A residue number system implementation of real orthogonal transforms via approximation over a direct product of quadratic number rings

Recent work has focused on doing residue computations that are quantization within a dense ring of integers in the real domain. The aims of the paper are to provide and efficient algorithm for approximation of the real input signal with arbitrarily small error as an element of a quadratic number ring, and to prove the restrictions of the RNS moduli used in order to simplify the multiplication in the ring. The proposed approximation scheme can be used for implementation of real-valued transforms and their multidimensional generalizations