A new FFT concept for efficient VLSI implementation: Part I - Butterfly processing element

This article describes a new approach for higher radix butterflies suitable for pipeline implementation. Based on the butterfly computation introduced by Cooley-Tukey [1], we introduce a novel approach for the factorization of the Discrete Fourier Transform (DFT), by redefining the butterfly computation, which is more suitable for efficient VLSI implementation. This proposed factorization motivated us to present a new concept of a radix-r Fast Fourier Transform (FFT), in which the radix-r butterfly computation concept was formulated as composite engines to implement each of the butterfly computations. This concept enables the radix r butterfly-processing element (BPE) to be designed by maintaining only one complex value multiplier in the butterfly critical path for any given r. Algorithmic description and performance of low complexity FFT method are considered in this paper and parallel pipelined FFT in a companion paper [15], Part II Parallel Pipelined FFT Processing.