Optimal VLSI complexity design for high speed pipeline FFT using RNS

Abstract

In this study a logic design, based on RNS units, to perform the N point FFT on a continuous data stream is proposed, and its performance is evaluated in terms of asymptotic VLSI complexity. Such a structure is based on quadratic residue number systems (QRNS), which allow a simplified processing of complex numbers. It is known in the literature that a lower bound on complexity for a single instance of the FFT problem is A( N) T 2( N)=Ω( N 2 log 2 N), and that optimal constructive designs were proposed with T( N)=ϑ(log 2 N). The architecture proposed here is based on a very high degree of processing parallelism and on a communication parallelism tailored to the response time of adders and multipliers used in the design; furthermore, pipelining data it performs as a single FFT instance optimal design and features an upper bound for the mean service time T m ( N)=ϑ(log log log N) for each FFT instance. The approach has been also applied in the design of a structure performing 1024-point FFT, with 23 bit data.