Novel Uncertainty Principles for Two-Sided Quaternion Linear Canonical Transform

The uncertainty principle, which offers information about a function and its Fourier transform in the time-frequency plane, is particularly powerful in mathematics, physics and signal processing community. In this paper, based on the fundamental relationship between the quaternion linear canonical transform (QLCT) and quaternion Fourier transform (QFT), we propose two different uncertainty principles for the two-sided QLCT. It is shown that the lower bounds can be obtained on the product of spreads of a quaternion-valued function and its two-sided QLCT from newly derived results. Furthermore, an example is given to verify the consequences. Finally, some possible applications are provided to demonstrate the usefulness of new uncertainty relations in the QLCT domain.