Inversion Formula for the Windowed Fourier Transform

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 $\bbR$ as well as in $L^p$ for all $1<p<\infty$ if the function to be reconstructed is.

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