Simple and practical algorithm for sparse fourier transform

Haitham Hassanieh, Piotr Indyk, Dina Katabi, Eric Price

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We consider the sparse Fourier transform problem: given a complex vector ÷of length n, and a parameter k, estimate the k largest (in magnitude) coefficients of the Fourier transform of x. The problem is of key interest in several areas, including signal processing, audio/image/video compression, and learning theory. We propose a new algorithm for this problem. The algorithm leverages techniques from digital signal processing, notably Gaussian and Dolph-Chebyshev filters. Unlike the typical approach to this problem, our algorithm is not iterative. That is, instead of estimating "large" coefficients, subtracting them and recursing on the reminder, it identifies and estimates the k largest coefficients in "one shot", in a manner akin to sketching/streaming algorithms. The resulting algorithm is structurally simpler than its predecessors. As a consequence, we are able to extend considerably the range of sparsity, k, for which the algorithm is faster than FFT, both in theory and practice.

Original languageEnglish (US)
Title of host publicationProceedings of the 23rd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2012
PublisherAssociation for Computing Machinery
Pages1183-1194
Number of pages12
ISBN (Print)9781611972108
DOIs
StatePublished - 2012
Externally publishedYes
Event23rd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2012 - Kyoto, Japan
Duration: Jan 17 2012Jan 19 2012

Publication series

NameProceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms

Other

Other23rd Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2012
CountryJapan
CityKyoto
Period1/17/121/19/12

ASJC Scopus subject areas

  • Software
  • Mathematics(all)

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