Theory and Applications of Convolution-Based short time offset linear canonical transform

Abstract

In this paper, we introduce a convolution based short time offset linear canonical transform (STOLCT) and investigate its fundamental mathematical properties. Specifically, we establish its continuity, orthogonality relations, inversion formulas, range theorem, and convolution theorem. We further explore several important applications of STOLCT, including the Poisson summation formula, the Paley Wiener criterion, and a sampling theorem. In addition, numerical simulations and graphical analyses are presented to compare signal reconstruction performance under different scenarios. A comparative study between STOLCT and STLCT is conducted with respect to their reconstruction formulas, demonstrating the effectiveness and potential advantages of the proposed transform.