Properties and synthesis of RNS digital circuits

The residue number system (RNS) digital circuit is defined as a circuit constituted by delays, modular adders, and multipliers. The synthesis of RNS digital circuits is considered starting from a given impulse response. The key requirement of the proposed synthesis procedures is the length of the sequence, which depends on the modulus, the type of the poles, and their multiplicity. The definitions of the different types of poles require the use of suitable extensions of the basic field corresponding to the modulus