Open Access
December 2007 Empirical evaluation of a sub-linear time sparse DFT algorithm
M.A. Iwen, A. Gilbert, M. Strauss
Commun. Math. Sci. 5(4): 981-998 (December 2007).


In this paper we empirically evaluate a recently proposed Fast Approximate Discrete Fourier Transform (FADFT) algorithm, FADFT-2, for the first time. FADFT-2 returns approximate Fourier representations for frequency-sparse signals and works by random sampling. Its implemen- tation is benchmarked against two competing methods. The first is the popular exact FFT imple- mentation FFTW Version 3.1. The second is an implementation of FADFT-2’s ancestor, FADFT-1. Experiments verify the theoretical runtimes of both FADFT-1 and FADFT-2. In doing so it is shown that FADFT-2 not only generally outperforms FADFT-1 on all but the sparsest signals, but is also significantly faster than FFTW 3.1 on large sparse signals. Furthermore, it is demonstrated that FADFT-2 is indistinguishable from FADFT-1 in terms of noise tolerance despite FADFT-2’s better execution time.


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M.A. Iwen. A. Gilbert. M. Strauss. "Empirical evaluation of a sub-linear time sparse DFT algorithm." Commun. Math. Sci. 5 (4) 981 - 998, December 2007.


Published: December 2007
First available in Project Euclid: 3 January 2008

zbMATH: 1134.65093
MathSciNet: MR2375057

Primary: 65T40 , 65T50 , 68W25 , 68W40

Keywords: compressive sensing , Fourier transforms , sub-linear time algorithms

Rights: Copyright © 2007 International Press of Boston

Vol.5 • No. 4 • December 2007
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