Inversion formula for the windowed Fourier transform
Copyright policy )Inversion formula for the windowed Fourier transform
AbstractIn 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 Lp for all 1 < p < ∞ if the function to be reconstructed is.
- Nankai University China (People's Republic of)
Mathematics - Functional Analysis, windowed Fourier transforms, Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type, inversion formula, FOS: Mathematics, 42B10, Fourier transforms, Functional Analysis (math.FA)
Mathematics - Functional Analysis, windowed Fourier transforms, Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type, inversion formula, FOS: Mathematics, 42B10, Fourier transforms, Functional Analysis (math.FA)
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