Implementation aspects of convolvers using non-binary arithmetic

The authors consider implementation aspects of convolutions using number theoretic transform techniques and nonbinary arithmetic. The main motivation is to relax the restrictions imposed by the well-known Mersenne number transforms (MNTs) and the Fermat number transforms (FNTs). These restrictions were the limited transformation length and lack of flexibility in choosing the modulus used for the arithmetic. Transforms are presented using arithmetic modulo M with M =r^t±c. This way, higher transformation lengths are obtained and higher flexibility in choosing the modulus M is achieved. The new transforms rely on scalings by powers of r and in order to efficiently perform these scalings radix-r arithmetic is used (with r>2). Then, such scalings become simple shifts and rotates in the radix-r system