A generalized Mobius transform, arithmetic Fourier transforms, and primitive roots

A general approach to arithmetic Fourier transforms is developed. The implementation is based on sine and cosine “killer” procedures pertaining to a generalized Mobius transform involving reduced periodic multiplicative arithmetical functions. It is shown that cosine killer procedures exist whenever one half of Euler´s totient function of the order of the transform is odd. Primitive roots and indices with respect to primitive roots play an important part in the derivation of the results