Octonion spectrum of 3D short-time LCT signals

Abstract

This work is devoted to the development of the octonion linear canonical transform (OLCT) theory proposed by Gao and Li in 2021 that has been designated as an emerging tool in the scenario of signal processing. The purpose of this work is to introduce octonion linear canonical transform of real-valued functions. Further more keeping in mind the varying frequencies, we used the proposed transform to generate a new transform called short-time octonion linear canonical transform (STOLCT). The results of this article focus on the properties like linearity, reconstruction formula and relation with 3D-short-time linear canonical transform (3D-STLCT). The crux of this paper lie in establishing well known uncertainty inequalities and convolution theorem for the proposed transform.