A New Fast Discrete Fourier Transform

Authors:
Feng Zhou;Peter Kornerup
Affiliations:
Department of Information and Electronic Engineering, Zhejiang University, Hangzhou, P.R.China;Department of Mathematics and Computer Science, Odense University, Odense, Denmark
Venue:
Journal of VLSI Signal Processing Systems
Year:
1998

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Abstract

This paper presents a new fast Discrete Fourier Transform (DFT)algorithm. By rewriting the DFT, a new algorithm is obtained that uses2n−2(3n−13)+4n−2 real multiplications and 2n−2(7n−29)+6n+2real additions for a real data N=2n point DFT, comparable to the number of operations in the Split-Radix method, but with slightly fewer multiply and add operations in total. Because of the organization of multiplications as plane rotations in this DFT algorithm, it ispossible to apply a pipelined CORDIC algorithm in a hardwareimplementation of a long-point DFT, e.g., at a 100 MHz input rate, a1024-point transform can be realized with a 200 MHz clocking of a singleCORDIC pipeline.