Abstract
A directionally sensitive variant of the short-time Fourier transform is introduced which sends functions on Rn to those on the parameter space Sn−1×R×Rn. This transform, which is named directional short-time Fourier transform (DSTFT), uses functions in L∞(R) as window and is related to the celebrated Radon transform. We establish an orthogonality relation for the DSTFT and explore some operator-theoretic aspects of the transform, mostly in terms of proving a variant of the Hausdorff–Young inequality. The paper is concluded by some reconstruction formulas.
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