Inversion formulas for the short-time Fourier transform

Hans G. Feichtinger, F. Weisz

Research output: Contribution to journalArticle

13 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. In the present article the so-called θ-summability (with a function parameter θ) is considered which induces norm convergence for a large class of function spaces. Under some conditions on θ we prove that the summation of the short-time Fourier transform of f{hook} converges to f{hook} in Wiener amalgam norms, hence also in the Lp sense for Lp functions, and pointwise almost everywhere.

Original languageEnglish
Pages (from-to)507-521
Number of pages15
JournalJournal of Geometric Analysis
Volume16
Issue number3
DOIs
Publication statusPublished - Sep 2006

Fingerprint

Short-time Fourier Transform
Inversion Formula
Function Space
Norm
Amalgam
Summability
Summation
Converge

Keywords

  • θ-summability
  • Herz spaces
  • Math Subject Classifications: 42B08, 42C15, 42C40, 42A38, 46B15
  • short-time Fourier transform
  • time-frequency analysis
  • Wiener amalgam spaces

ASJC Scopus subject areas

  • Mathematics(all)
  • Geometry and Topology

Cite this

Inversion formulas for the short-time Fourier transform. / Feichtinger, Hans G.; Weisz, F.

In: Journal of Geometric Analysis, Vol. 16, No. 3, 09.2006, p. 507-521.

Research output: Contribution to journalArticle

Feichtinger, Hans G. ; Weisz, F. / Inversion formulas for the short-time Fourier transform. In: Journal of Geometric Analysis. 2006 ; Vol. 16, No. 3. pp. 507-521.
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