A residue number system implementation of real orthogonal transforms

Abstract

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

A Fast QRNS-Based Algorithm for the DCT and Its Field-Programmable Logic Implementation

“…Furthermore, several papers have shown the advantages of the RNS for the computation of the DCT and other discrete transforms. [20][21][22] In order to overcome the disadvantage of using complex arithmetic for those FFT-based algorithms, the use of QRNS 6 arithmetic is examined in this paper. The advantages of QRNS are RNS-like speed and reduced multiplication complexity.…”

Representação Numérica em Inteiros de Gauss-Eisenstein

“…Trabalhos recentes contribuíram com diversas arquiteturas relacionadas com inteiros algébricos. Por exemplo, pode-se citar: (i) sistema de processamento de sinais baseado em sistema de resíduos de inteiros de Eisenstein [8], (ii) arquitetura de hardware para transformada discreta do cosseno 2-D 8×8 baseada em inteiros algébricos [3], e (iii) implementação da transformada real ortogonal usando sistema de resíduo numérico [9]. Este artigo propõe uma nova representação numérica queé resultado de uma combinação da estrutura dos inteiros gaussianos e os de Eisenstein.…”