## Combinatorial sublinear-time fourier algorithms,” Submitted. Available at http://www.ima.umn.edu/∼iwen/index.html (2008)

Citations: | 15 - 5 self |

### BibTeX

@MISC{Iwen08combinatorialsublinear-time,

author = {M. A. Iwen},

title = {Combinatorial sublinear-time fourier algorithms,” Submitted. Available at http://www.ima.umn.edu/∼iwen/index.html},

year = {2008}

}

### OpenURL

### Abstract

We study the problem of estimating the best k term Fourier representation for a given frequency-sparse signal (i.e., vector) A of length N ≫ k. More explicitly, we investigate how to deterministically identify k of the largest magnitude frequencies of Â, and estimate their coefficients, in polynomial(k, log N) time. Randomized sublinear time algorithms which have a small (controllable) probability of failure for each processed signal exist for solving this problem [24, 25]. In this paper we develop the first known deterministic sublinear time sparse Fourier Transform algorithm which is guaranteed to produce accurate results. As an added bonus, a simple relaxation of our deterministic Fourier result leads to a new Monte Carlo Fourier algorithm with similar runtime/sampling bounds to the current best randomized Fourier method [25]. Finally, the Fourier algorithm we develop here implies a simpler optimized version of the deterministic compressed sensing method previously developed in [30]. 1

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