The Serial Commutator FFT

Abstract

Abstract-This paper presents a new type of FFT hardware architectures called serial commutator (SC) FFT. The SC FFT is characterized by the use of circuits for bit-dimension permutation of serial data. The proposed architectures are based on the observation that in the radix-2 FFT algorithm only half of the samples at each stage must be rotated. This fact, together with a proper data management makes it possible to allocate rotations only every other clock cycle. This allows for simplifying the rotator, halving the complexity with respect to conventional serial FFT architectures. Likewise, the proposed approach halves the number of adders in the butterflies with respect to previous architectures. As a result, the proposed architectures use the minimum number of adders, rotators and memory that are necessary for a pipelined FFT of serial data, with 100% utilization ratio.

SFF—The Single-Stream FPGA-Optimized Feedforward FFT Hardware Architecture

“…Note, that the number of memory slots for the SC FFT differs between what is reported in [10]. For an arbitrary input order, the approach in [10] has lower memory requirements. Also, in our table the memory required inside the processing element is included.…”

“…In [10], the serial commutator (SC) FFT was proposed by Garrido et al The SC architecture is similar to those proposed in [3,21] in the sense that minimal number of adders/subtracters is achieved by time-sharing over the realimaginary dimension. Note, that the number of memory slots for the SC FFT differs between what is reported in [10].…”

“…As can be seen in Table 2, all four architectures proposed in [3,10,18,21] use (almost) the minimal number of additions, however at the cost of a higher number of memory words, about 3 2 N, more than what is required for the radix-2 SD 2 F architecture. All these architecture also contain a large number of multiplexers making them less suitable for implementation in FPGAs.…”

“…Since then several single-stream FFT architectures have been suggested [2,3,6,10,18,21,24]. Some decades later, a major milestone in this field came with the introduction of the radix-2 2 algorithm [14].…”

Optimum Circuits for Bit-Dimension Permutations

“…Permutations of serial data are used for bit reversal [9] and for the serial commutator FFT [20], [21].…”