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The quaternion offset linear canonical transform (QOLCT) which is timeshifted and frequency modulated version of the quaternion linear canonicaltransform (QLCT) provides a more general framework of most existing signalprocessing tools. For the generalized QOLCT, the classical Heisenbergs andLiebs uncertainty principles have been studied recently. In this paper, wefirst 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 knownuncertainty principles for the STQOLCT, including Donoho Starks uncertaintyprinciple, Hardys uncertainty principle, Beurlings uncertainty principle, andLogarithmic uncertainty principle.

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