Convolution algorithms for small-word-length digital-filtering applications

Implementation of rectangular transforms (r.t.) in modular arithmetic and computation of number theoretic transforms through Winograd's algorithm are discussed. The computational effort of various algorithms to implement real convolution is investigated. Considering the signal/noise ratio performance and hardware complexity, it is shown that the r.t.s are best suited for digital-filtering applications with word lengths less than about 16 bits. Finally, r.t.s are shown to be the most amenable to the application of the Chinese remainder theorem for increasing the dynamic range