  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.
