The directional short-time fractional Fourier transform of distributions

Abstract

We introduce the directional short-time fractional Fourier transform (DSTFRFT) and prove an extended Parseval's identity and a reconstruction formula for it. We also investigate the continuity of both the directional short-time fractional Fourier transform and its synthesis operator on the appropriate space of test functions. Using the obtained continuity results, we develop a distributional framework for the DSTFRFT on the space of tempered distributions ${\mathcal{S}}^{\prime }({\mathbb{R}}^n)$. We end the article with a desingularization formula.