Generalized Uncertainty Principles for the Two-Sided Quaternion Linear Canonical Transform

An uncertainty principle (UP), which offers information about a function and its Fourier transform (FT) in the time-frequency plane, is particularly powerful in the field of signal processing. In this paper, based on the fundamental relationship between the quaternion linear canonical transform (QLCT) and quaternion Fourier transform (QFT), we propose two different UPs related to the two-sided QLCT. Different from existing results in the spatial and frequency domains, new derived consequences can be regarded as a general form of the UP of the QLCT, which present lower bounds for the product of spreads of a quaternion-valued function in two different QLCT domains.