Inversion of the windowed linear canonical transform with Riemann sums

Abstract

In this paper, we study the inversion of the windowed linear canonical transform. We show that for certain window functions, a function can be recovered from its windowed linear canonical transform with a discrete series. We give necessary and sufficient conditions for the convergence of the series. Both the convergence in norm and the pointwise convergence are studied. Moreover, we get an inversion formula for integrable functions with the Cesàro summability.