Continuous quaternion Stockwell transform and Uncertainty principle

TL;DR

This paper introduces a new continuous quaternionic Stockwell transform, establishing its fundamental properties and applying it to derive uncertainty principles, expanding the tools for signal analysis in quaternionic domains.

Contribution

The paper presents the first formulation of the continuous quaternionic Stockwell transform, including its admissibility condition, properties, and applications to uncertainty principles.

Findings

Established Plancherel, Parseval, and inversion formulas for the transform.

Provided examples demonstrating the transform's application.

Derived uncertainty principles using the transform and quaternion Fourier analysis.

Abstract

In this paper we propose a novel transform called continuous quaternionic stockwell transform. We express the admissibility condition in term of the (two-sided) quaternion Fourier transform . We show that its fundamental properties, such as Plancherel, Parseval and inversion formula, can be established whenever the continuous quaternion stockwell satisfy a particular admissibility condition. We present several examples of the continuous quaternion stockwell transform. We apply the continuous quaternion stockwell transform properties and the two sided quaternion Fourier transform to establish a number of uncertainty principle for these extended Stockwell .