Quaternion Offset Linear Canonical Transform in One dimensional Setting

TL;DR

This paper introduces the quaternion offset linear canonical transform for 1D functions, establishing its fundamental properties and demonstrating its mathematical robustness for potential applications.

Contribution

The paper presents the first comprehensive study of the quaternion offset linear canonical transform, including its properties and theoretical foundations.

Findings

Transform satisfies inversion, linearity, and product theorems.

Establishes convolution theorem for the quaternion offset linear canonical transform.

Applicable to integrable and square integrable functions.

Abstract

In this paper, we introduce quaternion offset linear canonical transform of integrable and square integrable functions. Moreover, we show that the proposed transform satisfies all the respective properties like inversion formula, linearity, Moyals formula , product theorem and the convolution theorem