A characterization of sparse nonstationary Gabor expansions

Emil Solsbæk Ottosen, Morten Nielsen

Research output: Working paperResearch

Abstract

We investigate the problem of constructing sparse time-frequency representations with flexible frequency resolution, studying the theory of nonstationary Gabor frames in the framework of decomposition spaces. Given a painless nonstationary Gabor frame, we construct a compatible decomposition space and prove that the nonstationary Gabor frame forms a Banach frame for the decomposition space. Furthermore, we show that the decomposition space norm can be completely characterized by a sparseness condition on the frame coefficients and we prove an upper bound on the approximation error that occurs when thresholding the frame coefficients for signals belonging to the decomposition space.
Original languageEnglish
PublisherArXiv
Number of pages25
Publication statusPublished - Jun 2016

Keywords

  • Time-frequency analysis
  • nonstationary Gabor frames
  • decomposition spaces
  • Banach frames
  • nonlinear approximation

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