Inversion of the short-time fourier transform using Riemannian sums

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

The inversion formula for the short-time Fourier transform is usually considered in the weak sense, or only for specific combinations of window functions and function spaces such as L2 and modulation spaces. In the present note the Riemannian sums of the inverse short-time Fourier transform are investigated. Under some conditions on the window functions we prove that the Riemannian sums converge to f in the modulation spaces and inWiener amalgam norms, hence also in the Lp sense.

Original languageEnglish
Pages (from-to)357-368
Number of pages12
JournalJournal of Fourier Analysis and Applications
Volume13
Issue number3
DOIs
Publication statusPublished - Jun 2007

Fingerprint

Short-time Fourier Transform
Modulation Spaces
Inversion
Fourier transforms
Amalgam
Inversion Formula
Modulation
Function Space
Mercury amalgams
Converge
Norm

Keywords

  • Feichtinger's and Wiener's algebra
  • Modulation spaces
  • Riemannian sums
  • Short-time Fourier transform
  • Timefrequency analysis
  • Wiener amalgam spaces

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics
  • Analysis

Cite this

Inversion of the short-time fourier transform using Riemannian sums. / Weisz, F.

In: Journal of Fourier Analysis and Applications, Vol. 13, No. 3, 06.2007, p. 357-368.

Research output: Contribution to journalArticle

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