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Inversion formula for the windowed Fourier transform
Author(s) -
Sun W.
Publication year - 2012
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201000128
Subject(s) - inversion (geology) , mathematics , fourier transform , almost everywhere , mathematical analysis , function (biology) , pure mathematics , geology , paleontology , structural basin , evolutionary biology , biology
In this paper, we study the inversion formula for recovering a function from its windowed Fourier transform. We give a rigorous proof for an inversion formula which is known in engineering. We show that the integral involved in the formula is convergent almost everywhere on \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\mathbb {R}$\end{document} as well as in L p for all 1 < p < ∞ if the function to be reconstructed is.
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