A New Class of Short‐Time Linear Canonical Transform: Theory and Applications

ABSTRACT To localize the linear canonical spectrum of the time‐dependent signals, we propose a novel short‐time linear canonical transform that leverages the convolution structure of the linear canonical transform (LCT). Unlike the traditional approach, which replaces the Fourier kernel with the LCT kernel, this method employs convolution to capture the linear canonical spectrum over limited temporal intervals, constrained by a window function. This approach not only reduces computational complexity but also holds significant potential for applications in various scientific and engineering fields. We begin our investigation by examining fundamental properties of the proposed transform, such as the orthogonality relation, inversion formula, and characterization of the range, using tools from LCT and convolution theory. Further, we explore the time‐frequency resolution and the uncertainty principles associated with the proposed transform. Additionally, we present several potential applications, including the Poisson summation formula, Paley‐Wiener criterion, and a sampling formula. To support our theoretical findings, clear examples are provided throughout the paper.