of disjoint cubes to Generalized Adding and Arithmetic spectra. Since the known algorithms that generate Adding and Arithmetic spectra always start from the truth table of Boolean functions the method presented computes faster with a smaller computer memory. The method is extremely efficient for such Boolean functions that are described by only few disjoint cubes and it allows the calculation of only selected spectral coefficients, or all the coefficients can be calculated in parallel.