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2012
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Nearly optimal sparse fourier transform

8 years 6 months ago
Nearly optimal sparse fourier transform
We consider the problem of computing the k-sparse approximation to the discrete Fourier transform of an ndimensional signal. We show: • An O(k log n)-time randomized algorithm for the case where the input signal has at most k non-zero Fourier coefficients, and • An O(k log n log(n/k))-time randomized algorithm for general input signals. Both algorithms achieve o(n log n) time, and thus improve over the Fast Fourier Transform, for any k = o(n). They are the first known algorithms that satisfy this property. Also, if one assumes that the Fast Fourier Transform is optimal, the algorithm for the exactly k-sparse case is optimal for any k = nΩ(1) . We complement our algorithmic results by showing that any algorithm for computing the sparse Fourier transform of a general signal must use at least Ω(k log(n/k)/ log log n) signal samples, even if it is allowed to perform adaptive sampling.
Haitham Hassanieh, Piotr Indyk, Dina Katabi, Eric
Added 28 Sep 2012
Updated 28 Sep 2012
Type Journal
Year 2012
Where STOC
Authors Haitham Hassanieh, Piotr Indyk, Dina Katabi, Eric Price
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