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Inversion formula for the windowed Fourier transform

✍ Scribed by W. Sun

Publisher
John Wiley and Sons
Year
2012
Tongue
English
Weight
135 KB
Volume
285
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

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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