Donoho Starks and Hardys Uncertainty Principles for the Shortotime Quaternion Offset Linear Canonical Transform Donoho-Stark's and Hardy's Uncertainty Principles for the Short-time Quaternion Offset Linear Canonical Transform

TL;DR

This paper extends classical uncertainty principles to the short-time quaternion offset linear canonical transform (STQOLCT), broadening the theoretical framework for signal analysis in quaternionic signal processing.

Contribution

It introduces the STQOLCT, explores its relationship with the quaternion Fourier transform, and generalizes several key uncertainty principles for this new transform.

Findings

Generalized Donoho Starks uncertainty principle for STQOLCT

Extended Hardy's uncertainty principle to STQOLCT

Derived Beurlings and Logarithmic uncertainty principles for STQOLCT

Abstract

The quaternion offset linear canonical transform (QOLCT) which is time shifted and frequency modulated version of the quaternion linear canonical transform (QLCT) provides a more general framework of most existing signal processing tools. For the generalized QOLCT, the classical Heisenbergs and Liebs uncertainty principles have been studied recently. In this paper, we first define the shorttime quaternion offset linear canonical transform (STQOLCT) and drive its relationship with the quaternion Fourier transform (QFT). The crux of the paper lies in the generalization of several well known uncertainty principles for the STQOLCT, including Donoho Starks uncertainty principle, Hardys uncertainty principle, Beurlings uncertainty principle, and Logarithmic uncertainty principle.