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A deterministic sparse FFT algorithm for vectors with small support

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Abstract

In this paper we consider the special case where a signal x \({\in }\,\mathbb {C}^{N}\) is known to vanish outside a support interval of length m < N. If the support length m of x or a good bound of it is a-priori known we derive a sublinear deterministic algorithm to compute x from its discrete Fourier transform \(\widehat {\mathbf x}\,{\in }\,\mathbb {C}^{N}\). In case of exact Fourier measurements we require only \({\mathcal O}\)(m \(\log \) m) arithmetical operations. For noisy measurements, we propose a stable \({\mathcal O}\)(m \(\log \) N) algorithm.

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Authors and Affiliations

  1. University of Göttingen, Institute for Numerical and Applied Mathematics, Lotzestr. 16-18, 37083, Göttingen, Germany

    Gerlind Plonka & Katrin Wannenwetsch

Authors
  1. Gerlind Plonka
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  2. Katrin Wannenwetsch
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Correspondence to Gerlind Plonka.

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Plonka, G., Wannenwetsch, K. A deterministic sparse FFT algorithm for vectors with small support. Numer Algor 71, 889–905 (2016). https://doi.org/10.1007/s11075-015-0028-0

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