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An efficient multiplierless approximation of the fast Fourier transform using sum-of-powers-of-two (SOPOT) coefficients

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2 Author(s)
Chan, S.C. ; Dept. of Electr. & Electron. Eng., Hong Kong Univ., China ; Yiu, P.M.

This letter proposes a new multiplierless approximation of the discrete Fourier transform (DFT) called the multiplierless fast Fourier transform-like (ML-FFT) transformation. It makes use of a novel factorization to parameterize the twiddle factors in the conventional radix-2/sup n/ or split-radix FFT algorithms as certain rotation-like matrices and approximates the associated parameters using the sum-of-powers-of-two (SOPOT) or canonical signed digits (CSD) representations. The ML-FFT converges to the DFT when the number of SOPOT terms used increases and has an arithmetic complexity of O(N log/sub 2/ N) additions, where N = 2/sup m/ is the transform length. Design results show that the NM-FFT offers flexible tradeoff between arithmetic complexity and numerical accuracy in approximating the DFT.

Published in:

Signal Processing Letters, IEEE  (Volume:9 ,  Issue: 10 )