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 (2110.02754v1)

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.