Octonion Spectrum of 3D Short time LCT Signals

TL;DR

This paper introduces the short-time octonion linear canonical transform (STOLCT) for 3D signals, extending the OLCT theory to analyze time-varying frequencies with properties like linearity and uncertainty principles.

Contribution

It develops the STOLCT based on OLCT, establishing its properties and relations with existing transforms, and derives uncertainty inequalities and convolution theorems.

Findings

Properties like linearity and reconstruction formula are established.

The transform's relation with 3D-STLCT is demonstrated.

Uncertainty inequalities and convolution theorems are proved.

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.