Directional short-time Fourier transform

A directionally sensitive variant of the short-time Fourier transform is introduced which sends functions on R n to those on the parameter space S n − 1 × R × R n . 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.