IMPLEMENTATION OF CYCLIC CONVOLUTION BASED ON FNT

A.Laxman, A.Vamshidhar Reddy, L.Prakash, T.Satyanarayana

Abstract: Cyclic convolution is also known as circular convolution. It is simpler to compute and produce less output samples compared to linear convolution. There are many architectures for calculating cyclic convolution of any two signals. Implementation using Fermat Number Transform (FNT) is one of them. Fermat Number is a positive integer of the form where n is a nonnegative integer.The basic property of FNT is that they are recursive. This paper presents a cyclic convolution based on Fermat Number Transform(FNT) in the diminished-1 number system.A Code Convolution method Without Addition(CCWA) and a Butterfly Operation method Without Addition(BOWA) are proposed to perform the FNT and its inverse(IFNT) except their final stages in the convolution.The pointwise multiplication in the convolution is accomplished by Modulo 2n+1 Partial Product Multipliers(MPPM) and output partial products which are inputs to the IFNT.Thus Modulo 2n+1 carry propagation additions are avoided in the FNT and the IFNT except their final stages and Modulo2n+1 multiplier.The execution delay of the parallel architecture is reduced evidently due to the decrease of Modulo 2n+1 carry propagation addition.compared with the existing cyclic convolution architecture,the proposed one has better throughput performance and involves less hardware complexity.Synthesis results using 130nm CMOS technology demonstrate the superiority of the proposed architecture over the reported solution.

Keywords: FERMAT NUMBER THEORETIC TRANSFORM, BUTTERFLY ARCHITECTURE, PARALLEL ARCHITECTURE FOR CYCLIC CONVOLUTION, and COMPARISON AND RESULTS

DOI: https://doi.org/10.15623/ijret.2012.0103006