Linear canonical Stockwell transform

Abstract

The linear canonical transform (LCT) has long been recognized as a competent tool for optics and signal processing. However, the LCT cannot reveal the local LCT-frequency contents due to its global kernel and as such makes the LCT incompetent in situations demanding a joint information of time and linear canonical domain-frequency. In this paper, we propose the linear canonical Stockwell transform (LCST) in order to rectify the limitations of the LCT and the Stockwell transform (ST). Firstly, we examine the resolution of the novel transform in the time and LCT domains and then derive some of its basic properties, such as Moyal's formula, inversion formula and provide a characterization of the range. Furthermore, we derive a direct relationship between the well known Wigner distribution and the proposed LCST. In sequel, a discrete version of the linear canonical Stockwell transform is also presented. Finally, we extend the scope of the proposed work by studying the LCST in the realm of almost periodic functions.