Inversion formulas for the short-time Fourier transform |
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Authors: | Hans G Feichtinger Ferenc Weisz |
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Institution: | 1. Numerical Harmonic Analysis Group, Faculty of Mathematics, University of Vienna, Nordbergstra?e 15, A-1090, Vienna, Austria 2. Department of Numerical Analysis, E?tv?s L. University, Pázmány P. sétány 1/C., H-1117, Budapest, Hungary
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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 ƒ converges to ƒ in Wiener amalgam norms, hence also in the Lp sense for Lp functions, and pointwise almost everywhere. |
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